Abstract
The catalytic hydrolysis
of cellulose to produce 5-hydroxymethylfurfural
(HMF) is a powerful means of biomass resources. The current efficient
hydrolysis of cellulose to obtain HMF is dominated by multiphase reaction
systems. However, there is still a lack of studies on the synergistic
mechanisms and component transport between the various processes of
cellulose hydrolysis in a complex multiphase system. In this paper,
a liquid membrane catalytic model was developed to simulate the hydrolysis
of cellulose and its further reactions, including the adsorption of
the liquid membrane on cellulose particles, the consumption of cellulose
solid particles, the complex chemical reactions in the liquid membrane,
and the transfer of HMF at the phase interface. The simulations show
the synergistic effect between cellulose hydrolysis and multiphase
mass transfer. We defined an indicator (
) to characterize the sensitivity of HMF
yield to the initial liquid membrane thickness at different reaction
stages. 
decreased gradually when the glucose conversion
increased from 0 to 80%, and 
increased with the thickening of the initial
liquid membrane thickness. It was shown that the thickening of the
initial liquid membrane thickness promoted the HMF yield under the
same glucose conversion. In summary, our results reveal the mechanism
of the interaction between multiple physicochemical processes of the
cellulose liquid membrane reaction system.
1. Introduction
5-Hydroxymethylfurfural (HMF) is a significant chemical raw material that can be obtained from cellulose.1 However, the physicochemical properties of cellulose are very stable, and there are multitudes of hydrogen bonds within the single chains of the cellulose molecule and between the different chains, leading to cellulose being more difficult to be degraded into monosaccharides.2 In addition, the preparation of HMF from cellulose is complicated by multitudes of side reactions, and the conversion rate of the raw material is generally low.3 Therefore, an optimized reaction system is essential for the efficient conversion of cellulose to HMF.4−6
From the perspective of green chemistry, water is an ideal solvent because it is cheap, non-toxic, and non-flammable. Although cellulose hydrolysis reactions can be effectively carried out using water as the reaction medium, the yield of HMF is generally unsatisfactory due to the instability of HMF in aqueous solution in the presence of an acidic catalyst, which is prone to side reactions.7 In recent years, researchers have started to use organic solvents as solvents instead of or partially instead of ionic liquids for the preparation of HMF. Polar non-protonic organic solvents which do not contain hydrogen ions and are less prone to side reactions in the resulting HMF are generally used. In the preparation of 5-HMF from fructose, Benoit et al.8 partially replaced [BMIM]CL with glycerol as the reaction solvent and obtained a yield of 72% of 5-HMF. However, organic solvents also have some disadvantages, such as difficulty in volatilization and difficult product separation but high boiling points, which is not a general characteristic of all the organic solvents. It appears that neither organic solvents as partial or total substitutes nor water as solvents can give excellent yields of HMF and extract HMF with high purity. Therefore, a biphasic system was proposed to inhibit the re-degradation of HMF by combining the aqueous and organic phases, bringing together the reaction to generate HMF and the initial separation of HMF, thus advancing the conversion reaction and allowing for a higher yield of HMF. The group of Dumesic9−12 at Wisconsin, Madison, focused on the selective variability of HMF when the extracted phase was C3–C6 alcohols, ketones, and furans, making a remarkable contribution to the development of biphasic systems. The results of the research showed that the extraction of HMF was excellent in an organic solvent with carbon atoms of four, and the selectivity of the prepared HMF was the highest when tetrahydrofuran (THF) was used as an extractant.
A reaction system using ionic liquids or high-boiling point organic solvents as reaction media and chromium-containing catalysts showed excellent conversion of HMF from cellulose. 54% yield of HMF was obtained in a combined DMA–LiCl system using HCl and CrCl3 as catalysts, reported by Binder and Raines13 Yu et al.14 catalyzed the degradation of cellulose with CrCl3/LiCl bimetallic chloride salts in ionic liquid [EMIM]Cl to obtain 55% HMF. However, the high price of ionic liquids, the high toxicity of chromium chloride, and the high energy consumption for the separation of HMF from the abovementioned systems make it difficult to achieve industrial applications of these studies. Unlike ionic liquids and high-boiling point organic solvents, biphasic systems consisting of water and low-boiling point organic solvents are more industrially viable. In the biphasic system, the hydrolysis of cellulose and the formation of HMF take place in the aqueous phase, while the resulting HMF is rapidly transferred to the organic phase to avoid its subsequent degradation. The organic phases commonly used for extraction in biphasic systems are butanol, THF, methyl THF, methyl isobutyl ketone (MIBK), and so forth. However, the yield of HMF obtained in biphasic systems is still relatively low compared to systems consisting of ionic liquids and high-boiling point organic solvents.
Wang et al.15 obtained only 21% HMF from the conversion of cellulose in a biphasic system consisting of water and butyl phenol, and Yang et al.16 obtained only 37% yield using cellulose as a feedstock in a biphasic system consisting of water and THF. Shi17 presented a heterogeneous system for degradation of cellulose to HMF in a biphasic system of water and organic solvents with high concentrations of sulfate. Cellulose hydrolysis occurs on the solid surface. Then, the resulting glucose enters the liquid membrane phase and continues to react to form fructose and HMF. At the same time, HMF diffuses into the bulk phase to reduce the concentration of HMF in the liquid membrane that can significantly inhibit the subsequent side reaction of HMF. The system covers an extensive reaction network including the cellulose hydrolysis, glucose isomerization, HMF dehydration, and complex side reactions. In addition, the system includes three phases and possesses mass transfer at the phase interface. These studies are of great significance to the reaction kinetics and reactive transport phenomena of cellulose to HMF catalyzed by liquid membranes. However, more efforts should be made to gain insights into the mechanisms that influence the physical and chemical phenomena involved in the catalytic hydrolysis of cellulose in liquid membranes to produce HMF. On one hand, as mentioned above, only a few studies have focused on this issue and transport processes are often neglected when designing catalytic systems and reactors. On the other hand, direct measurement and observation of these processes within catalytic liquid membranes are almost impossible.
The lattice Boltzmann method (LBM), which is a mesoscopic numerical algorithm based on a minimal version of Boltzmann’s kinetic equation, has become a reliable and efficient simulation technique and received extensive attention. LBM was widely adopted to investigate a variety of physical and chemical phenomena, such as heat transfer,18,19 phase transition,20−22 nanofluid,23−25 and heterogeneous catalysis.26−28 For multiphase flows, several multiphase LBM models have been developed, of which the Shan–Chen (SC) pseudopotential model is the most widely used due to its superiority over the original concept and its high computational efficiency. Zhang et al.29 used the LBM to quantify the ionic diffusivity in unsaturated cementitious materials. The results show that the ionic diffusivity was strongly influenced by the degree of water saturation. The simulated relative ion diffusivity as a function of water saturation agreed well with the experimental data obtained from the literature. Model stability and efficiency can be achieved by incorporating a more realistic equation of state (EOS) into the S–C model.30 A pore-scale model was developed by Chen et al.31 based on the LBM for the transport of multiphase reactions with phase transitions and dissolution–precipitation processes. The multiphase reaction transport phenomena between liquid and gas phases and the dissolution–precipitation process of salt in a closed envelope were simulated, and the effect of initial envelope size was investigated. Recently, Wei et al.32 developed a pore-scale multiphase transport model based on the LBM to simulate La to GVL conversion over Ru/C catalysts. Chen et al.33 developed an SC LB-based pore-scale model by reconstructing the high-resolution porous structure of the cathode catalyst layer to study the reactive transport processes within the catalyst layer nanostructure. These studies demonstrate the power of the LBM in modeling physicochemical phenomena; however, the application of the LBM in heterogeneous catalysis of lignocellulosic biomass has rarely been reported, particularly for complex multicomponent, multiphase catalytic reaction systems such as the hydrolysis of cellulose to produce HMF.
In this context, we aim to develop a numerical model that takes into account multicomponent mass transfer, multiphase flow, phase transitions, and heterogeneous and homogeneous catalytic reactions to enhance the current understanding of the reactive transport phenomena in the production of HMF from cellulose. In this paper, we show a framework for a multiphase reaction transport model based on the SC LB approach, which is used to model the non-homogeneous catalysis of the conversion of cellulose particles to HMF through liquid membrane catalysis in an organic–liquid–solid three-phase system. The multiphase flow is simulated with the SC model with the C–S EOS, and the reactive transport process is treated with the multicomponent mass transport LBM model. A moving boundary condition was considered for the solid–liquid membrane phase interface due to cellulose consumption by the reaction. The effects of initial liquid membrane thickness, reaction temperature, and cellulose particle size were analyzed. We also compare the predictions of the model with experimental results from the literature.17 Ultimately, effective strategies were proposed to improve the reaction performance and the utilization of the catalytic system based on our conclusion.
2. Model Framework
2.1. Multiphase LB Model
In this paper, the Shan–Chen multiphase model (SC model) is used to simulate the liquid membrane reaction and mass transfer process of cellulose particles. The standard LB equation can be expressed as follows
 |
1 |
where 
is the particle distribution function of
component 
along the direction of microscopic
velocity 
at site 
and time 
. 
is the dimensionless relaxation time related
to the kinematic viscosity of the fluid flow. 
and 
are the lattice
time step and the equilibrium
density distribution function, respectively. The left hand side of eq 1 represents the streaming
step, and the right hand side illustrates the collisional relaxation
of BGK with the local equilibrium distribution function.
 |
2 |
The DmQn model
proposed by Qian is the basic model of the LBM, where m represents the spatial dimension and n represents
the number of directions in which the velocity is discrete. In this
paper, the two-dimensional D2Q9 model is used, ωi in eq 2 is the weight coefficient, which takes different values in different
discrete directions, 
= 4/9, 
= 1/9, 
= 1/36. 
is the lattice discrete velocity,
and 
is
the single relaxation time and is related
to the dynamic viscosity as follows
 |
3 |
The lattice sound velocity 
and the lattice velocity 
, where 
and 
represent the time step and the space step,
respectively.
The fluid density and velocity are obtained from which the zero- and first-order moments of the particle distribution function are calculated.
 |
4 |
 |
5 |
In the original SC model, Shan and Chen proposed an exponential effective density function, as shown below
 |
6 |
In order to achieve coexistence between different phase states and adsorption of liquids on solids, two forces are introduced into the LB equation based on the SC model: one is the cohesion between liquid particles on adjacent lattices and the other is the adsorption of a solid surface on a liquid.
The inclusion of a cohesive force that causes phase separation between particles of a particular “species” of fluid, which we call force cohesion, and it is calculated as follows
 |
7 |
In the equation, 
is the interaction force between neighboring
fluids, called cohesion and 
is the interaction strength constant,
whose
positive or negative value determines whether the fluid particles
attract or repel each other. 
is called the pseudopotential
function
or effective density, and its value depends on the actual density
of the fluid. 
is the weight coefficient.
For four adjacent
grid points 
, the
weight coefficient is 1/3; for four
adjacent grid points 
, the
weight coefficient is 1/12. When calculating
cohesion, we only consider the interaction between adjacent particles.
In the D2Q9 model, only the forces of the central particle and neighboring
particles in eight directions are calculated.
Based on the results of Yuan and Schaefer,34 the C–S equation of state is used in this paper, and the Carnahan–Starling equation of state performs better in terms of the two-phase density ratio and interface spurious velocity.
 |
8 |
The equation of state is used to describe
the relationship between
fluid pressure, temperature, and density, where 
and 
. In the LB approach,
for an ideal gas,
since the molecules have no interaction forces, 
. For the SC model, when cohesion within
the fluid is considered, the physical quantities are related as follows.
 |
9 |
Thus, when we combine eqs 9 with 8 for the C–S state,
we
can obtain an effective density expression for the variable 
and the C–S equation of
state.
 |
10 |
The adsorption force is calculated as follows
 |
11 |
In this equation, 
is the adsorption force of the solid surface
to the fluid.35
is
the interaction strength constant, which
controls the strength of the fluid–solid interaction. 
is an identification function.
It is equal
to 1 if the position is a solid phase; otherwise, it is equal to 0,
and 
is the virtual density of the solid.
By fixing the value of 
and varying 
, we
can combine the equations for cohesion
and adsorption. At the same time, we can treat the solid phase as
a liquid phase and set a virtual density (which is only used to calculate
the adsorption force by interacting with the liquid density).The distinction
between the two forces does not need to be taken into account when
programming by this method.
For the two interacting forces mentioned
above, we use the equilibrium
velocity correction method proposed by Shan and Chen36 to incorporate them into the LB equation. In the equilibrium
velocity correction method, we consider the influence of force by
changing the macroscopic velocity in the equilibrium distribution
function. Then, the equilibrium velocity 
) in eq 2 is modified
to include the force effect on the 
component as follows
 |
12 |
In the formula, 
and 
are the equilibrium velocity and common
velocity, respectively. The 
can be calculated as
 |
13 |
Substituting eqs 4, 5, and 13 into eq 12, the actual physical velocity is the average velocity before and after the collision and is determined by
 |
14 |
2.2. LB Equations for Multicomponent Reactive Transport
To simulate the coupling of passive solute reactive migration with multiphase fluid flow in the LB model, the concentration is modeled using the D2Q9 discrete velocity model, with the evolution equation
 |
15 |
In the formula, 
is the source term of the chemical
reaction,
which is related to the chemical reaction rate, 
is the relaxation time related to the diffusion
coefficient, and 
is the equilibrium function of the concentration
distribution and can be calculated by the following formula
 |
16 |
where 
is the concentration
of εth component. 
and 
are constants, 
= 1/2 for 2D simulation,
and 
is given by
 |
17 |
where 
can be selected from 0 to 1 for different
diffusion coefficients. The diffusivity and concentration can be obtained
by
 |
18 |
 |
19 |
where 
is the diffusivity of
the 
th
component and 
is
a lattice-dependent coefficient, which
is equal to 1/2 for the 2D simulation model.
2.3. Non-ideal Solute Component Modeling
Non-ideal solutes, such as the HMF studied in this paper, have different solubilities in different solvents. When they are dissolved in multiphase systems, concentration discontinuities occur at the phase interface. Therefore, we need to use methods that enable the solute concentration to pass smoothly through the phase interface.
As shown in Figure 1, the two solvent
components 
and 
are
mixed to form a phase interface, on
either side of which are two different phase states, such as the aqueous
phase and the organic phase. The whole system contains a non-ideal
solute, which is dissolved in both phases. In our simulations, the
concentration of the solute transitions smoothly at the phase interface,
which facilitates the stability of the numerical simulations. In order
to achieve a smooth transition of the solute concentration at the
phase interface, we introduce a solute–solvent interaction.
This interaction affects the distribution of the solute but not that
of the solvent. Antoine Riaud37 uses a
multiphase color model to study the diffusion and reaction of dilute
solutes in multiphase systems. With reference to the recoloring process
of the multiphase color model, we add an additional collision operator
to the mass transfer Boltzmann equation to reflect this interaction.
An arbitrary function 
is chosen to make the solute sensitive
to the solvent distribution. The concentration LB equation can be
rewritten as
 |
20 |
 |
21 |
Figure 1.
Example of non-ideal solute distribution in
a two-phase system.
(A) Two-phase system, the red area indicates component 
, and
the blue area indicates component 
; (B)
concentration distribution, non-ideal
solute concentrations are indicated by solid red lines.
In eq 20, the 
can be written as
 |
22 |
 |
23 |
Combining eqs 20, 22, and, 23, we obtain the following relationship
 |
24 |
We performed a perturbation analysis on this microdynamic equation and deduced the macroscopic species flux
 |
25 |
is
a geometric constant close to 0.150
for D2Q9, and the equation of state
of the solute can be derived
 |
26 |
 |
27 |
In eq 24, the vector 
is the normal vector 
of the solvent component
distribution.
In the pseudopotential model, this can be calculated by the following
equation
 |
28 |
is a Dirac function; the integral of the
force on the diffusion interface leads to the interfacial tension
of the sharp interface.
 |
29 |
 |
30 |
In the collision operator, the value of 
is overwhelmingly significant for the solubility
of solutes, which we will introduce in detail in specific cases later. 
is a physical
quantity which determines
the degree of solute dissolution in different phases.
2.4. Update of Cellulose Particles
To accurately model the catalytic reactions on the solid surface of cellulose particles, it is a prerequisite to consider the time evolution of the solid phase, especially when the dissolution of cellulose particles involves a mass transfer between the solid and liquid. The amount of dissolved solids is equal to the amount of injected species divided by the difference between the solid concentration and the actual concentration in the cells. In this study, the motion of the solid during fluid flow is not considered, so the volume of the fixed solid is satisfied
 |
31 |
where 
, 
, and 
are the dimensionless
volume, molar volume,
and specific surface area of the 
cellulose solids, respectively.
In this
study, the diffusion of the solute in the solid phase is ignored,
and the reaction of cellulose to glucose is considered to occur only
at the fluid–solid interface. Each interface node represents
a control volume of 
(lattice unit) (control area in 2D), located
in the center of the volume. The initial control volume is the dimensionless
volume 
. According to the equation, the volume
is explicitly updated at each time step.
 |
32 |
where 
is the time step and we use the VOP method to track and update the liquid–solid interface.
2.5. Handling Information on Phase-Change Nodes
Figure 2 illustrates
the time evolution of the solid–liquid–organic-phase
interface. During the interface evolution, the phase of the computational
node can be between the liquid and solid phases (due to reactive dissolution
of cellulose particles). How to handle the fluid flow and mass transport
information associated with the phase transition occurring at the
computational node is important to ensure the conservation of mass
and momentum in a closed system. For example, the initialization information
has various ways to be at the new fluid nodes during the dissolution
process and distributed during the multiphase reactive transport,
and the information is stored in the newly added entity nodes to the
interface. There are three types of nodes in the domain, namely solid
nodes, liquid nodes, and organic-phase nodes, and the nodes have dissolution-induced
solid to liquid changes. Note that there is no exchange between organic-phase
nodes and solid nodes because reactive dissolution occurs only at
the liquid–solid interface. When a solid node becomes a fluid
node due to dissolution, the density and velocity of that node must
be initialized to ensure mass conservation in the closed system and
convergence of the simulation. The handling of the flow and concentration
information of these nodes is challenging. When the reaction consumes
enough cellulose particles to change a solid node into a fluid node,
mass conservation, momentum conservation, and species conservation
in the system must be guaranteed. Chen et al.31 propose a phase transition boundary treatment strategy that can
guarantee mass conservation and simulation convergence of the system.
Specifically, when a solid node becomes a liquid node at time t, the
density of this new liquid node (
) is defined as the average density of the
nearest neighboring liquid node, and the speed is set as
 |
33 |
Figure 2.
Schematic of the moving boundary of the solid–liquid interface.
The subscripts “
” and “
” denote the new liquid-phase
node
and the old solid-phase node, respectively. As the reaction consumes
cellulose to change n nodes in the solid phase to the liquid phase,
the liquid-phase density is
 |
34 |
where 
is a random perturbation to achieve
phase
transition. 
is the total
density of the system at time 
. 
and 
are new liquid node and old solid node
density, respectively. Similar treatment can be adopted for the concentration
field.
3. Results and Discussion
3.1. Validation of the Model
3.1.1. Validation of the Multicomponent Multiphase Pseudopotential Model
We use several two-phase flow problems to verify the correctness of the multicomponent multiphase pseudopotential model.
The first problem is a gravity-free suspended droplet
in a vapor field, as shown in Figure 3. The number of meshes in the calculation zone is 200
l.u * 200 l.u. All four boundaries are periodic. At the initial moment,
a droplet of the radius 
is placed in the center of the
calculation
area and the density of the calculation area is initialized using
the following equation
 |
35 |
 |
36 |
Figure 3.
Simulation
results for gravity-free suspended droplets. (a) Suspended
droplet model. Medium temperature is 
, the
red area is droplets, the blue area
is vapor, and the initial droplet radius is 30 l.u. (b) Pressure distribution
along the horizontal center of the calculation domain, (c) capillary
pressure vs bubble radius, and calibration of Laplace’s law.
In eq 36: (
= 100, 
= 100)
is the center of the calculation
area. “
” is the hyperbolic tangent
function. 
and 
are
the theoretical density values at the
current temperature (using Maxwell and other density reconstruction
methods). In order to verify Laplace’s law, we simulate droplets
with different radii at temperature 
. The gas–liquid
pressure value is
taken from the horizontal middle line AB in (a). Figure 3b shows the pressure distribution
on AB when the temperature is 
and the radius is 
.
As shown in (b), the droplet pressure
takes the stable pressure value inside the droplet, the vapor pressure
takes the stable pressure value outside the droplet, and 
is the gas–liquid pressure difference.
At the gas–liquid interface, the pressure value changes drastically,
which is caused by the drastic change in density at the gas–liquid
interface. Figure 3c shows 
at different droplet radii. It can be found
that 
and 
have
a linear relationship, which complies
with Laplace’s law. The slope of the linear fit is 0.0133,
which is in good agreement with the theoretical solution of 0.009386.
The difference is due to the thermodynamic inconsistency of the LB
single-component multiphase model itself.
Another problem in
validating the pseudopotential multiphase model
is the contact angle. We have created a 200 l.u * 200 l.u grid with
a two-dimensional calculation area. The left and right boundaries
were periodic boundary conditions, and the top and bottom boundaries
were set as solid no-slip boundary conditions. The droplet was placed
on the solid wall at the bottom of the computational domain, and the
density of the solid was set to the virtual density 
(the virtual
density was only used to interact
with the fluid density to calculate the adsorption force). Finally,
we adjust the virtual density of the solid wall to vary the wettability
of the fluid on the solid surface. In the simulation, the virtual
density of the solid is defined as follows
 |
37 |
The coefficient 
in the formula determines the
wettability
of water on a solid surface and takes values from 0 to 1. When 
is equal to 0, water is not wettable
on
a solid surface and when β is 1, water is completely wettable
on a solid surface. 
and 
are
the liquid-phase density and the gas-phase
density, respectively. When varying the virtual density, the simulation
results are shown in Figure 4, where the contact angle gradually decreases from 180 to
0° as the value of β increases from 0 to 1.
Figure 4.
Simulation of the static
contact angle on smooth solid surfaces
with different 
. The inserted picture shows droplets
with
different contact angles under different 
.
3.1.2. Validation of the Mass Transport Model
In the model, we propose improvements to the mass transfer model for a non-ideal solute concentration distribution in the phase interface region. Therefore, we need to describe and validate the improvements further. In the organic-phase reaction system for the hydrolysis of cellulose to produce HMF, the whole reaction system was divided into three parts, including the solid phase, the liquid membrane phase, and the organic phase. The solutes in the reaction, such as glucose, fructose, and other byproducts, are only dissolved in the liquid membrane. However, there are also substances that dissolve in both the liquid membrane phase and the organic phase, such as HMF, which can dissolve in both phases with different solubilities.
To verify whether
the additional collision operator can resolve the interfacial concentration
discontinuity, a set of simulations was carried out based on the SC
model, with the center of the simulation domain being the liquid membrane
phase (the region where the y-axis is greater than 40 l.u and less
than 80 l.u) and the remainder being the bulk phase (the region where
the y-axis is less than 40 l.u and greater than 80
l.u). We adjusted the value of 
to observe the interfacial concentration
distribution of the two solutes. Initially, we set the concentration
of glucose in the liquid membrane phase to 1 and the concentration
of glucose in the bulk phase to 0. When diffusion reaches equilibrium,
glucose is only dissolved in the liquid membrane phase as shown in Figure 5A. In another set
of simulations, at the beginning, the concentration of HMF in the
liquid membrane was set to 0 and the concentration of HMF in the organic
phase was set to 1. When HMF is dissolved in both phases and at diffusion
equilibrium, the HMF in the organic phase should diffuse into the
liquid membrane due to the concentration gradient. As shown in Figure 5B, HMF is soluble
in both phases at diffusive equilibrium, and the concentration in
the organic phase is about five times higher than that in the liquid
membrane phase. The solute concentrations in both sets of simulations
can be smoothly transitioned in the phase interface region (at y equal to 40 or 60 l.u), where the difference in solubility
of the non-ideal solute HMF in the two phases depends on the value
of the parameter 
in eq 20.
Figure 5.
Concentration distribution of (A) HMF and (B) glucose in the two phases at equilibrium.
3.2. Organic–Liquid–Solid Three-Phase Single-Particle Liquid Membrane Catalytic Model
3.2.1. Single-Particle Liquid Membrane Catalytic Model
In the organic–liquid–solid three-phase system, the volume of water added in a general experimental investigation is smaller than the volume of THF. As shown in Figure 6a, the cellulose particles and the aqueous phase containing the catalyst are encapsulated in the organic phase of THF. Khazraji et al.38 suggest that due to a large number of hydroxyl groups in the cellulose molecule, it has strong hydrophilic properties, which means that it is also highly hygroscopic in multiphase solvent systems. At room temperature, the surface of cellulose is also covered with a layer of water molecules. The polarity of the water molecules is much higher at 10.2 than the polarity of THF at 4.2. The cellulose particles will inevitably preferentially adsorb the water phase and form an acidic liquid membrane on the surface of the cellulose particles.
Figure 6.
(a) Schematic diagram of HMF production from liquid membrane-catalyzed hydrolysis of cellulose particles in an organic-phase three-phase system. (b) Reaction network for catalytic glucose to HMF in the liquid membrane.
We can assume that the surface of the cellulose particles is completely covered by a water membrane; this liquid membrane containing a high concentration of the catalyst can effectively catalyze the cellulose hydrolysis reaction to prepare HMF, while the HMF molecules produced by the reaction are rapidly transferred to the organic phase to avoid subsequent side reactions. In this three-phase system, the organic phase has three functions. The first is to act as a solvent for extracting HMF and transferring it out of the reaction phase; the second is to act as a dispersant for the cellulose particles and the aqueous phase; the third function is a storage area for HMF. In addition, water also has three functions: one is to act as a green solvent, dissolving the catalyst and providing the reaction environment required for the reaction; another is to act as a reactant, hydrolyzing the cellulose to produce glucose, and the last is to change the volume ratio of the aqueous phase to the organic phase.
The hydrolysis of cellulose to HMF in the organic–liquid–solid system is a complex reaction. First, the hydrolysis of cellulose occurs on the surface of the particles, producing glucose, and then, the resulting glucose will diffuse into the liquid membrane for a subsequent series of reactions. The conversion of glucose to HMF can be divided into two steps. In the first step, glucose is converted to the more chemically active fructose by isomerization. Although there is still some debate about the reaction mechanism of the isomerization process, it is widely accepted that fructose is used as an intermediate product in the reaction process.39−46 The second step is the removal of three molecules of water from the fructose to produce HMF, which is chemically active in acidic aqueous solutions and is prone to a variety of side reactions. Therefore, timely transfer of HMF and inhibition of HMF side reactions in the liquid membrane are key aspects to improve HMF yield and achieve efficient preparation of HMF from cellulose. In liquid membranes, not only HMF undergoes side reactions but also the intermediate products glucose and fructose are accompanied by a correspondingly large number of side reactions, producing humins, levulinic acid, and formic acid.39−46 In this reaction, the catalyst comes into contact with the cellulose very easily, so the reaction system combines the advantages of both homogeneous and heterogeneous catalysts. Cellulose in liquid membrane catalysis itself acts as a catalyst carrier (Table 1).
Table 1. Setting of 
Values for Two Types of Solutes.
| type of solutes | dissolved in a single phase | dissolved in two phases | |||
|---|---|---|---|---|---|
|
|
|
Referring to the reaction network in Figure 6b, all reactions in the figure are considered as first-order reactions, and the following ordinary differential equations are derived
 |
38 |
 |
39 |
 |
40 |
 |
41 |
 |
42 |
where 
and 
are the rate constants for the isomerization
of glucose to fructose and fructose to glucose, respectively; 
is the net rate constant for isomerization
(
); 
is
the rate constant for the dehydration
of fructose to HMF; 
is
the rate constant for the rehydration
of HMF to FA/LA; 
, 
, and 
are
the rate constants for the degradation
of glucose, fructose, and HMF to FA and other products (oligomers,
humic substances, etc.), respectively; and 
, 
, and 
are
the rate constants for the polymerization
of glucose, fructose, and HMF to form humin substances, respectively.
The values of the reaction rate constants are quoted from Tang47 and Yan.48
We can obtain the kinetic constants for the reactions at different temperatures through the Arrhenius equation
 |
43 |
In the equation, 
is the molar gas constant, 
is the reaction temperature, 
is
the apparent activation energy, and 
is the pre-finger factor. The
values of
the reaction rate constants at different temperatures are shown in Table 2. The following equations
are used to connect the actual physical parameters to the dimensionless
physical parameters, the particle diameter is 4.2 × 10–4 m, and the kinematic viscosity 
is 1.006 × 10–6 m2 s–1.
 |
44 |
Table 2. Reaction Rate Constant.
| rate constant (×10–3 min–1) | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| entry | solvent | T (K) | Ka | K–a | Kb | Kc | Kd | Ke | Kf | Kg | Kh | Ki |
| 1 | H2O–THF | 413 | 5.2 | 2.3 | 2.9 | 0.003 | 10.1 | 3.9 | 2.5 | 0.07 | 0.6 | 0.001 |
| 2 | H2O–THF | 433 | 17.2 | 6.5 | 9.2 | 0.3 | 46.5 | 11.2 | 5.6 | 0.2 | 1.7 | 0.2 |
| 3 | H2O–THF | 453 | 55.2 | 13.3 | 27.1 | 8.69 | 217 | 27.7 | 10.6 | 0.73 | 5.61 | 8.97 |
| 4 | Ea (kJ mol–1) | 95 | 66 | 89 | 310 | 124 | 74 | 60 | 98 | 90 | 354 | |
We investigated the organic–liquid–solid three-phase system for the hydrolysis of cellulose to produce HMF using a previously validated numerical model. To simplify the numerical simulation work, a liquid membrane catalytic model was developed under the assumption that the cellulose particles are rigid spheres and that the cellulose particles will continue to dissolve during the reaction, as shown in Figure 7. The simulation area is 250 l.u*250 l.u, which is a three-phase system. Initially, we placed spherical cellulose particles with a particle size of 50 l.u (orange area) in the center of the calculation region. Due to the hydrophilic nature of the cellulose particles, a liquid membrane (pale-yellow area) with a thickness of 10 l.u is adsorbed on the surface of the cellulose particles. The outermost layer is the organic phase (light-blue area). In the middle of the pale-yellow and light-blue areas is the phase interface between the liquid and organic phases. Periodic boundary conditions were used for the flow and concentration fields at all four boundaries of the calculation zone, and half-way bounce-back boundary conditions were used for the flow and concentration fields at the solid surface. The simulation begins with the hydrolysis of cellulose at the particle surface to produce glucose, and the cellulose particles continue to dissolve and shrink. The glucose produced then diffuses into the liquid membrane and participates in subsequent reactions to produce fructose, HMF, and other byproducts. The HMF produced during this process will diffuse into the organic phase, which reduces the concentration of HMF in the liquid membrane and avoids its subsequent side reactions.
Figure 7.
Single-particle cellulose dissolved liquid membrane model for the organic–liquid–solid three-phase system.
3.2.2. Results of the Model
In the reaction of HMF formation from the hydrolysis of cellulose particles in the organic–liquid–solid-phase system, we focused on the variation of the three products, glucose, fructose, and HMF. Figure 8 shows a cloud chart of the distribution of the concentrations of HMF, glucose, and fructose throughout the reaction system with reaction time. At t = 10,000 t.s, only the HMF concentration near the organic–liquid membrane phase interface is higher in the entire organic phase; however, the HMF concentration is lower at the boundary of the calculated region. In addition, the HMF concentration in the liquid membrane phase is lower than the HMF concentration near the phase interface in the organic phase. The concentration of HMF in the organic phase spreads outward with the phase interface and shows a certain concentration gradient, with a relatively high concentration of HMF nearer to the phase interface. Glucose and fructose are distributed in the liquid membrane phase, where the concentration is higher, and the distribution is uniform and no concentration gradient occurs. The concentration of fructose and glucose decreases as the reaction proceeds, with fructose being more uniformly distributed in the liquid membrane phase and glucose being more highly distributed near the surface of the cellulose particles, where a concentration gradient has occurred. The concentration of glucose is lower near the interface between the organic and liquid membrane phases. As the reaction proceeded to t = 30,000 t.s, the concentration of HMF in the organic phase was higher near the phase interface and also increased at the edge of the organic phase. When the reaction proceeds to t = 40,000 t.s, the concentration of HMF in the organic phase is higher and the concentration at the boundary of the calculated region is already higher than that in the liquid membrane. When the reaction proceeds to t = 50,000 t.s, the concentration of HMF in the whole organic phase is already high and the low concentration of HMF in the liquid membrane can inhibit the occurrence of HMF side reactions, which is conducive to the increase in HMF yield.
Figure 8.
Cloud plot of the concentration distribution of HMF, glucose, and fructose when the cellulose particles are consumed and changes occur at different reaction times.
From the cloud chart in Figure 8, we can find the product concentration distribution characteristics of glucose, fructose, and HMF when they proceed through the entire reaction system. Glucose and fructose are distributed in the liquid membrane phase, where the glucose concentration is relatively low, further away from the solid–liquid phase interface. The glucose concentration distribution shows a linear relationship with the distance from the solid–liquid phase interface. The fructose concentration basically maintained the uniform distribution pattern in the liquid membrane phase.
We investigate their concentration
distribution comprehensively.
In particular, glucose and fructose are only distributed in the liquid
membrane phase, whereas HMF, a non-ideal solute, is distributed in
both the liquid membrane phase and the organic phase. Figure 9 illustrates the normalized
concentration distributions of glucose, fructose, and HMF during the
reaction. Since the main object is the concentration distribution
within the liquid membrane, the normalized concentration is defined
as 
. In this equation, 
represents the maximum value of the glucose
concentration throughout the reaction. We intercepted the reaction
concentration curve on a cross-section of y = 125
l.u to investigate the distribution of the concentrations of the three
products in the x-direction. The chart is divided into three parts,
namely the solid phase, the liquid membrane phase, and the organic
phase. Since we assume that the cellulose particles are rigid spheres,
the concentration of HMF in the solid phase is zero and does not need
to be discussed.
Figure 9.
Distribution of HMF, glucose, and fructose normalized concentrations in the reaction system at different reaction times (t = 10,000, 30,000, and 50000 t.s).
From Figure 9, we can investigate the distribution characteristics of glucose, fructose, and HMF in the whole reaction system. Glucose and fructose were only distributed in the liquid membrane phase, and the concentration of glucose was lower further away from the cellulose particles and showed a certain linear relationship with the distance from the phase interface. The concentration of fructose remained essentially uniform in the liquid membrane phase and decreased as the reaction time progressed. When the reaction proceeded up to t = 10,000 t.s, the concentration values of HMF in the liquid membrane phase or organic phase were low, and at t = 30,000 t.s when the reaction proceeded, the concentration of HMF started to increase in the liquid membrane phase, and the concentration of HMF was higher in the region close to the cellulose particles. At this point, because of the transport of HMF to the phase interface, concentration diffusion causes a lower concentration at the phase interface, while at the organic–liquid membrane phase interface, the concentration of HMF shifts dramatically because of the interfacial transport mechanism of the non-ideal solute. We observed that at the boundary of the calculated zone, the concentration values of HMF increased with reaction time and the high concentration of HMF in the organic phase favored the increase in HMF yield. Crucially, the low concentration of HMF in the liquid membrane phase significantly inhibited the subsequent side reactions of HMF and increased the yield of HMF significantly. At t = 50,000 t.s, the cellulose particles gradually decreased in size as the reaction proceeded further, and the peak HMF concentration in the liquid membrane phase of the reaction system did not increase. As the cellulose particles shrank further, the liquid membrane phase of the overall reaction system continued to increase. In the liquid membrane phase, the concentration of HMF is relatively low further away from the cellulose particles.
3.3. Mechanism of the Initial Liquid Membrane Thickness in the Reaction System
The initial liquid membrane thickness ξ plays an important role in the reaction system as a measure of the liquid membrane phase. By analyzing the simulation data, we obtained relevant conclusions about the role of the initial liquid membrane thickness in influencing the mechanism of the reaction system.
3.3.1. Conversion of Glucose
With different initial liquid membrane thicknesses, there is some variation in the conversion of glucose throughout the reaction system. As can be seen from Figure 10, when the reaction proceeds, the shortest reaction time is required for the conversion of glucose to reach 100% when the initial liquid membrane thickness is ξ = 3 l.u. When the initial liquid membrane thickness ξ continues to increase, the time required for the conversion of glucose to reach 100% also continues to increase. Because when the initial liquid membrane thickness is thinner, the concentration of catalyst H+ in the liquid membrane is higher. Therefore, the reaction rate of glucose is relatively fast, leading to a more rapid increase in the conversion of glucose.
Figure 10.
(a) Variation curves of glucose conversion at different initial liquid membrane thickness with the reaction time. (b) Enlarged view of the local area of figure (a).
3.3.2. Sensitivity of HMF Yield to Initial Liquid Membrane Thickness
After analyzing the mechanism of the effect
of different initial liquid membrane thicknesses on the conversion
of glucose, we proceeded to investigate the variation curves of the
yield of HMF with the glucose conversion proceeding at different initial
liquid membrane thicknesses for a cellulose particle size of 50 l.u.
Here, we propose 
to represent the indicator for the sensitivity
analysis of HMF yield to initial liquid membrane thickness. We take
the HMF yield at each glucose conversion with an initial liquid membrane
thickness of ξ = 3 l.u as a benchmark and establish the relative
increment of HMF yield for other initial liquid membrane thicknesses
relative to 3 l.u. The equation for 
is as follows
 |
45 |
Based on the data related to 
, we made the chart in (a) of Figure 11. According to
the trend of the chart (a), we divide it into three stages, 1, 2,
and 3. Figure 11b
shows the trend of the 
change in stage 1. In the first stage,
the value of 
gradually decreased as the conversion of
glucose increased from 0 to 80%. Furthermore, the value of 
increases as the initial liquid membrane
thickness ξ continues to increase. This indicates that in stage
1, the larger the initial liquid membrane thickness is, the higher
the value of 
is relatively. The thickening of initial
liquid membrane thickness plays a facilitating role in the growth
of HFM yield. It shows that the thicker the initial liquid membrane
thickness is at this stage, the more sensitive the effect on the HFM
yield is because at the beginning of the reaction, larger initial
liquid membrane thickness in the reaction leads to a relatively larger
volume of the liquid membrane phase, which also means that the reaction
area for the generation of HMF from glucose in the liquid membrane
phase is relatively larger. The growth rate of the yield of HMF also
increases with the increase in the initial liquid membrane thickness.
In stage 2, when the conversion of glucose increased from 80 to 96%,
we could obtain that 
was below 0% at this time, indicating that
the highest yield was achieved at the initial liquid membrane thickness
of 3 l.u in the second phase and 
decreased more rapidly with the increase
in the initial liquid membrane thickness. It shows that the initial
liquid membrane thickness played a suppressive role in the yield of
HMF at this stage as the initial liquid membrane thickness increased.
This is because when the reaction proceeds for a period of time, the
catalyst H+ concentration in the liquid membrane phase
decreases with the increase in the initial liquid membrane thickness
and the reaction rate decreases, which leads to a decrease in the
yield of HMF. Entering the third stage, the glucose conversion was
between 96 and 100% at this time. When the glucose conversion was
close to 100%, the value of 
showed an increasing trend at this time,
which was due to the fact that the side reactions occurred more significantly
after the complete reaction of glucose when the initial liquid membrane
thickness was thinner, leading to a decrease in HMF yield. As a result,
we derived a mechanism for the regulation of HMF yield and the reaction
system at different reaction stages by different initial liquid membrane
thicknesses. We can obtain relatively high HMF yields at different
reaction stages by varying different initial liquid membrane thicknesses.
Figure 11.
When the particle size of the cellulose particles is 50 l.u, the HMF yield as a function of glucose conversion change curve and the partially enlarged view under different initial liquid membrane thicknesses. (a) Variation curve of HMF yield with glucose conversion at different initial liquid membrane thicknesses. (b–d) Enlarged view of the variation of the HMF yield curve represented by stage of 1, 2, and 3, respectively.
3.3.3. Selectivity of HMF
After analyzing the mechanism of the initial membrane thickness on the HMF yield at different reaction stages, we then analyzed the effect on the HMF selectivity. Figure 12 shows the curve fitted to the HMF selectivity as a function of glucose conversion from 70 to 95%. It can be found that the HMF selectivity tends to increase and then decrease as the conversion rate of glucose increases. It is found that the HMF selectivity increases as the initial membrane thickness increases from 3 to 7 l.u, and then, the HMF selectivity reaches a maximum at an initial membrane thickness of 7 l.u.Then, the selectivity of HMF gradually decreases as the initial membrane thickness increases from 7 to 15 l.u. At this point, we can say that there exists an optimal liquid membrane thickness of 7 l.u that keeps the selectivity of HMF at its maximum.
Figure 12.
Graphs of HMF selectivity as a function of glucose conversion at different initial liquid membrane thicknesses for a cellulose particle size of 50 l.u.
3.4. Role of Cellulose Particle Size in the Reaction System
After we investigated the mechanism of the influence of different initial thicknesses in the overall reaction system in the previous section, we proceeded to investigate the role of different cellulose particle sizes r in the reaction. As shown in Figure 13, the variation curves of glucose conversion, HMF yield, and fructose selectivity at different cellulose particle sizes are shown. In Figure 13a, the reaction time required to reach 100% glucose conversion will be prolonged when the cellulose particle size keeps increasing because the increase in cellulose particle size corresponds to the decrease in H+ particle concentration, leading to reaction rate decreases, and the glucose conversion rate decreases subsequently. The maximum value of HMF yield decreases continuously as the cellulose particle size increases, and the yield of HMF at each moment decreases with the increase in cellulose particle size in Figure 13b. The selectivity of fructose was also correlated with the cellulose particle size in Figure 13c, and the selectivity of fructose was close to 0% when the reaction proceeded to t = 50 t.s. It was found that the selectivity of fructose decreased faster with the increase in cellulose particle size.
Figure 13.
Curves of (a) conversion of glucose, (b) yield of HMF, and (c) selectivity of fructose with time at different particle sizes of cellulose particles.
3.5. Effect of Reaction Temperature in the Reaction System
After investigating the roles played by the initial liquid membrane thickness and cellulose particle size in the reaction system, we proceeded to investigate the effects of different reaction temperatures on the reaction system. Figure 14 shows the cloud chart of the distribution of the three main product concentrations at different reaction temperatures at the reaction time of t = 30,000 t.s. When the temperature was increased from 413 to 433 K, the concentration of HMF increased significantly and was concentrated at the organic–liquid phase interface, while the concentrations of fructose and glucose decreased with the increase in temperature, and the distribution was more uniform at this time. When the temperature was increased from 433 to 453 K, the distribution of HMF in the organic phase was more concentrated and the concentration continued to increase. The concentrations of fructose and glucose continued to decrease and a concentration gradient appeared, with a relatively high concentration near the solid–liquid phase interface.
Figure 14.
Cloud chart of the concentration distribution of the three products with different reaction temperatures (t = 30,000 t.s).
We observed changes in the concentration distribution of the three main products by varying different reaction temperatures, which similarly affect the conversion of glucose and the yield of HMF. As shown in Figure 15, Figure 15a shows the curves of glucose conversion with time for different reaction temperatures. When the reaction temperature is higher, the glucose conversion grows faster and the time required to reach the maximum conversion is shorter, while at lower reaction temperatures, the glucose conversion grows slower and the time required to reach the maximum conversion is substantially longer, and the conversion of glucose cannot reach 100% at lower temperatures. Figure 15b shows the curves of HMF yield with reaction time at different reaction temperatures. An optimal reaction temperature of 453 K was exerted to get the highest yield of HMF in Figure 15b. After the reaction time exceeded t = 20 t.s, we can keep the HMF yield relatively high by regulating the reaction temperature.
Figure 15.
Variation curves of (a) glucose conversion and (b) HMF yield with reaction time at different reaction temperatures.
We compare the simulation results with the experimental results,17 and basically, the trend of the change is in agreement, as shown in Figure 16. In the experimental results, only 35.8% of HMF was generated at the lower temperature of 413 K, and when the temperature was increased, the yield of HMF increased significantly. When the temperature was increased from 413 to 433 K, the yield of HFM also increased to 53.2%. Then, when the temperature was increased to 453 K, the HMF yield decreased to 45%. This is also in line with the trend of our simulated results.
Figure 16.
Yield of HMF at different reaction temperatures. (a) Experiment and (b) LBM simulation.
4. Conclusions
An LBM-based organic–liquid–solid multiphase mixing model was developed to simulate physicochemical problems involving organic–liquid–solid-phase states and to model the liquid membrane catalytic system for the reaction of solid cellulose particles to generate HMF. The multiphase liquid membrane catalytic reaction model can capture well the multicomponent mass transfer, homogeneous and heterogeneous reactions, and reactive dissolution processes of the solid phase. The effects of initial liquid membrane thickness, reaction temperature, and cellulose particle size on the multicomponent multiphase reaction transport were investigated and discussed in detail. The following conclusions were drawn:
-
I.
When the reaction temperature was increased from 413 to 453 K, the presence of an optimum reaction temperature of 433 K allowed the yield of HMF to remain at the highest value for a longer reaction time.
-
II.
Under the conditions of constant reaction temperature and initial liquid membrane thickness, the yield of HMF gradually increased as the cellulose particle size increased from 40 to 60 l.u; however, the reaction time required to reach the maximum glucose conversion gradually increased with the increase in cellulose particle size.
-
III.
At different initial liquid membrane thicknesses, as the reaction proceeded, the shortest reaction time was required to achieve 100% conversion of glucose when the initial liquid membrane thickness was thin. An indicator
was defined
to characterize the sensitivity
of HMF yield to the initial liquid membrane thickness at different
reaction stages. 
decreased gradually when the glucose conversion
increased from 0 to 80%, and 
increased with the thickening of the initial
liquid membrane thickness. It was shown that the thickening of the
initial liquid membrane thickness promoted the HMF yield under the
same glucose conversion. When the glucose conversion rate increased
from 80 to 96%, 
decreased with the increase in the initial
liquid membrane thickness, and the results indicated that the thickening
of the initial liquid membrane thickness inhibited the increase in
HMF yield at the same glucose conversion. The selectivity of HMF tends
to increase with the increase in glucose conversion and then decreases,
and there is an optimal membrane thickness of 7 l.u to keep the selectivity
of HMF at the maximum.
Acknowledgments
This work was financially supported by the National Natural Science Foundation of China (no.51876210), the “Transformational Technologies for Clean Energy and Demonstration” Strategic Priority Research Program of the Chinese Academy of Sciences (no. XDA21060102), the National Key R&D program of China (2018 YFB1501402), and the National Natural Science Foundation of China (grants 51976220). The authors are particularly grateful to Prof. Fangming Jiang from Guangzhou Institute of Energy Conversion, for the help on the LBM.
Glossary
Nomenclature
- l.u
LB units
- cs
lattice sound speed
- C
concentration
- ξ
initial liquid membrane thickness
- ei
lattice velocity
- t.s
time step
- f
particle distribution function
- F
force
- g
concentration distribution function
- G
interaction strength
- r
cellulose particle size
an arbitrary function
solvent component distribution
- n
normal vector
degree of solute dissolution in different phases
- t
time
- T
temperature
- u
macroscopic velocity
- wi
weight factor in LBM
dimensionless volume
molar volume
specific surface area of the
cellulose
solids
Glossary
Greek Symbols
dimensionless relaxation time
- Δx
grid size
- Δt
time step
density
kinematic viscosity
mean-field potential function
- Δp
gas–liquid pressure difference
- β
coefficient determining the wettability of water on the solid surface
- k
reaction rate constants
- Ωa
indicator for sensitivity analysis of HMF yield to initial liquid membrane thickness
Glossary
Subscripts and Superscripts
- cohe
fluid–fluid
- adso
fluid–solid
- c
critical state
- liq
liquid
- eq
equilibrium
- vap
vapor
- cen
center
- l
liquid phase
- g
gas phase
The authors declare no competing financial interest.
References
- Wang H.; Zhu C.; Li D.; Liu Q.; Tan J.; Wang C.; Cai C.; Ma L. Recent advances in catalytic conversion of biomass to 5-hydroxymethylfurfural and 2, 5-dimethylfuran. Renew. Sustain. Energy Rev. 2019, 103, 227–247. 10.1016/j.rser.2018.12.010. [DOI] [Google Scholar]
- Wada M.; Heux L.; Nishiyama Y.; Langan P. The structure of the complex of cellulose I with ethylenediamine by X-ray crystallography and cross-polarization/magic angle spinning 13C nuclear magnetic resonance. Cellulose 2009, 16, 943–957. 10.1007/s10570-009-9338-5. [DOI] [Google Scholar]
- Dashtban M.; Gilbert A.; Fatehi P. Recent advancements in the production of hydroxymethylfurfural. RSC Adv. 2014, 4, 2037–2050. 10.1039/c3ra45396k. [DOI] [Google Scholar]
- Klein-Marcuschamer D.; Simmons B. A.; Blanch H. W. Techno-economic analysis of a lignocellulosic ethanol biorefinery with ionic liquid pre-treatment. Biofuels, Bioprod. Biorefin. 2011, 5, 562–569. 10.1002/bbb.303. [DOI] [Google Scholar]
- Sen S. M.; Binder J. B.; Raines R. T.; Maravelias C. T. Conversion of biomass to sugars via ionic liquid hydrolysis: process synthesis and economic evaluation. Biofuels, Bioprod. Biorefin. 2012, 6, 444–452. 10.1002/bbb.1336. [DOI] [Google Scholar]
- Liu Q.; Zhou L.; Fan D.; Guan M.; Ma Q.; Li S.; Ouyang X.; Qiu X.; Fan W. Adsorption-Enhanced Glucan Oligomer Production from Cellulose Hydrolysis over Hyper-Cross-Linked Polymer in Molten Salt Hydrate. ACS Appl. Mater. Interfaces 2021, 13, 52082. 10.1021/acsami.1c09360. [DOI] [PubMed] [Google Scholar]
- Qi X.; Watanabe M.; Aida T. M.; Smith R. L. Catalytical conversion of fructose and glucose into 5-hydroxymethylfurfural in hot compressed water by microwave heating. Catal. Commun. 2008, 9, 2244–2249. 10.1016/j.catcom.2008.04.025. [DOI] [Google Scholar]
- Benoit M.; Brissonnet Y.; Guélou E.; De Oliveira Vigier K.; Barrault J.; Jérôme F. Acid-catalyzed dehydration of fructose and inulin with glycerol or glycerol carbonate as renewably sourced co-solvent. ChemSusChem 2010, 3, 1304–1309. 10.1002/cssc.201000162. [DOI] [PubMed] [Google Scholar]
- Román-Leshkov Y.; Dumesic J. A. Solvent Effects on Fructose Dehydration to 5-Hydroxymethylfurfural in Biphasic Systems Saturated with Inorganic Salts. Top. Catal. 2009, 52, 297–303. 10.1007/s11244-008-9166-0. [DOI] [Google Scholar]
- Pagán-Torres Y. J.; Wang T.; Gallo J. M. R.; Shanks B. H.; Dumesic J. A. Production of 5-Hydroxymethylfurfural from Glucose Using a Combination of Lewis and Brønsted Acid Catalysts in Water in a Biphasic Reactor with an Alkylphenol Solvent. ACS Catal. 2012, 2, 930–934. 10.1021/cs300192z. [DOI] [Google Scholar]
- Gallo J. M. R.; Alonso D. M.; Mellmer M. A.; Dumesic J. A. Production and upgrading of 5-hydroxymethylfurfural using heterogeneous catalysts and biomass-derived solvents. Green Chem. 2013, 15, 85–90. 10.1039/c2gc36536g. [DOI] [Google Scholar]
- He J.; Liu M.; Huang K.; Walker T. W.; Maravelias C. T.; Dumesic J. A.; Huber G. W. Production of levoglucosenone and 5-hydroxymethylfurfural from cellulose in polar aprotic solvent–water mixtures. Green Chem. 2017, 19, 3642–3653. 10.1039/c7gc01688c. [DOI] [Google Scholar]
- Binder J. B.; Raines R. T. Simple chemical transformation of lignocellulosic biomass into furans for fuels and chemicals. J. Am. Chem. Soc. 2009, 131, 1979–1985. 10.1021/ja808537j. [DOI] [PubMed] [Google Scholar]
- Wang P.; Yu H.; Zhan S.; Wang S. Catalytic hydrolysis of lignocellulosic biomass into 5-hydroxymethylfurfural in ionic liquid. Bioresour. Technol. 2011, 102, 4179–4183. 10.1016/j.biortech.2010.12.073. [DOI] [PubMed] [Google Scholar]
- Wang T.; Pagán-Torres Y. J.; Combs E. J.; Dumesic J. A.; Shanks B. H. Water-compatible Lewis acid-catalyzed conversion of carbohydrates to 5-hydroxymethylfurfural in a biphasic solvent system. Top. Catal. 2012, 55, 657–662. 10.1007/s11244-012-9845-8. [DOI] [Google Scholar]
- Yang Y.; Hu C.-w.; Abu-Omar M. M. Conversion of carbohydrates and lignocellulosic biomass into 5-hydroxymethylfurfural using AlCl3·6H2O catalyst in a biphasic solvent system. Green Chem. 2012, 14, 509–513. 10.1039/c1gc15972k. [DOI] [Google Scholar]
- Shi N.; Liu Q.; Zhang Q.; Wang T.; Ma L. High yield production of 5-hydroxymethylfurfural from cellulose by high concentration of sulfates in biphasic system. Green Chem. 2013, 15, 1967–1974. 10.1039/c3gc40667a. [DOI] [Google Scholar]
- Yan Y. Y.; Zu Y. Q. Numerical simulation of heat transfer and fluid flow past a rotating isothermal cylinder–a LBM approach. Int. J. Heat Mass Transfer 2008, 51, 2519–2536. 10.1016/j.ijheatmasstransfer.2007.07.053. [DOI] [Google Scholar]
- Jafari M.; Farhadi M.; Sedighi K. Pulsating flow effects on convection heat transfer in a corrugated channel: A LBM approach. Int. Commun. Heat Mass Tran. 2013, 45, 146–154. 10.1016/j.icheatmasstransfer.2013.04.006. [DOI] [Google Scholar]
- Eshraghi M.; Felicelli S. D. An implicit lattice Boltzmann model for heat conduction with phase change. Int. J. Heat Mass Transfer 2012, 55, 2420–2428. 10.1016/j.ijheatmasstransfer.2012.01.018. [DOI] [Google Scholar]
- Gong S.; Cheng P. A lattice Boltzmann method for simulation of liquid–vapor phase-change heat transfer. Int. J. Heat Mass Transfer 2012, 55, 4923–4927. 10.1016/j.ijheatmasstransfer.2012.04.037. [DOI] [Google Scholar]
- Huang R.; Wu H.; Cheng P. A new lattice Boltzmann model for solid–liquid phase change. Int. J. Heat Mass Transfer 2013, 59, 295–301. 10.1016/j.ijheatmasstransfer.2012.12.027. [DOI] [Google Scholar]
- Sheikholeslami M.; Gorji-Bandpy M.; Ganji D. D. Numerical investigation of MHD effects on Al2O3–water nanofluid flow and heat transfer in a semi-annulus enclosure using LBM. Energy 2013, 60, 501–510. 10.1016/j.energy.2013.07.070. [DOI] [Google Scholar]
- Izadi M.; Mohebbi R.; Karimi D.; Sheremet M. A. Numerical simulation of natural convection heat transfer inside a shaped cavity filled by a MWCNT-Fe3O4/water hybrid nanofluids using LBM. Chem. Eng. Process. 2018, 125, 56–66. 10.1016/j.cep.2018.01.004. [DOI] [Google Scholar]
- Sheikholeslami M. Influence of magnetic field on Al2O3-H2O nanofluid forced convection heat transfer in a porous lid driven cavity with hot sphere obstacle by means of LBM. J. Mol. Liq. 2018, 263, 472–488. 10.1016/j.molliq.2018.04.111. [DOI] [Google Scholar]
- Falcucci G.; Amati G.; Krastev V. K.; Montessori A.; Yablonsky G. S.; Succi S. Heterogeneous catalysis in pulsed-flow reactors with nanoporous gold hollow spheres. Chem. Eng. Sci. 2017, 166, 274–282. 10.1016/j.ces.2017.03.037. [DOI] [Google Scholar]
- Falcucci G.; Montessori A.; Succi S. On the effects of reactant flow rarefaction on heterogeneous catalysis: a regularized lattice Boltzmann study. Comput. Phys. Commun. 2018, 23, 1279–1288. 10.4208/cicp.oa-2016-0250. [DOI] [Google Scholar]
- Montessori A.; Prestininzi P.; La Rocca M.; Falcucci G.; Succi S.; Kaxiras E. Effects of Knudsen diffusivity on the effective reactivity of nanoporous catalyst media. J. Comput. Sci. 2016, 17, 377–383. 10.1016/j.jocs.2016.04.006. [DOI] [Google Scholar]
- Zhang M.; Ye G.; van Breugel K. Modeling of ionic diffusivity in non-saturated cement-based materials using lattice Boltzmann method. Cem. Concr. Res. 2012, 42, 1524–1533. 10.1016/j.cemconres.2012.08.005. [DOI] [Google Scholar]
- Huang H.; Krafczyk M.; Lu X. Y. Forcing term in single-phase and Shan-Chen-type multiphase lattice Boltzmann models. Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 2011, 84, 046710. 10.1103/physreve.84.046710. [DOI] [PubMed] [Google Scholar]
- Chen L.; Kang Q.; Robinson B. A.; He Y.-L.; Tao W.-Q. Pore-scale modeling of multiphase reactive transport with phase transitions and dissolution-precipitation processes in closed systems. Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 2013, 87, 043306. 10.1103/physreve.87.043306. [DOI] [PubMed] [Google Scholar]
- Wei X.; Li W.; Liu Q.; Sun W.; Liu S.; Li S.; Wei H.; Ma L. Pore-scale investigation on multiphase reactive transport for the conversion of levulinic acid to γ-valerolactone with Ru/C catalyst. Chem. Eng. J. 2022, 427, 130917. 10.1016/j.cej.2021.130917. [DOI] [Google Scholar]
- Chen L.; Zhang R.; Kang Q.; Tao W.-Q. Pore-scale study of pore-ionomer interfacial reactive transport processes in proton exchange membrane fuel cell catalyst layer. Chem. Eng. J. 2020, 391, 123590. 10.1016/j.cej.2019.123590. [DOI] [Google Scholar]
- Yuan P.; Schaefer L. Equations of state in a lattice Boltzmann model. Phys. Fluids 2006, 18, 042101. 10.1063/1.2187070. [DOI] [Google Scholar]
- Chen L.; Kang Q.; Mu Y.; He Y.-L.; Tao W.-Q. A critical review of the pseudopotential multiphase lattice Boltzmann model: Methods and applications. Int. J. Heat Mass Tran. 2014, 76, 210–236. 10.1016/j.ijheatmasstransfer.2014.04.032. [DOI] [Google Scholar]
- Shan X.; Chen H. Lattice Boltzmann model for simulating flows with multiple phases and components. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 1993, 47, 1815–1819. 10.1103/physreve.47.1815. [DOI] [PubMed] [Google Scholar]
- Riaud A.; Zhao S.; Wang K.; Cheng Y.; Luo G. Lattice-Boltzmann method for the simulation of multiphase mass transfer and reaction of dilute species. Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 2014, 89, 053308. 10.1103/PhysRevE.89.053308. [DOI] [PubMed] [Google Scholar]
- Khazraji A. C.; Robert S. Self-Assembly and Intermolecular Forces When Cellulose and Water Interact Using Molecular Modeling. J. Nanomater. 2013, 2013, 1–12. 10.1155/2013/745979. [DOI] [Google Scholar]
- Tong X.; Ma Y.; Li Y. Biomass into chemicals: Conversion of sugars to furan derivatives by catalytic processes. Appl. Catal., A 2010, 385, 1–13. 10.1016/j.apcata.2010.06.049. [DOI] [Google Scholar]
- Ma J.; Yu W.; Min W.; Xiuquan J.; Fang L.; Jie X. Advances in selective catalytic transformation of ployols to value-added chemicals. Chin. J. Catal. 2013, 34, 492–507. 10.1016/s1872-2067(11)60501-9. [DOI] [Google Scholar]
- Román-Leshkov Y.; Moliner M.; Labinger J. A.; Davis M. E. Mechanism of glucose isomerization using a solid Lewis acid catalyst in water. Angew. Chem. 2010, 122, 9138–9141. 10.1002/ange.201004689. [DOI] [PubMed] [Google Scholar]
- Takagaki A.; Ohara M.; Nishimura S.; Ebitani K. A one-pot reaction for biorefinery: combination of solid acid and base catalysts for direct production of 5-hydroxymethylfurfural from saccharides. Chem. Commun. 2009, 41, 6276–6278. 10.1039/b914087e. [DOI] [PubMed] [Google Scholar]
- Saha B.; Abu-Omar M. M. Advances in 5-hydroxymethylfurfural production from biomass in biphasic solvents. Green Chem. 2014, 16, 24–38. 10.1039/c3gc41324a. [DOI] [Google Scholar]
- Pagán-Torres Y. J.; Wang T.; Gallo J. M. R.; Shanks B. H.; Dumesic J. A. Production of 5-hydroxymethylfurfural from glucose using a combination of Lewis and Brønsted acid catalysts in water in a biphasic reactor with an alkylphenol solvent. ACS Catal. 2012, 2, 930–934. 10.1021/cs300192z. [DOI] [Google Scholar]
- Li J.; Ma Y.; Wang L.; Song Z.; Li H.; Wang T.; Li H.; Eli W. Catalytic conversion of glucose into 5-hydroxymethylfurfural by Hf (OTf) 4 Lewis acid in water. Catalysts 2016, 6, 1. 10.3390/catal6010001. [DOI] [Google Scholar]
- Yang G.; Pidko E. A.; Hensen E. J. M. The mechanism of glucose isomerization to fructose over Sn-BEA zeolite: a periodic density functional theory study. ChemSusChem 2013, 6, 1688–1696. 10.1002/cssc.201300342. [DOI] [PubMed] [Google Scholar]
- Tang J.; Zhu L.; Fu X.; Dai J.; Guo X.; Hu C. Insights into the Kinetics and Reaction Network of Aluminum Chloride-Catalyzed Conversion of Glucose in NaCl–H2O/THF Biphasic System. ACS Catal. 2016, 7, 256–266. 10.1021/acscatal.6b02515. [DOI] [Google Scholar]
- Yan L.; Greenwood A. A.; Hossain A.; Yang B. A comprehensive mechanistic kinetic model for dilute acid hydrolysis of switchgrass cellulose to glucose, 5-HMF and levulinic acid. RSC Adv. 2014, 4, 23492–23504. 10.1039/c4ra01631a. [DOI] [Google Scholar]