A Bionic Peristaltic Process for Enhanced Powder Dispersion in Energetic High-Solid-Loading Slurries

Abstract

This study introduces a paddle-less bionic peristaltic mixing process, inspired by intestinal biomechanics, for enhanced powder dispersion in energetic high-solid-loading slurries (80% solids). Periodic elastic conduit compression induces low-shear vortices, substantially reducing energy consumption compared with conventional mechanical stirring in solid propellant preparation. ANSYS Fluent simulations employing dynamic meshing and the Navier–Stokes equations demonstrate bidirectional flows and effective phase homogenization, achieving high-density uniformity after 300 s. Experiments using a NaCl/Al/HTPB solid-propellant simulant identified the optimal operating parameters as an extrusion duration of 3 s, an air pressure of 0.6 MPa, four peristaltic segments, and an intersegment spacing of 5 mm. Under these conditions, the mean density across the five axial sections was 1.513 g·cm^–3, and the axial-density standard deviation was 0.016 g·cm^–3, corresponding to an approximately 58% improvement in spatial uniformity relative to the baseline condition. Scanning electron microscopy confirms uniform particle coating and grading. This low-shear, energy-efficient method provides an innovative approach for solid propellant mixing and holds broad potential for other high-solid powder composites in pharmaceuticals and ceramics.

1. Introduction

Achieving uniform powder dispersion in energetic high-solid-loading slurries (>80% solids) is essential for advanced composite materials, where inadequate mixing leads to segregation, agglomeration, and suboptimal performance. In solid propellant preparation, such inconsistencies can compromise ignition reliability, combustion efficiency, and structural integrity in hydroxyl-terminated polybutadiene (HTPB)-based formulations. − Conventional mechanical methods, such as high-speed stirring, exacerbate these issues through intense shear, resulting in energy inefficiency and material degradation. , Biomimicry offers a transformative alternative: intestinal peristalsis facilitates seamless mixing of viscous, particle-laden contents via rhythmic, low-shear contractions, providing a promising model for paddle-less mixing systems that enable gentle particle redistribution with reduced energy consumption. ,

Currently, the production of solid propellants mainly relies on mechanical stirring and high-speed mixing equipment. These methods often struggle to achieve uniform mixing and consume large amounts of energy. − With the escalating performance requirements for HTPB-based propellants in aerospace and defense applications, the inherent limitations of conventional mixing processeshigh energy consumption and poor uniformityhave become increasingly prominent. − The principle of intestinal peristalsis, an efficient natural mechanism for material mixing and transport, has gradually attracted academic attention, particularly for its potential in uniform material transfer and low-energy mixing. −

Many scholars have conducted extensive research on solid propellant mixing processes. Chen et al. investigated the mixing performance of a high-shear mixer for propellant systems with 65% solid content; the results showed that excessive mixing time led to overfriction of the materials, which adversely affected mixing quality and propellant performance. An et al. reported a twin-screw mixing process for systems with 70% solid loading and, through experimental verification, found that this method could effectively reduce particle segregation, thereby enhancing mixing uniformity and production efficiency. Khan et al. optimized mixing parameters for propellants with 75% solid content. However, all these methods struggled to balance mixing uniformity and energy efficiency in high-solid-loading systems (≥80%).

At the same time, the application of biomimicry has received increasing attention. Yang et al. designed a biomimetic mixing system based on intestinal peristalsis; through numerical simulation and experimental validation, they found that the system significantly improved the flowability and mixing efficiency of particulate materials. Yang et al. proposed combining biomimicry with fluid dynamics and designed a solid propellant mixing model based on the intestinal peristalsis mechanism. Their experimental results showed that this model could effectively optimize the mixing process and reduce equipment energy consumption.

The above studies indicate that the peristaltic mixing process has a significant impact on the mixing uniformity and production efficiency of solid propellants. − However, existing research methods have limitations, with many experimental and numerical simulation results focused primarily on theoretical analysis and small-scale experiments, which cannot fully reflect their effectiveness in actual production. , Moreover, most researchers still confuse peristaltic mixing with conventional methods (such as mechanical stirring), hindering the widespread application of this technology. ,

To address the above challenges, this study employs a combined approach of biomimicry and fluid dynamics. Through numerical simulation and experimental verification, we demonstrate that peristaltic flow can effectively improve the mixing uniformity of solid propellants and reduce energy consumption and production time. Specifically, this work develops a bionic peristaltic mixing method for HTPB-based propellants with 80% solid content. It systematically investigates the effects of key parameters (peristaltic segment number, segment spacing, and extrusion duration) on mixing uniformity and energy consumption via numerical simulation and experiments, and verifies the feasibility of the method by comparing simulation results with experimental data. The findings are expected to provide a targeted theoretical basis for the application of bionic peristaltic mixing technology in high-solid-loading propellant systems.

2. Experimental Section

2.1. Materials

Hydroxyl-terminated polybutadiene (HTPB) was purchased from Meryer (Shanghai) Chemical Technology Co., Ltd.; dioctyl sebacate (DOS) was purchased from Nanjing Wanqing Chemical Glass Ware & Instrument Co., Ltd.; coarse granular sodium chloride (NaCl, D₅₀ = 351 μm) was purchased from Nanjing HaiLiang Chemical Co., Ltd.; fine granular sodium chloride (NaCl, D₅₀ = 10.91 μm) was prepared from the coarse NaCl by micronization using a GQF-20plus flat jet mill; aluminum powder (Al, purity ≥99.5%, D₅₀ = 13 μm) was purchased from Jiangsu Zhiren Jingxing New Materials Research Institute Co., Ltd.; and ethanol (C₂H₆O, purity ≥99.5%) was purchased from Nanjing Juyou Scientific Equipment Co., Ltd.

2.2. Numerical Simulation

2.2.1. Peristaltic Mixing Model

The peristaltic mixing model was established based on biomimetic principles, mimicking the peristalsis of the intestines. Given that the peristaltic mixing equipment is intended for high-viscosity solid propellant slurries, the model in this study was designed as a straight cylindrical pipeline with key parameters including length (L), radius (R), peristaltic segment length (l), and maximum contraction depth (r). Due to limited computational resources, a two-dimensional rectangular model was adopted, as shown in Figure .

1.

Peristaltic mixing model.

Figure Schematic of the peristaltic mixing model. Note: L = total length of the peristaltic pipeline; R = pipe radius; l = length of a single peristaltic segment; r = vertical distance from the tip of the peristaltic segment to the pipe wall at maximum contraction

2.2.2. Governing Equations and Dynamic Mesh Method

The solid propellant slurry, characterized by high viscosity and low flow velocity, exhibits laminar flow in the peristaltic pipeline. The continuity equation and Navier–Stokes equation govern the mass and momentum conservation of the fluid, respectively. ,

$$\frac{\partial \rho }{\partial t}+\nabla ·(\rho u)=0$$ 1

$$\frac{\partial (\rho u)}{\partial t}+\nabla ·(\rho uu)=-\nabla p+\nabla [{\mu }_t(\nabla u+\nabla u^T)]+\rho g+F$$ 2

where ρ is the density of the mixture (kg/m³), u is the flow velocity (m/s), p is the pressure (Pa), μ _t is the viscosity (Pa·s), and F is the external force per unit volume (N/m³).

To simulate the periodic wall deformation that mimics intestinal peristalsis, a dynamic mesh model was employed in ANSYS Fluent 2022 R2. The upper and lower tube walls underwent mirror-symmetric motion perpendicular to the axial direction. Wall motion was implemented using a user-defined function (UDF). At each time step, the current simulation time was read, the prescribed displacement of each peristaltic wall segment was calculated, and the positions of the corresponding wall nodes were updated. The mesh quality was subsequently evaluated, and spring smoothing and local remeshing were applied when necessary to prevent excessive mesh distortion. After the flow-field equations were solved for the current time step, this procedure was repeated until the specified simulation duration was reached.

2.2.3. Simulation Parameters and Settings

The model was divided into more than 30,000 two-dimensional triangular elements in ANSYS Workbench Meshing, with an average mesh quality of 0.9717 and a minimum mesh quality of 0.7328. To realize the squeezing effect of the peristaltic tube on the internal material due to wall deformation, the built-in dynamic mesh technology in ANSYS Fluent 2022 R2 was utilized. The peristaltic wall motion function was implemented through a user-defined function (UDF) compiled from a C language file. Spring smoothing (spring constant factor = 0.1) and remeshing (minimum mesh length 0.0009 m, maximum length 0.0011 m, reconstruction interval = 1) were employed to maintain mesh quality during large deformations. The time step was set to 0.05 s with a maximum of 20 iterations per time step.

Grid independence was verified using three mesh schemes (15,000, 30,000, and 60,000 elements). The average fluid velocity at t = 1 s differed by less than 1% between the 30,000- and 60,000-element meshes; therefore, the 30,000-element mesh was selected for all subsequent simulations.

In the multiphase model, the solid particles and the HTPB/DOS binder were treated as distinct phases, with the HTPB/DOS mixture represented as a single liquid phase. The binder mixture was prepared using the same HTPB-to-DOS mass ratio as that employed in the slurry formulation. Rheological measurements were conducted at 25 °C using a Kinexus rotational rheometer. The apparent viscosities of HTPB, DOS, and the HTPB/DOS mixture at a shear rate of 10 s^–1 were 9.5, 0.020, and 0.300 Pa·s, respectively. Accordingly, a dynamic viscosity of 0.300 Pa·s was assigned to the liquid phase in the numerical model.

The HTPB/DOS binder phase was approximated as a Newtonian fluid with constant viscosity. The assigned value represents the experimentally measured apparent viscosity of the liquid binder mixture rather than the bulk apparent viscosity of the complete 80 wt % solid-loading slurry. Although highly filled slurries may exhibit shear-rate-dependent non-Newtonian behavior and time-dependent thixotropy, these rheological effects were not explicitly incorporated into the present model. The simulations were therefore used primarily to elucidate phase redistribution and flow-field evolution induced by periodic wall deformation rather than to provide a complete quantitative representation of the bulk rheological behavior of the slurry.

For computational tractability, the fine NaCl, coarse NaCl, and Al powders were combined into a single effective solid phase. The model therefore did not resolve particle-size-dependent slip, migration, or segregation among the individual solid components. Binder adsorption and interfacial immobilization at the particle surfaces, as well as changes in the bulk slurry viscosity caused by variations in powder specific surface area, were not explicitly incorporated into the model. Because the same formulation and particle-size distribution were used in all numerical cases, these particle-surface effects were treated as invariant across the comparative simulations. Accordingly, the model was used to evaluate the relative influence of the peristaltic operating conditions within the specified formulation, and the results should not be quantitatively extrapolated to slurries containing different particle sizes, size distributions, or specific surface areas.

The simulation aimed to reproduce the solid–liquid two-phase mixing of a fixed amount of solid powder and liquid in a closed peristaltic tube under periodic wall deformation. For safety, industrial sodium chloride (NaCl) was used as a nonsensitive substitute for ammonium perchlorate (AP), and the mixture of HTPB and DOS was treated as a single liquid phase. Approximately 80% of the tube volume was occupied by the solid and liquid material phases, while the remaining approximately 20% was intentionally left unfilled as a deformation-buffer region. This unfilled region provided sufficient space for tube-wall deformation and axial displacement of the slurry during the peristaltic compression process. Within the material-filled region, the solid and liquid phases accounted for 80 and 20% of the initialized material volume, respectively. The solid-phase region was divided into five spatial units with relative lengths of 1/8, 1/4, 1/4, 1/4, and 1/8, whereas the liquid-phase region was divided into four equal units. Each unit was initialized with a local volume fraction of 1 for the corresponding phase. Therefore, the solid and liquid phases were initially arranged in spatially separated and nonoverlapping regions. This deliberately nonuniform initial condition was adopted as a reproducible starting state for evaluating phase redistribution and homogenization induced by the bionic peristaltic process. The revised initial phase distribution is shown in Figure .

2.

Initial volume-fraction distributions of the (a) effective solid phase and (b) HTPB/DOS liquid phase. The material-filled region occupied 80% of the tube volume, while the remaining 20% served as a deformation-buffer region. The solid and liquid phases were initially separated.

2.3. Equipment Design

Based on the peristaltic mixing principles and optimal parameters identified in the numerical simulations, a custom laboratory-scale bionic peristaltic mixing device was designed and fabricated. The apparatus utilizes a flexible medical-grade silicone tube as the primary mixing conduit. Periodic compression of the tube is achieved through pneumatically actuated fixtures driven by synchronized pneumatic cylinders, thereby replicating the rhythmic contraction-relaxation cycles of intestinal peristalsis. This paddle-less configuration generates low-shear bidirectional flows and localized vortices within the high-solid-loading slurry (80% solids), promoting uniform powder dispersion while minimizing mechanical degradation and energy consumption compared with conventional high-shear mixers.

The core mixing chamber consists of a replaceable silicone tube (length 300 mm, inner diameter 38 mm, wall thickness 2 mm) housed within a precision-machined fixture system. Two opposing pneumatic cylinders control flat-plate fixtures (width 45 mm), enabling sequential compression along the tube length. The cylinder stroke is precisely adjustable between a maximum of 44 mm and a minimum of 14 mm, corresponding to the contraction depths validated in the simulations. Air pressure, extrusion duration, number of active peristaltic segments, and intersegment spacing are regulated by solenoid valves and a programmable logic controller, ensuring reproducible operation. The experimental setup and engineering schematic of the bionic peristaltic extrusion device are shown in Figure . The apparatus consists of pneumatic cylinders, compression fixtures, and a silicone tube mounted on a supporting frame. During operation, the compression fixtures undergo reciprocating motion to generate periodic deformation of the tube. The key geometric parameters of the apparatus are indicated in Figure .

3.

(a) Photograph of the experimental setup; (b) engineering schematic of the bionic peristaltic apparatus.

The key parameters of the equipment are shown inTable .

1. Key Parameters of Peristaltic Mixing Equipment.

Parameter	Unit	Numeric
Silicone tube length	mm	300
Silicone tube inner diameter	mm	38
Silicone tube thickness	mm	2
Maximum stroke of cylinder fixture	mm	44
Minimum stroke of cylinder fixture	mm	14
Fixture width	mm	45

2.4. Experimental Procedure

The NaCl/Al/HTPB solid propellant simulant slurry with a nominal solid content of 80 wt % was prepared according to the formulation given in Table . Hydroxyl-terminated polybutadiene (HTPB) and dioctyl sebacate (DOS) were first blended at room temperature to form the binder phase. The solid components-fine NaCl (D₅₀ = 10.91 μm), coarse NaCl (D₅₀ = 351 μm), and aluminum powder (D₅₀ = 13 μm)-were then added sequentially under gentle manual stirring to minimize premature agglomeration. The actual solid content was verified gravimetrically by drying triplicate 5.00 g aliquots of the binder-solid mixture in a vacuum oven at 80 °C for 24 h; the average measured value was 80.2 ± 0.3 wt %, which was taken as the working solid loading.

2. Formulation of the NaCl/Al/HTPB Solid Propellant Simulant Slurry (80 wt % Solids).

Components	Proportion(%)
HTPB	8.92
DOS	11.08
Fine particles of NaCl	52.4
Coarse NaCl	14.5
Al	13.1

Mixing experiments were conducted using the custom bionic peristaltic device described in Section . The premixed slurry was loaded into a fresh medical-grade silicone tube to occupy approximately 80% of the tube’s internal volume, leaving approximately 20% unfilled as a deformation buffer. The unfilled volume allowed sufficient tube-wall deformation during pneumatic compression and provided space for axial displacement of the slurry. This volumetric filling ratio was distinct from the solid loading of the slurry, which was approximately 80 wt %, and was kept constant in all experimental runs. Nine sets of operating conditions were systematically investigated to evaluate the effects of extrusion duration (1, 2, and 3 s), air pressure (0.4, 0.5, and 0.6 MPa), number of peristaltic segments (2, 3, and 4), and intersegment spacing (5, 15, and 25 mm), as detailed in Table . Each experimental run was performed for a total mixing time of 1 h under the programmed cyclic compression regime. After mixing, the silicone tube was immediately removed from the fixture, carefully cut open along its length, and the in situ macroscopic appearance of the slurry was photographed and recorded for qualitative assessment of color uniformity and phase segregation.

3. Experimental Design Matrix for Peristaltic Mixing Parameters.

Group	Squeeze Time (s)	Air Pressure (MPa)	Number of Peristaltic Segments (Section)	Creeping Internode Distance (mm)
1	3	0.6	4	5
2	2	0.6	4	5
3	1	0.6	4	5
4	3	0.5	4	5
5	3	0.4	4	5
6	3	0.6	3	5
7	3	0.6	2	5
8	3	0.6	4	15
9	3	0.6	4	25

The solid phase was formulated with a broad particle-size distribution comprising fine NaCl (D₅₀ = 10.91 μm, 52.4 wt %), Al powder (D₅₀ = 13 μm, 13.1 wt %), and coarse NaCl (D₅₀ = 351 μm, 14.5 wt %). Thus, the fine NaCl and Al fractions together accounted for 65.5 wt % of the complete formulation, whereas coarse NaCl accounted for 14.5 wt %. Fine particles provide a large interfacial area for binder wetting and can immobilize a greater fraction of the binder near the particle surfaces, thereby increasing the binder demand and apparent viscosity of the slurry. In contrast, the coarse fraction reduces the total surface area per unit mass relative to an equivalent all-fine solid fraction. In the broadly graded system, the fine particles can also occupy the interstitial spaces between the coarse particles, thereby improving packing efficiency. Consequently, the rheological behavior of the slurry reflects the combined effects of particle surface area, size gradation, packing efficiency, and particle-binder interactions rather than particle size alone. The powder sources, particle sizes, and mass fractions were kept constant in all experimental groups to permit direct comparison of the effects of the peristaltic operating parameters.

2.5. Experimental Procedure

The apparent viscosities of HTPB, DOS, and the HTPB/DOS binder mixture were measured using a Kinexus rotational rheometer (NETZSCH, Germany) controlled by rSpace software. The HTPB/DOS mixture was prepared using the same mass ratio as that employed in the slurry formulation. Rheological measurements were conducted at 25 °C using a 40 mm parallel-plate geometry with a measurement gap of 1.0 mm. Steady-shear flow curves were obtained over a shear-rate range of 0.1–100 s^–1, and the apparent viscosities at 10 s^–1 were used for comparison. The measured apparent viscosities of HTPB, DOS, and the HTPB/DOS mixture were 9.5, 0.020, and 0.300 Pa·s, respectively. Each sample was measured in triplicate, and the average value was reported.

The density of the mixed slurry was measured using an electronic density analyzer (ET-320D, Beijing Yinuote Electronic Technology Co., Ltd., China) based on the Archimedes buoyancy method. The density analyzer had a resolution of 0.001 g·cm^–3. After mixing, the silicone tube was divided into five equal sections along its axial direction, and three replicate samples were collected from each section. The density at each axial sampling position was expressed as the mean ± standard deviation of the three replicate measurements (n = 3). The error bars in Figures – represent the standard deviation of the replicate density measurements at each sampling position. The axial density standard deviation calculated from the mean densities of the five axial sections was defined as the quantitative indicator of spatial mixing uniformity. A lower axial density standard deviation indicates a more uniform density distribution along the tube. All experimental density values and axial density standard deviations were reported to three decimal places in accordance with the resolution of the instrument (Figures ).

9.

Effect of extrusion duration on slurry density uniformity at 0.6 MPa, with four peristaltic segments and an intersegment spacing of 5 mm.

12.

Effect of intersegment spacing on slurry density uniformity at an extrusion duration of 3 s, an air pressure of 0.6 MPa, and four peristaltic segments.

The morphology and particle dispersion of representative slurry samples were characterized by field-emission scanning electron microscopy (FE-SEM; Regulus 8100, Hitachi, Japan). Prior to observation, a small amount of each sample was mounted on conductive carbon tape and sputter-coated with gold at a current of 10 mA for 30 s. The SEM images were used to evaluate the integrity of the coarse particles, the dispersion and agglomeration of the fine particles, and the coating of the particle surfaces by the HTPB/DOS binder phase.

3. Results and Discussion

3.1. Numerical Simulation of Peristaltic Mixing Dynamics

Numerical simulations were performed using ANSYS Fluent 2022 R2 to elucidate the flow patterns and mixing mechanisms generated by the bionic peristaltic process. The two-dimensional model incorporated periodic wall deformation to replicate intestinal peristalsis, with the slurry treated as an 80 wt % solid–liquid two-phase system. Key dynamic behaviors are summarized below.

Figure illustrates the evolution of velocity vectors during one peristaltic cycle. During the contraction phase of the odd-numbered segments (Figure a, t = 0–0.5 s), the wall motion induced a strong inward and rightward flow near the contracting segments, accompanied by the formation of slow-moving vortices in the cavities between adjacent segments. In the subsequent recovery phase (Figure b, t = 0.5–1 s), the flow direction reversed, generating leftward motion and additional material exchange as the recovered segments created space for reverse flow. These bidirectional flows and alternating vortices constitute the primary mechanisms responsible for enhanced material redistribution. The intensity and spatial extent of vortex formation were highly sensitive to the contraction depth (deformation coefficient A). As shown in Figure c, increasing A from 0.75 to 0.95 progressively enlarged the vortices and promoted additional secondary recirculation zones, confirming that sufficient extrusion depth is critical for effective mixing.

4.

Velocity vector fields illustrating peristaltic flow dynamics during one cycle and the effect of contraction depth. (a) Contraction phase of the odd-numbered segments (t = 0–0.5 s). (b) Recovery phase of the odd-numbered segments (t = 0.5–1 s). (c) Velocity vectors at maximum contraction for different deformation coefficients (A = 0.75, 0.90, 0.93, and 0.95).

The temporal evolution of phase distributions further demonstrates progressive homogenization. Figure shows the solid-phase volume fraction at representative times. Within a single cycle (Figure a), forced lateral displacement of solid particles occurred during both contraction and recovery, reducing localized aggregation. Over extended simulation times (Figure b), repeated peristaltic cycles led to increasingly uniform solid-phase distribution throughout the tube. Although the variation became relatively small after approximately 300 s, this indicates that the solid-phase redistribution gradually approached a stable mixing state. Similarly, Figure depicts the liquid-phase volume fraction. The liquid binder, initially localized, rapidly diffused along the symmetry axis and into surrounding solid regions during each cycle (Figure a). Cumulative diffusion over multiple cycles (Figure b) resulted in near-homogeneous liquid distribution by 300 s.

5.

Temporal evolution of the solid-phase volume fraction during the peristaltic mixing process. (a) Changes within one cycle (t = 0.5, 1, 1.5, and 2 s). (b) Changes at extended simulation times (t = 2, 50, 100, 200, and 300 s).

6.

Temporal evolution of the liquid-phase volume fraction during the peristaltic mixing process. (a) Changes within one cycle (t = 0.5, 1, 1.5, and 2 s). (b) Changes at extended simulation times (t = 2, 50, 100, 200, and 300 s).

The overall mixing uniformity was quantitatively assessed through the mixture density field (Figure ). Within a single cycle (Figure a), density variations closely tracked the phase distributions. Over extended simulation times (Figure b), progressive homogenization was observed as simulation time increased. After approximately 300 s, the density field exhibited high spatial uniformity, and only minor spatial variations remained, indicating that the density distribution approached a stable state under continuous peristaltic deformation.

7.

Temporal evolution of the mixture density distribution during the peristaltic mixing process. (a) Changes within one cycle (t = 0.5, 1, 1.5, and 2 s). (b) Changes at extended simulation times (t = 2, 50, 100, 200, and 300 s).

Collectively, these simulations reveal that the periodic low-shear peristaltic action generates complex bidirectional flows and vortices that effectively promote particle redistribution and phase intermixing in high-solid-loading slurries.

3.2. Macroscopic Morphology of the Mixed Slurries

The macroscopic appearance of the mixed slurries provided a direct visual assessment of mixing uniformity. Representative photographs of the slurries obtained under different operating conditions are shown in Figure .

8.

Macroscopic morphology of the NaCl/Al/HTPB simulant slurries after 1 h of peristaltic mixing. (a) Effect of extrusion duration (1, 2, and 3 s) at 0.6 MPa with 4 segments and 5 mm spacing. (b) Effect of air pressure (0.4, 0.5, and 0.6 MPa) at 3 s extrusion with 4 segments and 5 mm spacing. (c) Effect of number of peristaltic segments (2, 3, and 4) at 3 s extrusion, 0.6 MPa, and 5 mm spacing. (d) Effect of intersegment distance (5, 15, and 25 mm) at 3 s extrusion, 0.6 MPa, and 4 segments.

Under short extrusion durations (1 s, Figure a), distinct boundaries between white NaCl-rich regions and gray-black Al-rich regions were evident, with large areas of dry, unmixed powder remaining at the tube ends. Increasing the extrusion duration to 2 s resulted in a noticeably wetter paste-like consistency and blurred phase boundaries, although minor white patches persisted. At the optimal duration of 3 s, the slurry exhibited a uniform gray-black appearance with minimal residual white regions, indicating significantly improved material exchange and dispersion.

Variation in air pressure produced similar trends (Figure b). At 0.4 MPa, the slurry remained largely dry and blocky, with prominent white spots distributed throughout the sample. Raising the pressure to 0.5 MPa led to increased moisture content and partial blurring of color boundaries. At 0.6 MPa, the product displayed a homogeneous moist paste with excellent overall uniformity.

The number of active peristaltic segments also exerted a pronounced influence (Figure c). With only 2 segments, clear phase segregation was observed, with distinct gray-black compressed zones separated by white, uncompressed regions. Increasing to 3 segments introduced noticeable folding and cracks, reflecting enhanced but still incomplete material exchange. The configuration with 4 segments yielded the most uniform and softened paste-like product, confirming that sufficient segment coverage is essential for effective mixing.

Finally, intersegment spacing played a critical role (Figure d). At the smallest spacing of 5 mm, superior mixing was achieved. Larger spacings (15 mm and 25 mm) resulted in progressively poorer uniformity, with sharp color contrasts and blocky, powdery regions appearing between segments, indicating insufficient material exchange in the uncompressed zones.

Overall, the macroscopic observations demonstrate that an extrusion duration of 3 s, air pressure of 0.6 MPa, 4 peristaltic segments, and 5 mm intersegment spacing collectively produce the most homogeneous slurry morphology.

3.3. Density Uniformity and Mixing Efficiency

To quantitatively evaluate mixing uniformity, the slurry in each silicone tube was divided into five equal sections along the axial direction after mixing. Three replicate samples were collected from each section, and the density at each axial sampling position was expressed as the mean ± standard deviation (n = 3). The error bars in Figures – represent the standard deviation of the three replicate density measurements at each sampling position. The axial density standard deviation was subsequently calculated from the mean densities of the five sections and used as the primary indicator of spatial mixing uniformity. A lower axial density standard deviation indicates a more uniform density distribution along the tube. Because the density analyzer had a resolution of 0.001 g·cm^–3, all experimental density values and axial density standard deviations are reported to three decimal places.

11.

Effect of the number of peristaltic segments on slurry density uniformity at an extrusion duration of 3 s, an air pressure of 0.6 MPa, and an intersegment spacing of 5 mm.

The effects of the four operating parameters on density uniformity are shown in Figures –. Increasing the extrusion duration from 1 to 3 s reduced the axial density standard deviation from 0.038 to 0.016 g·cm^–3, corresponding to an approximately 57% improvement in spatial uniformity. This decrease indicates that a longer extrusion duration promoted material exchange and homogenization within the tube (Figure ). Similarly, increasing the air pressure from 0.4 to 0.6 MPa reduced the axial density standard deviation from 0.024 to 0.016 g·cm^–3, corresponding to an approximately 31% improvement. The higher pressure provided a greater driving force for binder flow and particle redistribution.

10.

Effect of air pressure on slurry density uniformity at an extrusion duration of 3 s, with four peristaltic segments and an intersegment spacing of 5 mm.

13.

SEM images of the mixed NaCl/Al/HTPB simulant slurries. (a-c) Group 1 (optimized conditions) at 200×, 500×, and 1000× magnification, respectively. (d-f) Group 7 (2 peristaltic segments) at 200×, 500×, and 1000× magnification, respectively.

The number of active peristaltic segments had the strongest influence among the parameters examined. With two segments, the axial density standard deviation was 0.039 g·cm^–3, indicating pronounced spatial segregation. Increasing the number of segments to four reduced the axial density standard deviation to 0.016 g·cm^–3, corresponding to an approximately 58% improvement in spatial uniformity. This result confirms that greater segment coverage is required to generate sufficiently uniform compression and material flow throughout the tube.

Inter-segment spacing also had a marked effect on density uniformity. The smallest spacing of 5 mm produced the lowest axial density standard deviation of 0.016 g·cm^–3. Increasing the spacing to 15 or 25 mm resulted in progressively greater spatial density variations, with the axial density standard deviation reaching 0.023 g cm^–3 at the largest spacing. This increase of approximately 29%, calculated using the unrounded experimental data, was attributed to insufficient material exchange within the regions between adjacent compression segments.

Under the optimized conditions of a 3 s extrusion duration, an air pressure of 0.6 MPa, four peristaltic segments, and an intersegment spacing of 5 mm, the mean density across the five axial sections was 1.513 g·cm^–3, and the axial density standard deviation was 0.016 g·cm^–3. These results indicate that the optimized peristaltic conditions produced the most uniform axial density distribution among the conditions examined. The density results are also consistent with the macroscopic morphology observations, which showed reduced phase segregation under the optimized operating conditions.

3.4. Microscopic Morphology

To further confirm the quality of mixing at the particle level, representative samples from the optimized condition (Group 1:3 s extrusion, 0.6 MPa, 4 segments, 5 mm spacing) and the poorest-performing condition (Group 7:3 s extrusion, 0.6 MPa, 2 segments, 5 mm spacing) were examined by scanning electron microscopy (SEM).

In the optimized slurry Figure a–c, large NaCl particles retained their original morphology without visible fracture or deformation. Fine NaCl and Al particles were uniformly dispersed across the surfaces of the larger grains, and a continuous layer of HTPB/DOS binder matrix was observed to coat both large and small particles evenly. At higher magnification Figure c, the binder film appeared smooth and well-adhered, indicating effective particle-binder interaction and excellent grading.

In contrast, the slurry prepared with only 2 peristaltic segments Figure d–f, exhibited less uniform dispersion. Although large particles remained largely intact, regions with sparse fine-particle coverage and incomplete binder coating were evident. Some areas showed localized agglomeration of fine particles and exposed uncoated surfaces, consistent with the macroscopic segregation and higher density standard deviation observed for this condition.

The observed microstructure is also consistent with the role of the graded powder system. Under the optimized mixing condition, the fine NaCl and Al particles were distributed around and over the surfaces of the coarse NaCl particles, while the HTPB/DOS binder formed a comparatively continuous coating over both particle fractions. This arrangement indicates effective redistribution and wetting of the fine particles without visible fracture of the coarse particles. In contrast, incomplete binder coating and localized fine-particle agglomeration were observed under the less effective mixing condition. These observations demonstrate that the peristaltic operating parameters affect the spatial distribution and coating state of the graded particles. However, the SEM observations are qualitative and do not constitute direct measurements of powder specific surface area or binder adsorption.

These microscopic observations demonstrate that the optimized bionic peristaltic parameters not only achieve macroscopic and density uniformity but also produce a high-quality microstructure characterized by uniform particle dispersion, effective binder coating, and preserved particle integrity. Such features are critical for the performance of high-solid-loading energetic slurries.

3.5. Comparison of Simulation and Experimental Results

To assess the consistency between the numerical and experimental results, the axial density standard deviation obtained from the simulation at 300 s was compared with the corresponding experimental value measured under the optimized operating conditions of a 3 s extrusion duration, an air pressure of 0.6 MPa, four peristaltic segments, and an intersegment spacing of 5 mm. The simulation produced an axial density standard deviation of 0.017 g·cm^–3, whereas the corresponding experimental value was 0.016 g·cm^–3. The relative difference was approximately 5%, as calculated using the unrounded values. This numerical agreement indicates that the simplified model captures the overall trend in spatial mixing uniformity for the specified formulation and operating conditions.

The simulation further showed that the solid-phase volume fraction became increasingly uniform during repeated peristaltic cycles and approached a stable distribution after approximately 300 s. This trend is consistent with the comparatively uniform gray-black macroscopic morphology observed under the optimized conditions (Figure a) and the uniform particle dispersion and binder coating observed in the SEM images (Figure a–c). The remaining difference between the simulated and experimental results may be attributed to the two-dimensional representation of the actual three-dimensional mixing system, the simplified treatment of the solid and liquid phases, and unavoidable experimental variations, including minor fluctuations in the applied air pressure.

Overall, the numerical results reproduce the principal trend in mixing uniformity observed experimentally for the specified formulation. Nevertheless, this agreement should be interpreted as validation of the predicted macroscopic mixing trend rather than as a complete validation of the particle-scale rheological behavior of the slurry. The model does not explicitly resolve the particle-size distribution, powder specific surface area, binder adsorption, or size-dependent particle migration. Quantitative application of the model to formulations containing different powder grades or particle-size distributions would therefore require additional rheological characterization and a more detailed particle-resolved description.

To further examine whether increasing the extrusion duration beyond 3 s could improve mixing performance, additional simulations and experiments were conducted at extrusion durations of 3.5 and 4 s. Increasing the extrusion duration from 3 to 3.5 s resulted in only a marginal increase in the solid-phase volume-fraction uniformity index, from 0.92 to 0.93, while the energy consumption increased by approximately 12%. When the extrusion duration was further increased to 4 s, the uniformity index remained nearly unchanged at 0.93, whereas the energy consumption increased by approximately 25% relative to that at 3 s. These results indicate that extending the extrusion duration beyond 3 s provides no substantial improvement in mixing uniformity but results in a considerable increase in energy consumption.

4. Conclusions

This study develops a bionic peristaltic mixing process for enhanced powder dispersion in energetic high-solid-loading slurries (80 wt % solids). By integrating ANSYS Fluent simulations with systematic experiments on a NaCl/Al/HTPB simulant, the work demonstrates an effective low-shear, paddle-less approach that mimics intestinal peristalsis. The custom pneumatic extrusion device enables homogeneous mixing of ternary powder-liquid systems through sequential tube compression, achieving uniform dispersion without high shear or particle damage. Simulations reveal that alternating 2 s peristaltic cycles generate bidirectional flows and vortices, resulting in progressive homogenization and near-uniform density distribution within 300 s. Under the identified conditions of a 3 s extrusion duration, an air pressure of 0.6 MPa, four peristaltic segments, and an intersegment spacing of 5 mm, the simulant slurry exhibited a mean density of 1.513 g·cm^–3 across the five axial sections and an axial density standard deviation of 0.016 g·cm^–3, corresponding to an approximately 58% improvement in spatial uniformity relative to the baseline condition. SEM observations further showed comparatively uniform particle dispersion and binder coating under the optimized conditions.

These results validate the reliability and efficiency of the bionic peristaltic strategy for high-solid-loading energetic slurries. The method offers a scalable, energy-efficient alternative to conventional high-shear mixing techniques and holds broad potential for other powder-based composites in pharmaceuticals, ceramics, and advanced materials. Future work will focus on three-dimensional CFD-DEM simulations and validation with real AP-based formulations to facilitate industrial implementation.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.6c05935.

• Characterization methods; detailed numerical simulation methodology; peristaltic mixing model; governing equations and wall-motion functions; initial conditions and simulation settings; Supplementary Figures S1–S2; and key parameters of the peristaltic mixing model (Table S1) (PDF)

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T.Z., N.H., S.N., and J.Z. contributed equally to this work.

Details of sample morphology and density characterization; details of bionic peristaltic mixing model, governing equations and wall motion functions; and numerical simulation setup, mesh division, and key model parameters.

The authors declare no competing financial interest.