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. 2020 Jun 22;12(30):34254–34264. doi: 10.1021/acsami.0c03572

Probing Ink–Powder Interactions during 3D Binder Jet Printing Using Time-Resolved X-ray Imaging

Srimanta Barui †,‡, Hui Ding †, Zixin Wang †, Hu Zhao †, Shashidhara Marathe §, Wajira Mirihanage †, Bikramjit Basu ‡, Brian Derby †,*
PMCID: PMC7467558  PMID: 32567300

Abstract

graphic file with name am0c03572_0008.jpg

Capillary-driven ink infiltration through a porous powder bed in three-dimensional (3D) binder jet printing (inkjet printing onto a powder bed) controls the printing resolution and as-printed “green” strength of the resulting object. However, a full understanding of the factors controlling the kinetics of the infiltration remains incomplete. Here, high-resolution in situ synchrotron radiography provides time-resolved imaging of the penetration of an aqueous solution of eythylene glycol through a porous alumina powder bed, used as a model system. A static drop-on-demand inkjet printer was used to dispense liquid droplets onto a powder surface. The subsequent migration of the liquid front and its interactions with powder particles were tracked using fast synchrotron X-radiography in the Diamond Synchrotron, with phase-contrast imaging at a frame rate of 500 Hz. Image processing and analysis reveal that both the time-dependent increment in the wetting area and the propagation of the “interface leading edge” exhibit heterogeneous behavior in both temporal and spatial domains. However, mean infiltration kinetics are shown to be consistent with existing infiltration models based on the Washburn equation modified to account for the spreading of the liquid drop on the powder surface and using a modified term for the bed porosity.

Keywords: inkjet printing, ink−powder interaction, capillary infiltration, Washburn model, X-radiography, synchrotron in situ imaging

Introduction

In the last 2 decades, the field of additive manufacturing has witnessed rapid advancement in various sectors, encompassing prototype modeling, for structural, aerospace, defense, and healthcare applications.1−6 Layer-by-layer manufacturing of individual sections or slices, derived from a three-dimensional (3D) computer-aided design (CAD) model of the object to be fabricated, is a generic feature for all of the current variants of additive manufacturing.7−9 One such method, 3D binder jet printing, uses inkjet printing to selectively deposit drops of an adhesive or binder ink onto a leveled powder bed. Where the ink is present, it infiltrates into a thin layer (100–300 μm) of freshly deposited powder bed, selectively binding the powder according to slices derived from the 3D CAD model. The sequence is repeated with a fresh layer of powder followed by another deposition of the binder ink, selectively adhering adjacent layers until the desired 3D object is built. Since its original realization by Sachs et al.,10 it has been used successfully to print engineering alloys,11,12 biomaterials,6,13−15 transparent polymers,16 and ceramics.17

To ensure adequate binding between adjacent droplets and to define the spatial resolution attainable by this method, it is necessary to understand and predict the kinetics of the penetration of the liquid through the powder. Multiphase flow in porous media is a significant research area in hydrology, oil recovery, and geosciences, where a number of in situ and ex situ experimental investigations have studied the flow patterns and liquid interface evolution through solid porous media.18−20 However, compared to 3D binder jet printing, similar length scales of droplets and powder particles may lead to different underlying mechanisms from prior studies in geosciences and hydrology.

The manufacturing tolerance, minimum feature size, and as-printed strength (green strength) of the object predominantly rely on the nature of the ink–powder interaction in terms of wettability, infiltration time, and spreading of the ink on the powder bed surface. The relative importance of these parameters has been the subject of prior study for both powder bed additive manufacturing and controlled manufacture of granules from powders.16,21,22 Much of the previous work has focused on the problem of understanding how a single drop, sufficiently small that its shape is controlled by capillarity, drains into a powder bed of depth considerably larger than the drop radius. Marmur first recognized that the problem has two limiting cases that depend on the behavior of the drop once it has spread to equilibrium on the surface of the powder bed:23 (1) The contact line at the drop’s limit remains pinned to the surface when the liquid is drawn into the powder bed by capillary infiltration. This leads to a dynamic decrease in the contact angle as the infiltration proceeds. The area of the liquid/material contact remains constant, and this is defined as the condition of constant drawing area (CDA). (2) The contact line is not pinned during draining; it thus retracts as the drop volume decreases, maintaining a constant contact angle but decreasing the drop base area as liquid is drawn into the powder bed. This is the condition of decreasing drawing area (DDA). Denesuk et al. modeled both these cases of drop drainage, using a simplified model of the powder bed represented by a bunch of parallel capillaries of constant radius and applying the Washburn equation to balance capillarity and viscous forces.24,25 This approach gives the following expression for volume as a function of time, V(t), that has drained from a drop resting on the surface

graphic file with name am0c03572_m001.jpg 1

where b(t) is the base diameter of the spherical cap of the liquid at a given time and κ is a combination of material constants given by

graphic file with name am0c03572_m002.jpg 2

where ap is the pore area surface fraction, γLV is the surface tension of the liquid–vapor interface, θ is the liquid/capillary wall contact angle, R is the radius of one capillary, and η is the dynamic viscosity of the liquid. When this method is used to model liquid infiltration into a powder bed, the pore volume surface fraction is replaced by the porosity, p (pore volume fraction), and R is now an “effective radius” representing the porous network between the powder particles. The model compared favorably with experimental data; however, it was only tested by Denesuk against infiltration into parallel capillary channels.25

Whether Denesuk’s model is appropriate for modeling the penetration of liquids into powder beds, given its approximation of cylindrical pores, has been questioned. Popovich studied the infiltration of six fluids into powder beds made from carbon black and determined that approaches based on the Washburn equation could not fully explain fluid drainage from single drops and hypothesized that particle rearrangement during infiltration may explain the poor fit to experimental data.21 Hapgood et al. proposed a model of an inhomogeneous powder bed and suggested that the presence of larger macrovoids would inhibit capillary flow.26 To account for this, they proposed a modification of Denesuk’s model using an effective porosity that did not include larger voids, which do not take part in the infiltration process, and this provided a better fit with experimental data. Holman et al.27 modified Denesuk’s approach for the case, when drop spreading has a similar time scale to drop infiltration and found a good fit with data for the interaction of small drops (≈100 pL), as did Wang et al.16 An approach based on the Washburn equation was also used in a previous study by some of the authors to model liquid infiltration during thermal inkjet printing on metallic powder beds.28

There are parallels between the effective porosity arguments reviewed in the previous section and observations in the powder bed additive manufacturing literature concerning the saturation level of powder compacts after printing onto powder beds. Miyanaji et al. developed a model for the infiltration of a powder bed considering the displacement of air by the infiltrating fluid.29 This two-phase model showed the possibility of flow instability and bifurcation within a pore distribution providing a mechanism for the large pore bypass model of Popovich and Hapgood.21,26 The importance of partial infiltration and <100% saturation of a powder compact during additive manufacturing is recognized in prior work and can be controlled by a drying step between the printing of adjacent layers.30

In all of these prior studies, the infiltration dynamics is assumed to follow a direct relationship with the rate of liquid depletion from the surface to allow comparison with experiments tracking the liquid drop evolution with time. However, such analyses did not account for loss caused by evaporation, and thus validation of models is uncertain. Many of the above studies are limited in predicting time scales for infiltration of droplets into a finite thickness of powder bed because of the need to use large drops to allow optical tracking of drop volume change with time. The studies of Denesuk, Popovich, and Charles-Williams all used spherical droplets of diameter approximately 2 mm,21,22,25 while that of Hapgood used larger drops of diameter 6 mm.26 These are considerably larger than the drop sizes typically found with inkjet printing, where the droplet diameters are normally in the range of 10–80 μm (similar to the printhead nozzle diameter), and this case was studied by Holman et al. and Wang et al.16,27 However, the small size of droplets in inkjet printing makes dynamic studies of drop infiltration more difficult. Hence, there have been only a few studies comparing the relative time scales for drop spreading and infiltration with inkjet delivered drops. Charles-Williams and Holman both reported that drop spreading on powder beds can be described using Tanner’s law and is of a time scale comparable to droplet infiltration.31 However, Wang16 came to the opposite conclusion as did Dou et al.32 Tan et al. presented a computational fluid dynamics study of the interaction of a 20 pL drop with a powder bed where the powder size was comparable to the drop size. This study predicted that the drop was absorbed into the powder bed at a time scale of <50 μs.33 However, this time scale is substantially shorter than the experimental observations reviewed here.16,22,27,32

In all of the above-mentioned prior experimental studies, dynamic processes were monitored by observing changes to the draining drop. However, none of the above studies could capture the real-time powder–liquid interactions that take place below the surface during infiltration. Parab et al.34 used synchrotron X-ray imaging to investigate the binder–powder interaction, revealing the effect of powder particle size on the stability of the powder bed after droplet impact. They reported defect formation due to ejection of particles at the impact site, in the case of coarser and spherical particles. However, their study did not analyze the spatio-temporal evolution of ink–powder interaction in the subsurface region.

Fast X-ray imaging has been used to dynamically monitor subsurface phenomena and solid–liquid interactions in real time with other manufacturing techniques.35−37 In the present study, our objective is to characterize the binder/ink infiltration mechanism during droplet deposition onto a powder bed in situ using synchrotron high-intensity X-ray imaging to provide a time-resolved measure of the infiltration of liquid drops into a finite thickness of powder bed. The results, obtained from the experiments, are compared to a model based on Washburn’s capillary infiltration approach. Experimental constraints limit us to studying liquid volumes that are larger than the individual drops typically used with inkjet printing; however, the capillary-dominated infiltration mechanisms are believed to be the same.

Materials and Methods

Ink Preparation, Assessment of Physical Parameters and Powder Bed Preparation

A model ink was prepared by mixing 75 mL of ethylene glycol (EG) and 25 mL of deionized water (DI) to best mimic the physical properties of a typical printable fluid. The viscosity of the ink was measured using a cone-plate viscometer (DHR3, TA Instruments, New Castle, DE) in flow sweep mode. A contact angle goniometer (OCA 15EC, DataPhysics, Filderstadt, Germany) was deployed to measure the surface tension of the ink in pendant drop mode. All of the experiments were carried out at 25 °C under standard laboratory conditions.

A set of rectangular cuvettes was designed using 3D modeling software, each having an internal cavity of 2 mm (W) × 5 mm (D) × 10 mm (H) with a uniform wall thickness of 1 mm. The 3D models of the polymeric cuvettes were 3D-printed using a Polyjet 3D printer (Stratasys, Eden Prairie, MN). Alumina powders with a mean diameter of ∼15 μm (ANTS Ceramics, Mumbai, India) were loaded in the polymer cuvettes without any pressure to mimic the powder bed deposited during 3D inkjet powder printing.

Powder Bed Porosity and Powder Morphology

Helium gas pycnometry (ULTRAPYC 1200e, Quantachrome Instruments, Boynton Beach, FL) was used to measure the powder bed porosity and specific volume (m3 g–1). For full experimental details, see the Supporting Information. The BET (Autosorb iQ, Quantachrome Instruments, Boynton Beach, FL) methodology was used to measure the specific surface area (m2 g–1) of the powder to calculate the Sauter mean diameter. The volume and surface area of a finite amount of powder was used to calculate the Sauter mean diameter (D32) using the following formula

graphic file with name am0c03572_m003.jpg 3

where Vp and Ap are the specific volume and specific surface area of the powder, which were measured using He gas pycnometry and a BET surface area analyzer, respectively. Particle size distribution was studied under a scanning electron microscope (JCM-6000 Plus, JEOL, Tokyo, Japan) to investigate the topography of the particles before infiltration.

Washburn Capillary Rise: Contact Angle Measurement of Ink with Particles

The contact angle of a liquid on a substrate is a key metric for wettability, which is a preliminary requirement for good ink–powder interaction. A capillary rise method was used to measure the contact angle between the infiltrating liquid and the powder bed. This is believed to be more representative of the solid–liquid interaction within a powder bed than that between a sessile drop and a planar surface of the nominal composition of the powder bed. The method used was as reported elsewhere:38,39 a two-liquid technique is adapted where a liquid, which completely wets the powder (contact angle = 0°), is allowed to infiltrate through a reproducible powder bed as a reference, followed by a second experiment with the ink (in this case, the EG–DI solution). Full experimental details are given in the Supporting Information.

In Situ Synchrotron Imaging

A stationary single-jet piezoelectric inkjet drop generator was installed on the I13-2 beamline (Diamond Light Source, Harwell, U.K.). An ink syringe with controlled pressure was fixed vertically on the beamline sample stage to supply fluid to a piezoelectrically actuated inkjet printhead with an internal orifice diameter of 60 μm (MJ-AT-01-60-8MX, MicroFab Technologies, Inc., Plano, TX) using a simple holder. The printhead was controlled by a driver board (JetDrive III, MicroFab) interfaced to a PC and controlled in a LabVIEW (National Instruments, Austin, TX) environment. The printing waveform was a single unipolar pulsed waveform. The rise time, fall time, and echo time are all 3 μs. The dwell time is 30 μs, and the dwell voltage is 90 V. The echo voltage and idle voltage are both 0 V. The polymer cuvette containing the alumina powder bed was placed below the printhead (printhead-to-powder surface distance, ca. 2–3 mm, to mimic the typical arrangement used in 3D inkjet powder bed printing).

The experimental setup is schematically depicted in Figure 1. It was not possible to directly measure the drop volumes generated by the printing setup directly, but prior work has determined that inks with similar rheological properties form droplets with volume in the range of 100–120 pL under the driving waveform used in this study.40 The drop velocity is expected to be in the range of 2–3 ms–1. These characteristics of the droplet are within the range of commercial piezoelectric actuated drop generators and are similar to those used by Holman et al. and Barui et al.27,28 Unfortunately, the resolution of the imaging system does not allow the dynamic tracking of the penetration of a single drop into the powder bed. Instead, a sequence of droplets were generated at 3000 Hz and up to 5000 droplets were printed in an experiment. In all cases, drops were printed continuously during the imaging experiments. We recognize that this does not provide an accurate simulation of a single drop/powder bed interaction, but we believe that the unique nature of our experiments will provide valuable information to better understand the liquid–powder interaction during 3D binder jet printing.

Figure 1.

Figure 1

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Experimental setup to study infiltration dynamics during inkjet powder printing, in situ, under synchrotron X-ray beamline.

A pink X-ray beam was used, which has a broad energy spectrum of 10–35 keV and a weighted mean spectral energy of around 24 keV. Although water-based ink was relatively transparent to X-rays, predetermined near-field imaging offered appreciable refraction-based first-order phase contrast at the liquid–air interface, providing the details of the liquid front propagation through the powder bed. X-rays pass through the sample, and the transmitted beam interacts with the scintillator. A 300 μm LuAG:Ce scintillator was used to convert X-rays into visible light, and a Pco-Dimax CMOS detector system was positioned such that the camera is focused on to the scintillator. This arrangement provides a field of view of 2.2 × 2.2 mm2. Image sequences were captured at a 500 Hz frame rate, with a 1 ms exposure time, without detectible dynamic blurring. Before each infiltration experiment, the sample was rotated over 180°, and 2001 projections were recorded to render 3D micro-computed tomography (m-CT) of the powder loaded cuvette to probe the preinfiltration powder bed characteristics.

Data Analyses

The set of the raw projection image data were imported in Avizo Fire 9 (Thermo Fisher Scientific, Waltham, MA) to analyze the particle size distribution, pore volume fraction, and pore interconnectivity. A median filter was applied to minimize the noise in the data. Interactive thresholding was carried out to binarize the image followed by applying “separate object” module to discretize the adjacent particle boundaries by incorporating fine watershed lines in the distance map. By selecting the range in the obtained bimodal histogram, the particular material/pore phases were taken into consideration to calculate the particle size distribution.

The stacks of two-dimensional (2D) projection image sequences during infiltration were imported into ImageJ (NIH, Bethesda, MA). The sequence of the background images is also imported and averaged out in a single image. The infiltration image sequence is divided by the averaged background image to obtain a new sequence of images with background correction. The image sequence is cropped both in “time” (selected frames) and “space” (region of infiltration in the frame), where the infiltration phenomena are distinguishable. To capture the time-dependent incremental changes in the powder bed owing to infiltration, the new image sequence was divided by the first image of the same sequence (Figure 2a).

Figure 2.

Figure 2

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Schematic of the image analysis algorithm. (a) Time-resolved evolvement of the wetting contours during printing. (b) Segmented image stacks to detect the outline of the wetting contours. (c) Binarized outlines of the wetting contour stacks; the vertical arrows show the leading edge propagation of the wetting contour with time. (d) Superimposed frames of the time-dependent wetting contours in an experimental session to calculate the time-dependent evolution of the wetting area.

After this, to improve the visualization of the propagating liquid/air interface, the wetted phases of the image sequence are binarized, masked, smoothened, and the dynamic interface is highlighted using the edge detection tool (Figure 2b). Further image processing was carried out to enhance the visualization of the vertical and lateral dynamics of the wetting front, with inverted contrast with the background powder bed (see Supporting Information Movie S1). To calculate the vertical infiltration rate, the wetting contours were superimposed in a “time stack” to obtain a single image with all of the frames of interface contours. The rate of vertical infiltration with time was obtained from the linear distance (indicated by the arrows in Figure 2c).

Results and Discussion

Ink and Powder Bed Properties

An EG–DI mixture (3:1 vol/vol) was used as a simulated ink in all subsequent experiments. The ink exhibits Newtonian flow behavior under shear stress an ink experiences during ejection through an inkjet nozzle.1,41,42 The physical properties of the ink were measured and are summarized in Table 1. Based on these values, the dimensionless Ohnesorge number (Oh) and Z, its inverse, were evaluated to be 0.12 and 8.33, respectively. These values were found to be in the range considered suitable for inkjet printing.1,3

Table 1. Physical Properties of the EG–DI Ink Used in This Study and the Computed Values of the Dimensionless Numbers Oh and Z Used to Predict the Printability of Inksa.

density (kg m–3) dynamic viscosity (mPa·s) surface tension (mN m–1) Oh Z
1080 7 52 0.12 8.33
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a

All properties were measured at room temperature (20 °C) under ambient laboratory conditions.

The particles that form the powder bed were characterized by X-ray computed tomography imaging prior to infiltration experiments. The Sauter mean diameter analysis also confirms the same particle diameter range, which can be directly used to calculate the effective capillary radius of the powder bed. These data are presented in Figure 3. The specific volume and specific surface area were measured to be 2.48 × 10–7 m3 g–1 and 10 m2 g–1, respectively. The Sauter mean diameter was calculated from eq 3 to be ∼15 μm with good reproducibility, which was almost same as derived from the image analysis from the micro-CT data.

Figure 3.

Figure 3

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Micro-computed tomography (m-CT) and scanning electron microscopy (SEM) were used to characterize the particles and as-loaded powder bed prior to the infiltration experiment. (a) Volume rendered and 3D labeled particles with soft agglomeration; (b) particle size distributions obtained from m-CT; and (c) SEM image showing the agglomerated nature of the individual particles.

The alumina powder bed porosity was determined to be ∼70% using He gas pycnometry before infiltration experiments. In this method, the presence of soft agglomerates, which are present in all kinds of powdered materials, will not influence the measurement because He can easily penetrate through them and the porosity measured is independent of individual powder size. The soft particle aggregates will break down as spreading under a roller occurs during powder surface preparation prior to 3D binder jet printing.

The critical dimension for fluid infiltration into a particle bed is the mean capillary pore radius. This is related to the mean particle diameter, particle arrangement, and the packing density/porosity within the powder bed.25,27,28,38,43 This can be estimated using the following relationship

graphic file with name am0c03572_m004.jpg 4

where D32 is the mean Sauter diameter and p is the powder bed porosity fraction. Using the experimentally measured Sauter mean diameter and porosity fraction (Table 2) in eq 4, the effective capillary radius is ∼11. 7 μm.

Table 2. Physical Properties of the Powder Bed Used in This Study and the Computed Values of Denesuk’s Infiltration Parameter κ.

porosity particle diameter (μm) contact angle effective radius (μm) κ (m s–1/2)
0.70 15.0 70° 11.67 9.6 × 10–3
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The dynamic contact angle of the EG–DI (3:1) ink measured using capillary rise (≈70°) is considerably higher than the value measured on a flat monolithic specimen using the sessile drop method (≈40°). This discrepancy is likely caused by inhomogeneity of the powder bed and the assumptions in the approach using the Washburn equation. Nonetheless, we will use the capillary rise value for subsequent calculations because it is believed to better capture the liquid/solid interfacial interaction within a powder bed.

X-ray Images of Droplet Infiltration

The data produced by the synchrotron experiments are in the form of 2D projections showing the presence of the fluid–air interface within the powder bed, imaged as a series of wetting areas recorded at 2 ms intervals. It was not possible to obtain sufficient quality image data from images of a single 100 pL drop on the powder bed. Thus, images were obtained by printing a stream of droplets at a single location on the powder bed. The objective of this study is to track the interface between the propagating liquid front and the surrounding dry powder particles, and the nature of the interaction is expected to be the same as that between a single drop and the powder, as long as the binder physical properties and the powder bed properties remain constant. A minimum of 500 drops were required to obtain high-quality images of the liquid penetration front. Figure 4 shows sequences of the projected area of the wetting front displayed at 0.1 s intervals. For the representative appearance of all of the evolved contours, time stacked in one frame (see Supporting Information Figure S1). All projections imaged show a similar morphology and evolution with time, with the following features. The projection of the liquid–air interface is irregular and only approximates to the expected ellipsoidal shape. The evolution of the wetted area was not uniform, and the liquid penetration rate varied considerably with location and time.

Figure 4.

Figure 4

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Time-dependent representations of vertical ink–particle interface propagation and the increment in wetting area. (a, b) Representative plots of the interface propagation rate and the corresponding evolved wetting contours represented with the color-coded time scale (0.1 s resolution). (c, d) Rate of increment in the wetting area spatially projected in 2D with time.

A more detailed plot of infiltration at 100 ms intervals shows that the maximum penetration depth (Figure 4a,b) and the projected area (Figure 4c,d) follow a staccato behavior with a relatively slow rate of change interspersed with rapid jumps in infiltration. This behavior is believed to be analogous to “Haines Jumps”, which are instabilities of the fluid–air interface accompanied by a transient pressure response associated with the distribution and penetration of liquids through porous media, first observed and reported with the penetration of water through soils by Haines44 and recently reviewed by Sun and Santamarina.45

Although there are considerable local (both temporal and spatial) variations in the rate of liquid penetration as a drop drains into a powder bed, the behavior of individual drops is seen to converge over the time taken for a complete drop to drain. Figure 5 shows quantitative data extracted from the synchrotron projections of the infiltrated region within the powder bed at 0.1 s intervals after the arrival of the first printed drop. Figure 5a shows the spreading of the liquid on the surface of the powder bed; note that the liquid is arriving as a train of droplets at 3000 Hz. Figure 5d shows the computed volume infiltrated into the powder bed assuming that this can be modeled as a radially symmetrical ellipsoid (Figure 6). The infiltrated “wetting volume”, V, is thus

graphic file with name am0c03572_m005.jpg 5

where A and d are the projected wetting area and penetration depth, respectively.

Figure 5.

Figure 5

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Capillary infiltration post-impact (time from the initial first drop contact) from three imaging experiments. (a) Lateral spread of the droplet on the surface of the powder bed. (b) Maximum penetration depth of the fluid into the powder bed. (c) Projected area of the wetted region of the powder bed. (d) Estimated wetting volume in the powder bed approximated to an equivalent ellipsoid.

Figure 6.

Figure 6

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Infiltration and surface spreading of ink liquid under capillary pressure; in the case of highly interconnected porous powder bed, the two rates can be considered equivalent, where rs and rv are the rates of surface spreading and volume penetration depth, respectively. Powder bed surface, where the droplet impacted (red), is represented by the rectangular plane.

Ink–Powder Interaction Behavior

A porous powder bed can be modeled as a bundle of infinite numbers of capillaries having diameters being limited by the particle size and nature of packing.25,27,28 The infiltration rate is predominantly governed by the wettability or dynamic contact angle of the ink with the powder particles. The primary driving parameter in capillary infiltration is the “capillary pressure”, which is usually very strong (in kPa) in the micron-sized capillary diameter range. Denesuk’s model (eq 1) can be integrated to predict the time, τ, taken for a single drop to drain into a powder bed

graphic file with name am0c03572_m006.jpg 6

where b is the diameter of the liquid drop on the powder bed (assumed constant). Hence, the form of eq 6 predicts the liquid volume infiltrated to be proportional to τ1/2. However, the data in Figure 5d present an approximately linear relation between infiltration volume and time.

There are many reasons why there may be a poor fit between Denesuk’s model and our experimental results. First of all, the Washburn model is one dimensional (1D), i.e., it considers a bundle of parallel capillaries. In reality, the pores are highly interconnected (∼99% interconnectivity) in 3D, making the process more complex and slower than predicted, predominantly due to the unpredictable distribution of the fluid supply in all possible directions. Reports on powder infiltration, e.g., Hapgood et al., have proposed that the presence of larger pores (macropores) effectively resists fluid movement through local increases in pore radius, when Kozeny’s approach is used, as the “liquid stops at the opening of the larger void space”.26 This may be appropriate in our case because the powders were loaded into the cuvettes prior to infiltration without an external applied pressure; thus, soft agglomerates in the powder may lead to locally large pores. The discontinuities (vertical dotted lines) in the growth of the wetting area and interface penetration may be a result of pores or soft agglomerates acting as local barriers that must be overcome or bypassed (Figure 4a–d). This phenomenon can also be seen in the real-time infiltration video provided in the Supporting Information (Movie S1). These movements are believed to be associated with particle motion as the infiltration front passes through the powder bed. Unfortunately, there was not sufficient spatial or temporal resolution to track the movement of individual particles during the experiments, so it was not possible to determine whether any compaction/densification occurred during infiltration. However, detailed differences between the pore shape and structure within a powder bed and the idealized constant diameter capillary used in the Washburn model for capillary infiltration26 and its adaptation to the modeling of capillary rise and infiltration38,39,43 have normally been accommodated through the use of semiempirical constants, such as the capillary bed constant, that are based on the physics of infiltration but with the addition of geometrical or morphological constants to allow accurate modeling of experiment. Such modifications to Denesuk’s model would alter the constant, κ, but would not be expected to alter the τ1/2 power law dependence. Denesuk considered the case when the drop on the surface does not have constant radius but retracts at a constant contact angle. However, this did not affect the τ1/2 power law dependence.

An important distinction between our experiment and Denesuk’s model is the initial liquid volume on the surface of the powder bed. Denesuk assumes that infiltration starts at time t = 0 in the presence of a spherical liquid cap already formed on the powder surface. Holman observed that in the case of inkjet printing the drop spreads dynamically across the surface after impact and that Denesuk’s model needs to be modified to account for this. In our case, the fluid drop is built up over a finite time through the addition of individual drops. Hence, the contact diameter of the drop, b, is a function of time or b(t). By considering the data for the spreading of the liquid on the powder bed, we obtained the following empirical relation b(t) = 2.86(t + 0.016)0.51, which is superimposed on the experimental data in Figure 5a. Note that in the case of a stationary printhead, as here, b(t) will be strongly influenced by the rate at which drops arrive at the surface. The competition between spreading flow and the arrival of fluid by impacting drops is important in determining the stability of liquid structures during inkjet printing when the printhead moves relative to the substrate.46,47 Thus, it is likely that a similar approach will be needed to model liquid draining during printing as well as for the case of a stationary printhead studied here.

Holman adapted Denesuk’s model to incorporate an advancing drop, where the time-dependent volume V(t) infiltrated by draining a droplet into a porous body could be expressed as

graphic file with name am0c03572_m007.jpg 7a

where

graphic file with name am0c03572_m008.jpg 7b

Note that in eq 7a the area fraction of the pores has been approximated by the powder bed porosity. It is also noteworthy that eq 7a provides the values of the infiltrated volume of the liquid. This is smaller than the total wetting volume determined by X-radiography because this includes the fluid volume (in the pores) and the wetted particle volume. To obtain the “total wetting volume”, eq 7a is multiplied by a porosity correction factor of 1/p, giving

graphic file with name am0c03572_m009.jpg 7c

The prediction of eq 7c is plotted in Figure 7 and compared to the experimental data for volume infiltration from Figure 5d.

Figure 7.

Figure 7

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Plot of the prediction of total infiltrated volume (eq 7ccc) compared to data obtained for X-radiography experiments. The value of porosity (p) used in the equation ranges from 0.1 to 0.7 (the value determined by pycnometry); p = 0.5 gives the best fit with experiment.

Comparing with Figure 5d, it is clear that the linear form of the volume infiltration with time is correctly obtained, but when we use the porosity value determined by pycnometry, p = 0.7, the wetting volume is somewhat greater than experiment. Further simulations were carried out using a range of porosities from p = 0.1 to 0.7, and these are also plotted in Figure 7. Note that the constant, κ, is also a function of porosity (eqs 7b and 7c). The best fit to experimental data occurs if the porosity is taken as p = 0.5, a slightly lower value than that obtained by pycnometry.

From Figure 7, we see that the best fit between experimental data and the prediction of the Washburn equation occurs for the porosity of 0.5, somewhat lower than that obtained by our pycnometry measurement (0.7), but closer to what would be expected with a normal tap density, suggesting that the pycnometry-derived porosity value might be anomalously high. However, despite the seemingly good relation between the experimentally observed wetting volume and that predicted by the Washburn equation for a powder bed with a porosity of 0.5, there is a difference between the actual volume of liquid ink deposited on the surface of the powder bed and the predicted fluid volume drained. The droplet dispenser operates at a frequency of 3 kHz, and the expected drop diameter, Vd, is in the range of 100–120 pL. In the experiments considered in Figures 4 and 5, drops are deposited for a period of 0.6 s; hence, the total volume of fluid is 1800 Vd or approximately 0.2 μL. Comparing this with the model prediction in Figure 7, the wetted volume is close to 2 μL, and if the porosity is 0.5, the predicted drained liquid volume is 1 μL. Thus, the apparent volume of liquid drained is 5 times greater than the volume deposited. Previous studies by both Popovich et al.21 and Hapgood et al.26 found similar trends in terms of the differences between the measured drained volume and the Washburn equation, with Hapgood finding about 30% of the volume unwetted by the fluid and Popovich up to 60%. They explained this by considering a heterogeneous distribution of pore volume within the powder bed, with pores above a certain size not penetrated by the fluid because the capillary radius of the particles is insufficient. This leads to the powder not being fully saturated by the liquid, with a fraction of the porosity remaining dry. Thus, the trailing region of the liquid penetrating front contains both fluid-filled and unfilled (dry) porosity. Therefore, the presence of nonpenetrated regions in the powder bed may explain the similar discrepancy between the predicted and observed fluid volume within the powder bed in our experiments. The model of Miyanaji et al. suggested that the interaction between the imbibing fluid (the printed ink) and the displace fluid (air) can also lead to inhomogeneous infiltration, providing a mechanism for this observation.29

Another reasonable possibility is that as the degree of saturation is a function of the wetting angle between the fluid and the powder particles, the low levels of saturation implied by our measurements may be because of the relatively higher contact angle (≈70°). Previous works using reactive fluid/powder polymer combinations, where a contact angle of 0° can be inferred, have produced optically clear compacts, indicating a complete absence of porosity.16 This hypothesis could be tested by repeating our experiments with powder/fluid combinations covering a range of contact angles and carrying out a tomographic reconstruction of the compact density at the end of the experiment to identify the partially wet voids behind the liquid penetration front.

Finally, we return to our initial intention of better understanding the role of powder bed infiltration and 3D binder jet printing. Given that a typical inkjet-printed drop has a volume in the range 20–100 pL, our experiments with fluid volumes approximately 1000 times greater (or 10 times greater on a 1D length scale) and over a longer time scale are not an exact mimic of the process. However, the general consensus in the literature is that drop–powder interactions are governed by capillary processes, and thus our tracking of the infiltration in real time provides useful data that can be used to understand the mechanisms operating on the smaller length and time scales of individual droplet interactions. We have demonstrated that high-resolution, time-resolved X-radiography can be used to acquire real-time data of the penetration of fluids into a powder bed. The resulting data can be used to validate models for the kinetics of fluid penetration into a powder bed but caution is needed for the analysis and interpretation of the data regarding saturation levels behind the liquid penetration front. Further work is needed to explore different combinations of fluid and powder as well as optimizing the experimental conditions to allow data acquisition from “smaller fluid volumes”. An obvious second-stage experiment is to track the printing of a line of overlapping drops rather than drops impacting at a single location to produce a better mimic of drop–drop and drop–powder interactions to more closely approach the conditions of 3D binder jet printing.

Conclusions

We have used refraction-based phase-contrast synchrotron X-ray imaging to carry out a time-resolved study of capillary-driven ink infiltration of powdered materials mimicking the processes that occur during 3D binder jet printing. The key findings are summarized as follows:

  • (a)

    Fluid infiltration proceeds in a highly nonuniform manner with dramatic differences in fluid penetration rate occurring locally and temporally as infiltration proceeds. This confirms the behavior already reported in the literature in parallel fields of study, monitoring global changes in fluid drainage and pressure through porous media.

  • (b)

    The rate of fluid infiltration and fluid surface spreading occur at similar time scales during the experiment, and the two phenomena cannot be considered independently.

  • (c)

    Fluid infiltration models developed by Denesuk and based on the simplified Washburn model for capillary infiltration can be used to successfully predict the time dependence of fluid infiltration, if they are modified considering the spreading of the liquid across the powder bed.

  • (d)

    The Washburn/Denesuk model needs to be modified to validate our experimental data if the powder bed is assumed to have an “effective porosity” somewhat lower than that actually measured through pycnometry, with the total porosity a combination of fluid-filled regions and areas of unwetted dry voids within the apparent wetting volume. This is in agreement with other studies of fluid penetration into powder compacts that indicate the lack of full saturation of the powder by the infiltrating liquid.

Acknowledgments

The authors wish to acknowledge funding provided by the Engineering and Physical Sciences Research Council (EPSRC, U.K.) [grant nos. EP/L012022/1 and EP/P025021/1] and Department of Biotechnology (DBT, India) [grant no. BT/PR13466/COE/34/26/2015]. Diamond Light Source is acknowledged for granting beamtime MT19533-1 (I13-2). The technical support of Andy Wallwork (UoM) and Kaz Wanelik (DLS) is greatly appreciated. The authors are thankful to Prof. K. K. Nanda and Omeshwari (IISc, Bangalore) for their kind support in terms of the BET facility. Prof. Gurumoorthy (CPDM, IISc, Bangalore) and Prof. Ananthasuresh (Mechanical Eng., IISc, Bangalore) are specially acknowledged for providing their SLA printers to manufacture the powder holder cuvettes. The authors are also thankful to Deepa Mishra, Soumitra Das, Vidushi Sharma, and Swati Sharma for their help and cooperation in sample packaging for the synchrotron experiments. S.B. acknowledges the Commonwealth Scholarship Commission, U.K., for provision of a split-site Ph.D. scholarship.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsami.0c03572.

  • Pycnometry experimental details; experimental details of the Washburn capillary rise method; composite image showing progression of liquid infiltration front (PDF)

  • Progress of liquid infiltration (MP4)

The authors declare no competing financial interest.

Supplementary Material

am0c03572_si_001.pdf (240.2KB, pdf)
am0c03572_si_002.mp4 (2.6MB, mp4)

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Supplementary Materials

am0c03572_si_001.pdf (240.2KB, pdf)
am0c03572_si_002.mp4 (2.6MB, mp4)

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