Cylindrical Throats Research Articles

Pore-scale study of coupled heat and mass transfer during primary freeze-drying using an irregular pore network model

This study presents a pore network (PN) model with transient heat transfer and quasi-steady transitional vapor transport that is for the first time applied to irregular porous structures that are obtained by reconstruction of X-ray tomography image data. In contrast to previous studies, the irregular pores are not approximated by spheres but implemented in their original shape. Secondly, instead of assuming cylindrical throats as pore connections, the actual distance between pore centers as well as the pore cross sections are used for the computation of the vapor transport coefficient. The control volume elements of the computational model are matched with the cells obtained by Voronoi tessellation. The improvements have clear advantages over former approaches where the reconstructed void space is usually strongly simplified by balls and sticks confined in a regular lattice structure. A freeze-dried sample of maltodextrin DE12 with 20% (w/w) solid content is used for benchmarking the new methodology. Its morphological and thermal properties are determined by the novel PN model. The simulation results of primary freeze-drying (FD) are compared to reference cases in two ways. First, the differences in heat and mass transfer kinetics as compared to regular PNs are emphasized. Secondly, the PN simulation results are confronted with a simple literature model that neglects pore size distribution (PSD) and transient heat transfer. It is shown that already in small domains with relatively narrow PSD, the variation of the mass transfer coefficient affects the computed sublimation fluxes and yields a significant deviation from the simpler literature model. Moreover, it is revealed in this study that the structure has a significant impact on the sublimation front temperature. This is demonstrated by the comparison of FD in the irregular PN to a regular PN with almost identical PSD but different porosity. The development, verification, and benchmarking of the new PN model can be seen as an important step for studies of the structure dependence of FD.

Multiscale simulation for sound transmission loss of a particulate filter in an exhaust system using a homogenization method

Most vehicles have diesel or gasoline particulate filters to remove particulate matter contained in gas from internal combustion engines. On the other hand, regulations have been in effect for vehicle-noise emission, with several studies conducted on reducing noise from the exhaust systems of automobiles. Generally, mufflers with expansion chambers and sound-absorbing materials have been used to reduce noise emissions; however, diesel or gasoline particulate filters have also been observed to reduce noise transmitted through the filter. Herein, a novel approach based on a microstructure model is proposed to predict the sound transmission loss through a diesel/gasoline particulate filter, the wall of which is made of a ceramic porous material. In this approach, a homogenization method for sound-absorbing poroelastic materials based on the asymptotic expansion approach is applied. The method was originally developed by one of the authors of this study. Microscopic structural images are obtained through μX-ray computed tomography, and a pore network model that consists of spherical pores and cylindrical throats is constructed to represent the characteristics of the porous filter wall. A microscopic unit cell model is derived from the expected values of the pore- and throat-size distributions obtained using the pore network model. Homogenized properties, such as permeability, equivalent density, and equivalent bulk modulus, are obtained through microscopic calculations using the unit cell model. Finally, the sound transmission loss is predicted through macroscopic calculations using the homogenized properties. The calculated sound transmission loss agreed well with the values measured using an acoustic tube and simplified exhaust systems.

Towards Bottom-up Design of Porous Electrode Microstructures – an Approach Coupling Evolutionary Algorithms and Pore Network Modeling

Porous electrodes are performance- and cost-defining components in modern electrochemical systems such as redox flow batteries, fuel cells, and electrolyzers. They must facilitate mass transport, provide surfaces for electrochemical reactions, and conduct electrons and heat. Thus, understanding and optimizing the porous electrode microstructure offers a promising pathway to cost reduction by increasing power density (1). However, our current arsenal of materials is limited to fibrous carbonaceous electrodes that were developed for low temperature fuel cells and are now repurposed to emerging systems (i.e., redox flow batteries), which fundamentally limits the performance. The empirical design of electrodes is time- and resource-intensive which limits exploration of the wider design space. To accelerate progress, microstructure-informed multiphysics simulations can be leveraged to aid the theoretical understanding and design of advanced electrode architectures but has primarily focused to the investigation of existing, carbon-fiber-based electrodes (2–4). In this work, we explore the following scientific question: Can we deploy three-dimensional simulations in combination with evolutionary algorithms to enable bottom-up artificial generation of porous electrodes? In the first part of this talk, I will discuss the modeling framework and experimental validation. Using a pore network modeling open-access platform (OpenPNM) (4, 5), we built a microstructure-informed, electrolyte-agnostic simulation framework. In this work, we focus on redox flow batteries as an application case. The model utilizes a network-in-series approach to account for species depletion over the entire length of the electrode, thus enabling the simulation of large electrode sizes (17 mm x 1 mm x 210-400 μm). To validate the robustness of the modeling framework, we performed symmetric flow cell experiments for two distinct electrolytes - an aqueous Fe2+/Fe3+ and a non-aqueous TEMPO./TEMPO+ - and two types of porous electrodes – a Freudenberg carbon paper and an ELAT carbon cloth - (Figure 1a). The dry electrode microstructures were obtained with x-ray computed tomography and converted into a network of spherical pores and cylindrical throats using the SNOW algorithm (6). The electrochemical model is solved for the electrolyte fluid transport and couples both half-cells by iteratively solving the species and charge transport with low computational cost (-1 – 0 V, with -0.05 V step intervals takes 60-120 min on an Intel® Core(TM) i7-8750H CPU). The electrochemical performance of the non-aqueous electrolyte was well captured by the model without fitting parameters, allowing rapid benchmarking of porous electrode microstructures. For the aqueous electrolyte, we find that incomplete wetting of the electrode results in overprediction of the electrochemical performance. To account for incomplete wetting, we successfully employ a fitting parameter to account for the near-surface mass transfer coefficient (7).In the second part of the talk, I will describe a genetic algorithm that optimizes porous electrode microstructures from the bottom-up by coupling the pore network modeling framework with an evolutionary algorithm. Our goal is to optimize electrode microstructures by only having the electrolyte chemistry and flow field geometry as inputs. The microstructure evolves driven by a fitness function that minimizes pumping power requirements and maximizes electrochemical power output. The analyzed systems show significant improvement of the networks’ fitness, which increased by 30-400%. For flow-through flow fields, the pumping requirements are dominant and were reduced by 60-70%, resulting in a bimodal pore size distribution with large-pore longitudinal electrolyte flow pathways (Figure 1b). Additionally, the surface area at the membrane-electrode interface is increased for all systems, resulting in an increased electrochemical performance of 3-8%. The presented framework offers great potential for predictive design of electrode microstructures tailored for specific redox chemistries and reactor architectures, which will accelerate and broaden the design and fabrication process of advanced electrode structures. While applied to flow batteries here, this methodology can be leveraged to advance other electrochemical systems by adapting the relevant physics. References A. Forner-Cuenca, F. R. Brushett, Curr. Opin. Electrochem., 10 (2019).G. Qiu et al., Electrochim. Acta. 64, 46–64 (2012).A. G. Lombardo, et al., J. Energy Storage. 24 (2019).M. A. Sadeghi et al., J. Electrochem. Soc. 166, A2121–A2130 (2019).J. Gostick et al., Comput. Sci. Eng. 18, 60–74 (2016).J. T. Gostick, Phys. Rev. E. 96, 1–15 (2017).K. V. Greco, et al., ACS Appl. Mater. Interfaces. 10, 44430–44442 (2018). Figure 1

Topology and hydraulic permeability estimation of explosively created fractures through regular cylindrical pore network models

Purpose This research study aims to develop regular cylindrical pore network models (RCPNMs) to calculate topology and geometry properties of explosively created fractures along with their resulting hydraulic permeability. The focus of the investigation is to define a method that generates a valid geometric and topologic representation from a computational modelling point of view for explosion-generated fractures in rocks. In particular, extraction of geometries from experimentally validated Eulerian smoothed particle hydrodynamics (ESPH) approach, to avoid restrictions for image-based computational methods. Design/methodology/approach Three-dimensional stabilized ESPH solution is required to model explosively created fracture networks, and the accuracy of developed ESPH is qualitatively and quantitatively examined against experimental observations for both peak detonation pressures and crack density estimations. SPH simulation domain is segmented to void and solid spaces using a graphical user interface, and the void space of blasted rocks is represented by a regular lattice of spherical pores connected by cylindrical throats. Results produced by the RCPNMs are compared to three pore network extraction algorithms. Thereby, once the accuracy of RCPNMs is confirmed, the absolute permeability of fracture networks is calculated. Findings The results obtained with RCPNMs method were compared with three pore network extraction algorithms and computational fluid dynamics method, achieving a more computational efficiency regarding to CPU cost and a better geometry and topology relationship identification, in all the cases studied. Furthermore, a reliable topology data that does not have image-based pore network limitations, and the effect of topological disorder on the computed absolute permeability is minor. However, further research is necessary to improve the interpretation of real pore systems for explosively created fracture networks. Practical implications Although only laboratory cylindrical rock specimens were tested in the computational examples, the developed approaches are applicable for field scale and complex pore network grids with arbitrary shapes. Originality/value It is often desirable to develop an integrated computational method for hydraulic conductivity of explosively created fracture networks which segmentation of fracture networks is not restricted to X-ray images, particularly when topologic and geometric modellings are the crucial parts. This research study provides insight to the reliable computational methods and pore network extraction algorithm selection processes, as well as defining a practical framework for generating reliable topological and geometrical data in a Eulerian SPH setting.

Estimation of Shale Intrinsic Permeability with Process-Based Pore Network Modeling Approach

A multi-scale pore network model is developed for shale with the process-based method (PBM). The pore network comprises three types of sub-networks: the $$\upmu $$ m-scale sub-network, the nm-scale pore sub-network in organic matter (OM) particles and the nm-scale pore sub-network in clay aggregates. Process-based simulations mimic shale-forming geological processes and generate a $$\upmu $$ m-scale sub-network which connects interparticle pores, OM particles and clay aggregates. The nm-scale pore sub-networks in OM and clay are extracted from monodisperse sphere packing. Nm-scale throats in OM and clay are simplified to be cylindrical and cuboid-shaped, respectively. The nm-scale pore sub-networks are inserted into selected OM particles and clay aggregates in the $$\upmu $$ m-scale sub-network to form an integrated multi-scale pore network. No-slip permeability is evaluated on multi-scale pore networks. Permeability calculations verify that shales permeability keeps decreasing when nm-scale pores and throats replace $$\upmu $$ m-scale pores. Soft shales may have higher porosity but similar range of permeability with hard shales. Small compaction leads to higher permeability when nm-scale pores dominate a pore network. Nm-scale pore networks with higher interconnectivity contribute to higher permeability. Under constant shale porosity, the shale matrix with cuboid-shaped nm-scale throats has lower no-slip permeability than that with cylindrical throats. Different from previous reconstruction processes, the new reconstruction process first considers the porous OM and clay distribution with PBM. The influence of geological processes on the multi-scale pore networks is also first analyzed for shale. Moreover, this study considers the effect of OM porosities and different pore morphologies in OM and clay on shale permeability.

Discrete pore network modeling of superheated steam drying

ABSTRACTA nonisothermal two-dimensional pore network model is developed to describe the superheated steam drying of a capillary porous medium. The complex void space is approximated by a network of spherical pores interconnected by cylindrical throats. In this model, the condensation of water vapor at the network surface as well as the network drying are taken into account. During the network drying period, the liquid transport is driven by capillary action, whereas vapor transport occurs because of convection. The condensation of water vapor within the pores is modeled based on newly formulated liquid invasion rules. The simulation results, presented as temperature and moisture content profiles over time, indicate qualitative agreement with available experimental observations. The inclusion of the liquid invasion rules is shown to accommodate more of the condensed water mass compared to earlier models, in which condensation is only partly treated. Due to the viscous vapor flow, the vapor overpressure within the network, which is the driving force of vapor transport, is reproduced in these simulations. The influence of vapor overpressure on the disintegration of the liquid phase is also discussed.

On applying an external-flow driven mass transfer boundary condition to simulate drying from a pore-network model

A novel method to simulate drying from a pore-network model is presented. Due to the evaporative mass-flux going out from the network as well as the outside airflow, a vapor mole-concentration boundary layer forms around the network. Concentration Boundary Layer Thickness (CBLT) and consequently the mass transfer coefficient are usually assumed constant in the literature. However, CBLT varies during drying owing to the changes in the outgoing mass flux from the network. To investigate the variation in CBLT and its dependence on convective effects due to the airflow, a numerical code based on the finite volume method has been developed to simulate drying characteristics of a pore-network. Laminar, steady state and two-dimensional Navier–Stokes equations as well as the vapor mole-concentration equation with both the convective and diffusive terms are discretized and solved according to the SIMPLE algorithm. A 20×20 two-dimensional pore-network after including cylindrical throats with circular cross sections is considered to model slow (isothermal) evaporation. Due to the geometry of throats and the network size, the effects of liquid film, viscous and gravitational forces are not considered. Therefore the capillary effect remains the dominant force for liquid transport inside the pore network. The drying algorithm applied inside the pore-network is the same as the one proposed by Metzger et al. (2007) [14], and it is verified that the convective effects are negligible within the gas phase inside the network. The effect of air flow over the exposed surface of the network causes a sudden decrease in evaporation rate from the pore-network after a short time period. This confirms the existence of the first drying period, as addressed in previous publications (e.g. Metzger et al. [14]). Also, a unique CBLT that grows along the length of the pore-network has been obtained. It is shown that the thickness of the concentration boundary layer decreases with time everywhere along the top surface of the network; therefore the assumption of constant CBLT that is used in the literature is merely a rough estimate. The present model provides a more accurate analysis of the isothermal evaporation from the porous structures exposed to laminar external air flow.

Determination of oxygen effective diffusivity in porous gas diffusion layer using a three-dimensional pore network model

In proton exchange membrane fuel cell (PEMFC) models, oxygen effective diffusivity is the most important parameter to characterize the oxygen transport in the gas diffusion layer (GDL). However, its determination is a challenge due to its complex dependency on GDL structure. In the present study, a three-dimensional network consisting of spherical pores and cylindrical throats is developed and used to investigate the effects of GDL structural parameters on oxygen effective diffusivity under the condition with/without water invasion process. Oxygen transport in the throat is described by Fick's law and water invasion process in the network is simulated using the invasion percolation with trapping algorithm. The simulation results reveal that oxygen effective diffusivity is slightly affected by network size but increases with decreasing the network heterogeneity and with increasing the pore connectivity. Impacts of network anisotropy on oxygen transport are also investigated in this paper. The anisotropic network is constructed by constricting the throats in the through-plane direction with a constriction factor. It is found that water invasion has a more severe negative influence on oxygen transport in an anisotropic network. Finally, two new correlations are introduced to determine the oxygen effective diffusivity for the Toray carbon paper GDLs.

Infiltration time and imprint shape of a sessile droplet imbibing porous medium

The infiltration of a sessile droplet into a homogeneous porous medium for a constant droplet base radius case is solved numerically, where the porous medium is represented as a capillary network consisting of pores and throats. For a homogeneous medium, the network is built of the spherical pores of constant radius, and the cylindrical throats of constant radius and height. Having such defined network, the droplet imbibes porous medium in a single-phase flow for which the free interface in porous medium is smooth, and the liquid phase permeability and the capillary pressure are constant. Using the numerical solution we carry out the parametric study in which: (i) liquid viscosity and surface tension, (ii) droplet volume and base radius, and (iii) porous medium porosity and permeability are varied. The droplet infiltration time, and the imprint shape that is given with two spheroid half-axes are calculated. The dimensionless analysis is utilized to correlate the droplet infiltration parameters from which master curves for the droplet infiltration time and the droplet imprint shape are obtained. Using the infiltration time correlation, both numerical and experimental results show a linear behavior.

Modelling diffusion from simulated porous structures

An algorithm has been developed for the simulation of liquid diffusion from a porous material in the presence of a concentration gradient. A network model, Pore-Cor, was used to create simulated porous networks. These structures comprised cubic pores connected by cylindrical throats each centred on the coordinates of a three-dimensional 10 × 10 × 10 Cartesian matrix of positions. The simulated structure was then saturated with a mixture of benzene and cyclohexane and immersed in static pure cyclohexane. The algorithm then simulated the diffusion of benzene from the porous structure into the surrounding cyclohexane. The effects on the diffusion process of the geometries of the simulated structures were investigated by generating predefined structures and isolating the effect of each geometric parameter. The method presented in this study should lead to a predictive tool for studying the diffusion processes within real samples, as the pore network model can generate void structures which have porosity and percolation properties that closely match experimental mercury intrusion porosimetry data of real porous materials.

Estimation of structural element sizes in sand and compacted blocks of ground calcium carbonate using a void network model

An algorithm has been developed for the calculation of the size of the effective structural or skeletal elements which make up the solid phase of an unconsolidated or consolidated porous block. It is based on a previously presented algorithm, but it has now been validated on unconsolidated samples and tested on consolidated samples. It also includes a virtual reality representation of the structures. First, a network model named Pore-Cor is made to reproduce the percolation behaviour of the experimental sample, by matching its simulated percolation characteristics to an experimental mercury intrusion curve. The algorithm then grows skeletal elements between the cubic pores and cylindrical throats of the void network model until they touch up to four of the adjacent void features. The size distributions of the simulated solid elements are compared with each other and with experimentally determined particle size distributions, using a Mann–Whitney test. The algorithm was shown to simulate skeletal elements with the correct trends in size distribution for two different sand samples, provided the sand packed itself optimally under the applied mercury pressure. It was also applied to two samples of variously compressed calcium carbonate powder, having fine and coarse particle size distributions respectively. The simulation demonstrated that on compressing the powder at the minimum force, the skeletal elements differed from the constituent particle sizes, as expected. The average size of the skeletal elements increased as the compression force was increased on the calcium carbonate powders. The results suggest that the method could be useful as a tool for probing the effect of compaction on aggregation or sintering, and for studying other effects such as cementation in geological samples, where other more direct techniques cannot be applied.

Water Absorption into Construction Materials: Comparison of Neutron Radiography Data with Network Absorption Models

Two different porous building materials have been previously measured and analysed (El-Abd and Milczarek, 2004, IEEE Trans. Nuclear Sci.; El-Abd et al., 2004, J. Phys. D) using neutron radiography to measure the water front position over time. The results from this experimental approach show a similar behaviour to the predictions from idealised model structures, in that there is a cross over point where the fastest rate of absorption at first favours the finer structure material and at later times favours the coarser pore structure material. The computer model, Pore-Cor** is used to generate the idealised structures and the absorption of fluid into porous structures follows a Bosanquet wetting algorithm for fluids undergoing both inertial and viscous dynamical flow (Ridgway and Gane, 2002, Colloids Surfaces A: Physicochem. Eng. Aspects 206, 217–239.). The model structures comprise cubic pores connected by cylindrical throats on a three-dimensional 10× 10× 10 position matrix simulating the void structure of porous media by fitting as closely as possible the modelled mercury intrusion curve to that of the experimentally determined mercury intrusion curve of the actual sample. They show the transition that occurs in the absorption behaviour from the linear t-dependent short timescale inertial regime to the familiar √t Lucas-Washburn viscous regime. The simulated absorption algorithm applied to these model structures also shows a fluid position behaviour that replicates qualitatively, given the limitation of representative sample volume, the cross over seen experimentally. Furthermore, the existence of a preferred wetting path is demonstrated in the experimental as well as the model wetting front behaviour. In the case of the structure containing the broader range of pore sizes, the wetting front is considered to proceed by a network of optimal size combinations (inertial wetting versus viscous drag) and connectivity, leaving some pores behind the wetting front unfilled or only partially filled.

Estimation of the effective particle sizes within a paper coating layer using a void network model

A range of calcium carbonate-based tablets and paper coating layers, with latex or starch as binder, were prepared. Their dry porous structures were analysed by mercury porosimetry. Some of these samples were also examined by electron microscopy. The porous space of these structures has been simulated using a network model named Pore-Cor, which creates network structures with percolation behaviour and porosity matching those of the experimental sample. Representative particles were grown between the cubic pores and cylindrical throats of the void network model until they touched up to four of the adjacent void features. The sizes of these representative particles, or skeletal elements, have been previously shown to be realistic for the case of unconsolidated sand and glass beads. The size distributions of these skeletal elements were compared with each other and with experiment using a Mann–Whitney test. The sizes of the skeletal elements were found to increase with the particle size of the calcium carbonate powder. The properties of the binders, used in the paper coating formulations, were found to have a major influence on the sizes of the skeletal elements, whose sizes also increased with coating thickness. These findings give insights into the wet structure and the drying process of paper coatings.

Absorption Rate and Volume Dependency on the Complexity of Porous Network Structures

Results of simulated supersource imbibition into model network structures are compared with experimental observations of real network structures determined by dynamical gravimetric fluid uptake. A computer model, Pore-Cor, has been used previously to simulate the imbibition of fluid into porous structures by applying an imbibition algorithm for fluids undergoing both inertial and viscous dynamical absorption (Schoelkopf et al., 2000). The structures comprise cubic pores connected by cylindrical throats on a three-dimensional 10 × 10 × 10 position matrix. The absorption curves for model structures with monosized pore and throat size ranges and for polydisperse pore and throat size distributions centred around 0.1 µm, increasing from 0.1 µm as a lower limit, and decreasing from 0.1 µm as an upper limit, respectively, are analysed. A relevant observable porosity and 50% volume intrusion radius (r50) are obtained using simulated mercury intrusion. Experimental network pore structures were made using compressed tablets, formed under a series of pressures, of two finely ground calcium carbonates with defined differences in skeletal particle size distribution. The surface chemical, particulate and morphological pore characteristics were maintained constant over a range of porosities using controlled wet grinding and careful use of dispersant levels such that the ratio of dispersant to BET surface area was held constant. The experimental porosities were determined by mercury intrusion porosimetry applying corrections for mercury compression and penetrometer expansion together with a correction for sample skeletal compression (Gane et al., 1996). The applicability of the Lucas–Washburn equation is examined by defining two equivalent hydraulic radii, one based on a Darcy absorption length (rehcDarcy) and the other on a volume uptake (rehc), respectively. The results from the model structures having distributions of pores and throats, which contain either small or large pores, respectively, follow the experimental results qualitatively. Both approaches show a long timescale macroscopic absorption rate depending approximately, but not exactly, on the square root of time. The two experimental series, however, fail to scale with each other via the Lucas–Washburn equation in accordance with pore size, r50. Porosity is shown to be the main factor determining the volume absorption rate, and, when used as a weighting factor, gives linear correlation-scaling between r50 and a derived volume-based r′ehc equivalent hydraulic radius, obtained from an analytical expression of the observed Darcy-based rehcDarcy. The experimental samples showed that the directly observed rehc and the calculated r′ehc, derived from Darcy length, were equal, but this was not the case for the model values. A factor β = r′ehc/r50 is shown to be a possible descriptor of the sample network complexity and an indicator for the probability level of pore filling during the absorption dynamic.

Dynamic absorption into simulated porous structures

Abstract A computer model, pore-cor 1 , has been used to simulate the permeation of fluid into porous structures by applying a wetting algorithm for fluids undergoing both inertial and viscous dynamical absorption. These structures comprise cubic pores connected by cylindrical throats on a three-dimensional 10×10×10 position matrix. Previously, pore-cor has been used to simulate the void structure of porous media by fitting as closely as possible the simulated mercury intrusion curve of the model structure to that of the experimentally determined mercury intrusion curve of the actual sample. This refined model structure was then used to simulate the absorption of a number of different fluids and confirmation with experimental absorption data, adopting the same fluid, provided the necessary confidence in the model. Based on this practical experience, the framework is developed from experimental comparison so that pore-cor can now be applied as a ‘predictor’ tool rather than a simulator of existing experimental results. The structures used here have been generated with the aim of isolating certain parameters so their influence on the absorption behaviour of a fluid can be identified. It is shown how, keeping the porosity constant, structures can be represented in a number of different ways and that these structures will have vastly different absorption behaviour. Reducing the value of the fluid density in the simulation has also been investigated to show where the transition occurs in the absorption behaviour from the linear t -dependent short timescale inertial Bosanquet regime to the √ t Lucas–Washburn (LW) viscous regime. Such a system of connecting pores is representative of pigmented paper coating structures and, for example, by changing the particle size distribution of the pigment under suitably modified calendering conditions, pore structures of equal porosity could exist in practice and have drastically different effects on fluid absorption. Implications on, say, the way an ink would set on the coating surface, can have dramatic practical significance. To be able to predict these effects and to design optimal coating structures for the fluids and inks used in a variety of printing, lacquering and glueing processes is seen as a significant advance, obviating the need for expensive matrix-designed production trialling.

The Effects of Void Geometry and Contact Angle on the Absorption of Liquids into Porous Calcium Carbonate Structures

The absorption (permeation) of alcohols into porous blocks of calcium carbonate has been studied experimentally and with a computer model. The experimental measurement was of change in apparent weight of a block with time after contact with liquid. The modeling used the previously developed ‘Pore-Cor’ model, based on unit cells of 1000 cubic pores connected by cylindrical throats. To gain some insight into absorption into voids of complex geometry, and to provide a representation of heterogeneities in surface interaction energy, the cylindrical throats were converted to double cones. Relative to cylinders, such geometries caused hold-ups of the percolation of nonwetting fluids with respect to increasing applied pressure, and a change in the rate of absorption of wetting fluids. Both the measured absorption of the alcohols and the simulated absorption of the alcohols and of water showed significant deviations from that predicted by an effective hydraulic radius approximation. The simulation demonstrated the development of a highly heterogeneous wetting front, and of preferred wetting pathways that were perturbed by inertial retardation. The findings are useful in the design of high-performance, low-waste pigments for paper coatings, and environmentally friendly printing inks, as well as in wider industrial, environmental, and geological contexts.