Dynamic Pore Network Modeling of Imbibition in Real Porous Media with Corner Film Flow.

Wetting films can develop in the corners of pore structures during imbibition in a strongly wetting porous medium, which may significantly influence the two-phase flow dynamics. Due to the large difference in scales between main meniscus and corner film, accurate and efficient modeling of the dynamics of corner film remains elusive. In this work, we develop a novel two-pressure dynamic pore network model incorporating the interacting capillary bundle model to analyze the competition between the main meniscus and corner film flow in real porous media. A pore network with four-point star-shaped pore bodies and throat bonds is extracted from the real porous medium based on the pore shape factor and pore cross-sectional area, which is then decomposed into several layers of sub-pore networks, where the first layer of sub-pore network simulates the main meniscus flow while the upper layers characterize the corner film flow. The two-phase flow conductance of throat bonds for different layers of sub-pore networks are determined by high-resolution two-phase lattice Boltzmann modeling, thus inherently considering the viscous coupling effect. In addition, two artificial neural network models are developed to predict the two phases' flow conductance based on the shape of the throat cross section and the fluid properties. The accuracy of the developed model is validated with a lattice Boltzmann simulation of imbibition in a strongly wetting square tube. Then the model is used to simulate imbibition in a strongly wetting sandstone porous medium, and the competition between the main meniscus and the corner film flow is analyzed. The results show that with decreasing capillary number and viscosity ratio between wetting and nonwetting fluids, the development of the wetting corner film becomes more significant.

Anisotropic Deformation in a Polymer Slab Subjected to Fluid Adsorption.

Nanoporous adsorbents can mechanically swell or shrink once upon the accumulation of guest fluid molecules at their internal surfaces or in their cavities. Existing theories in this field attribute such sorption-induced swelling to a tensile force, while shrinkage is always associated with a contractive force. In this study, however, we propose that the sorption-induced deformation of a porous architecture is not solely dictated by the stress conditions but can also be largely influenced by its mechanical anisotropy. In more detail, the sorption-induced deformation of a polymeric slab is investigated using a hybrid molecular dynamics and Monte Carlo algorithm. When subjected to water loading, the slab is found to swell along its normal direction and display an overall positive volumetric strain. Moreover, the surface roughness is enhanced as a response to the surface energy decrease induced by the water covering the slab external surface. Unexpectedly, the in-plane deformation of the slab material seems to be highly constrained, so that it is far below its normal counterpart. This anisotropy is enhanced when the slab thickness decreases. With a thickness of around 1.35 nm, an in-plane shrinkage is observed throughout the entire hygroscopic range. A theoretical analysis based on a poromechanical model suggests that the anisotropic mechanical properties, which are common for a slab material, are the essence of the constrained in-plane swelling or even shrinkage under the isotropic sorption-induced tensile forces. This study, unveiling overlooked mechanisms of sorption-induced shrinkage in mechanically anisotropic materials, provides new insights into this field.

Sorption-Deformation Interplay in Hierarchical Porous Polymeric Structures Composed of a Slit Pore in an Amorphous Matrix.

Prevailing absorbents like wood-derived porous scaffolds or polymeric aerogels are normally featured with hierarchical porous structures. In former molecular simulation studies, sorption, deformation, and coupled sorption-deformation have been studied for single-scale materials, but scarcely for materials where micropores (<2 nm) and mesopores (2-50 nm) coexist. The present work, dealing with a mesoscopic slit pore between two slabs of microporous amorphous cellulose (AC), aims at modeling sorption-deformation interplay in hierarchical porous cellulosic structures inspired by polymeric modern adsorbents. Specifically, the atomic system is modeled by a hybrid workflow combining molecular dynamics (MD) and grand canonical Monte Carlo (GCMC) simulations. The results clarify the multiple sorption/deformation mechanisms in porous materials with different slit-pore sizes, including water filling in micropores, surface covering at the solid-air interface, and subsequent capillary condensation in mesopores. In particular, before the onset of capillary condensation, the sorption behavior of the AC matrix in the hybrid system is almost the same as that of bulk AC, in which sorption and deformation enhance each other through sorption-induced swelling and additional sorption in the newly created voids. Upon capillary condensation, the interaction between the micropores and the mesopore emerges. Water molecules in the mesopore exert a negative hydrostatic pressure perpendicular to the slab surface on the matrices, resulting in an increase in porosity and water content, a decrease in distance between the centers of mass (COMs) of the slabs, and thus a thinning of the slit pore. As described by Bangham's Law, the surface area of the rough slit-pore slab increases proportionally to the surface energy variation during surface covering. For a system composed of a compliant polymer like AC, however, the surface area enlargement does not result in an in-plane swelling as expected but instead in an in-plane shrinkage along with an increase in local roughness or irregularity (an accordion effect).

Pore-Scale Study on Convective Drying of Porous Media.

In this work, a numerical model for isothermal liquid-vapor phase change (evaporation) of the two-component air-water system is proposed based on the pseudopotential lattice Boltzmann method. Through the Chapman-Enskog multiscale analysis, we show that the model can correctly recover the macroscopic governing equations of the multicomponent multiphase system with a built-in binary diffusion mechanism. The model is verified based on the two-component Stefan problem where the measured binary diffusivity is consistent with theoretical analysis. The model is then applied to convective drying of a dual-porosity porous medium at the pore scale. The simulation captures a classical transition in the drying process of porous media, from the constant rate period (CRP, first phase) showing significant capillary pumping from large to small pores, to the falling rate period (FRP, second phase) with the liquid front receding in small pores. It is found that, in the CRP, the evaporation rate increases with the inflow Reynolds number (Re), while in the FRP, the evaporation curves almost collapse at different Res. The underlying mechanism is elucidated by introducing an effective Péclet number (Pe). It is shown that convection is dominant in the CRP and diffusion in the FRP, as evidenced by Pe > 1 and Pe < 1, respectively. We also find a log-law dependence of the average evaporation rate on the inflow Re in the CRP regime. The present work provides new insights into the drying physics of porous media and its direct modeling at the pore scale.

Wicking fingering in electrospun membranes.

Pronounced fingering of the waterfront is observed for in-plane wicking in thin, aligned electrospun fibrous membranes. We hypothesize that a perturbation in capillary pressure triggers the onset of fingering, which grows in a non-local manner based on the waterfront gradient. Vertical and horizontal wicking in thin electrospun membranes of poly(ethylene-co-vinyl alcohol) (EVOH) fibers with varying fiber alignment and degree of orientation is studied with backlight photography. A non-local transport model considering the gradient of the waterfront is developed, where fiber orientation is modeled with a correlated random field. The model shows that a transition from straight to highly fingered waterfront occurs during water uptake as observed in the experiment. The size and shape of the fingers depend on fiber orientation. Based on good model agreement, we show that, during wicking in thin electrospun membranes, fingering is initially triggered by a perturbation in capillary pressure caused by the underlying anisotropic and heterogeneous membrane structure which grows in a non-local manner depending on the waterfront gradient.

Identifying in silico how microstructural changes in cellular fruit affect the drying kinetics.

Convective drying of fruits leads to microstructural changes within the material as a result of moisture removal. In this study, an upscaling approach is developed to understand and identify the relation between the drying kinetics and the resulting microstructural changes of apple fruit, including shrinkage of cells without membrane breakage (free shrinkage) and with membrane breakage (lysis). First, the effective permeability is computed from a microscale model as a function of the water potential. Both temperature dependency and microstructural changes during drying are modeled. The microscale simulation shows that lysis, which can be induced using various pretreatment processes, enhances the tissue permeability up to four times compared to the free shrinkage of the cells. Second, via upscaling, macroscale modeling is used to quantify the impact of these microstructural changes in the fruit drying kinetics. We identify the formation of a barrier layer for water transport during drying, with much lower permeability, at the tissue surface. The permeability of this layer strongly depends on the dehydration mechanism. We also quantified how inducing lysis or modifying the drying conditions, such as airspeed and relative humidity, can accelerate the drying rate. We found that inducing lysis is more effective in increasing the drying rate (up to 26%) than increasing the airspeed from 1 to 5 m s-1 or decreasing the relative humidity from 30% to 10%. This study quantified the need for including cellular dehydration mechanisms in understanding fruit drying processes and provided insight at a spatial resolution that experiments almost cannot reach.

Moisture-induced crossover in the thermodynamic and mechanical response of hydrophilic biopolymer.

The use of natural sustainable resources such as wood in green industrial processes is currently limited by our poor understanding of the impact of moisture on their thermodynamic and mechanical behaviors. Here, a molecular dynamics approach is used to investigate the physical response of a typical hydrophilic biopolymer in softwood hemicellulose-xylan-when subjected to moisture adsorption. A unique moisture-induced crossover is found in the thermodynamic and mechanical properties of this prototypical biopolymer with many quantities such as the heat of adsorption, heat capacity, thermal expansion and elastic moduli exhibiting a marked evolution change for a moisture content about 30 wt%. By investigating the microscopic structure of the confined water molecules and the polymer-water interfacial area, the molecular mechanism responsible for this crossover is shown to correspond to the formation of a double-layer adsorbed film along the amorphous polymeric chains. In addition to this moisture-induced crossover, many properties of the hydrated biopolymer are found to obey simple material models.

Non-Lithography Hydrodynamic Printing of Micro/Nanostructures on Curved Surfaces.

A key issue of micro/nano devices is how to integrate micro/nanostructures with specified chemical components onto various curved surfaces. Hydrodynamic printing of micro/nanostructures on three-dimensional curved surfaces is achieved with a strategy that combines template-induced hydrodynamic printing and self-assembly of nanoparticles (NPs). Non-lithography flexible wall-shaped templates are replicated with microscale features by dicing a trench-shaped silicon wafer. Arising from the capillary pumped function between the template and curved substrates, NPs in the colloidal suspension self-assemble into close-packed micro/nanostructures without a gravity effect. Theoretical analysis with the lattice Boltzmann model reveals the fundamental principles of the hydrodynamic assembly process. Spiral linear structures achieved by two kinds of fluorescent NPs show non-interfering photoluminescence properties, while the waveguide and photoluminescence are confirmed in 3D curved space. The printed multiconstituent micro/nanostructures with single-NP resolution may serve as a general platform for optoelectronics beyond flat surfaces.

Molecular Simulation of Sorption-Induced Deformation in Atomistic Nanoporous Materials.

An atomistic slit pore model is built to study the sorption-induced deformation of nanoporous materials with the help of molecular simulation. Both sorption and strain isotherms are determined to probe the anisotropic deformation behavior induced upon molecular adsorption. A detailed analysis shows that the driving microscopic mechanisms at different sorption stages are different. At high relative pressure, as expected from the classical macroscopic picture, the pore deformation is governed by the Laplace pressure as the pore gets filled with liquid because of capillary condensation. In such situation, the strain in normal and longitudinal directions can be predicted from the stiffness modulus in the corresponding direction. At low pressure, when liquid films are adsorbed at the pore surfaces and separated by the vapor phase, the strain is driven by the attractive solid-fluid forces and in-plane pressure within the film, and the deformation is confined in the direction parallel to the film-solid interface. Because of the interplay of the two factors, the strain changes from shrinkage to expansion upon increase of pressure. Analysis of isosteric heat of adsorption shows that the contribution arising from the deformation is small compared to the sorption contribution, which indicates that the influence of deformation on the sorption process is limited.

Dynamics of Contact Line Pinning and Depinning of Droplets Evaporating on Microribs.

The contact line dynamics of evaporating droplets deposited on a set of parallel microribs is analyzed with the use of a recently developed entropic lattice Boltzmann model for two-phase flow. Upon deposition, part of the droplet penetrates into the space between ribs because of capillary action, whereas the remaining liquid of the droplet remains pinned on top of the microribs. In the first stage, evaporation continues until the droplet undergoes a series of pinning-depinning events, showing alternatively the constant contact radius and constant contact angle modes. While the droplet is pinned, evaporation results in a contact angle reduction, whereas the contact radius remains constant. At a critical contact angle, the contact line depins, the contact radius reduces, and the droplet rearranges to a larger apparent contact angle. This pinning-depinning behavior goes on until the liquid above the microribs is evaporated. By computing the Gibbs free energy taking into account the interfacial energy, pressure terms, and viscous dissipation due to drop internal flow, we found that the mechanism that causes the unpinning of the contact line results from an excess in Gibbs free energy. The spacing distance and the rib height play an important role in controlling the pinning-depinning cycling, the critical contact angle, and the excess Gibbs free energy. However, we found that neither the critical contact angle nor the maximum excess Gibbs free energy depends on the rib width. We show that the different terms, that is, pressure term, viscous dissipation, and interfacial energy, contributing to the excess Gibbs free energy, can be varied differently by varying different geometrical properties of the microribs. It is demonstrated that, by varying the spacing distance between the ribs, the energy barrier is controlled by the interfacial energy while the contribution of the viscous dissipation is dominant if either rib height or width is changed. Main finding of this is study is that, for microrib patterned surfaces, the energy barrier required for the contact line to depin can be enlarged by increasing the spacing or the rib height, which can be important for practical applications.

Beyond-Cassie Mode of Wetting and Local Contact Angles of Droplets on Checkboard-Patterned Surfaces.

Droplet wetting and distortion on flat surfaces with heterogeneous wettability are studied using the 3D Shan-Chen pseudopotential multiphase lattice Boltzmann model (LBM). The contact angles are compared with the Cassie mode, which predicts an apparent contact angle for flat surfaces with different wetting properties, where the droplet size is large compared to the size of the heterogeneity. In this study, the surface studied consists in a regular checkboard pattern with two different Young's contact angles (hydrophilic and hydrophobic) and equal surface fraction. The droplet size and patch size of the checkboard are varied beyond the limit where Cassie's equation is valid. A critical ratio of patch size to droplet radius is found below which the apparent contact angle follows the Cassie mode. Above the critical value, the droplet shape changes from a spherical cap to a more distorted form, and no single contact angle can be determined. The local contact angles are found to vary along the contact line between minimum and maximum values. The droplet is found to wet preferentially the hydrophilic region, and the wetted area fraction of the hydrophilic region increases quasi-linearly with the ratio between patch and droplet sizes. We propose a new equation beyond the critical ratio, defining an equivalent contact angle, where the wetted area fractions are used as weighting coefficients for the maximum and minimum local contact angles. This equivalent contact angle is found to equal Cassie's contact angle.

Energy Budget of Liquid Drop Impact at Maximum Spreading: Numerical Simulations and Experiments.

The maximum spreading of an impinging droplet on a rigid surface is studied for low to high impact velocity, until the droplet starts splashing. We investigate experimentally and numerically the role of liquid properties, such as surface tension and viscosity, on drop impact using three liquids. It is found that the use of the experimental dynamic contact angle at maximum spreading in the Kistler model, which is used as a boundary condition for the CFD-VOF calculation, gives good agreement between experimental and numerical results. Analytical models commonly used to predict the boundary layer thickness and time at maximum spreading are found to be less correct, meaning that energy balance models relying on these relations have to be considered with care. The time of maximum spreading is found to depend on both the impact velocity and surface tension, and neither dependency is predicted correctly in common analytical models. The relative proportion of the viscous dissipation in the total energy budget increases with impact velocity with respect to surface energy. At high impact velocity, the contribution of surface energy, even before splashing, is still substantial, meaning that both surface energy and viscous dissipation have to be taken into account, and scaling laws depending only on viscous dissipation do not apply. At low impact velocity, viscous dissipation seems to play an important role in low-surface-tension liquids such as ethanol.

Modeling the Maximum Spreading of Liquid Droplets Impacting Wetting and Nonwetting Surfaces.

Droplet impact has been imaged on different rigid, smooth, and rough substrates for three liquids with different viscosity and surface tension, with special attention to the lower impact velocity range. Of all studied parameters, only surface tension and viscosity, thus the liquid properties, clearly play a role in terms of the attained maximum spreading ratio of the impacting droplet. Surface roughness and type of surface (steel, aluminum, and parafilm) slightly affect the dynamic wettability and maximum spreading at low impact velocity. The dynamic contact angle at maximum spreading has been identified to properly characterize this dynamic spreading process, especially at low impact velocity where dynamic wetting plays an important role. The dynamic contact angle is found to be generally higher than the equilibrium contact angle, showing that statically wetting surfaces can become less wetting or even nonwetting under dynamic droplet impact. An improved energy balance model for maximum spreading ratio is proposed based on a correct analytical modeling of the time at maximum spreading, which determines the viscous dissipation. Experiments show that the time at maximum spreading decreases with impact velocity depending on the surface tension of the liquid, and a scaling with maximum spreading diameter and surface tension is proposed. A second improvement is based on the use of the dynamic contact angle at maximum spreading, instead of quasi-static contact angles, to describe the dynamic wetting process at low impact velocity. This improved model showed good agreement compared to experiments for the maximum spreading ratio versus impact velocity for different liquids, and a better prediction compared to other models in literature. In particular, scaling according to We(1/2) is found invalid for low velocities, since the curves bend over to higher maximum spreading ratios due to the dynamic wetting process.

Water diffusion in amorphous hydrophilic systems: a stop and go process.

The diffusion of H2O in three amorphous polymer-H2O systems is studied as a function of H2O content using molecular dynamics. A picture of H2O molecule motion comprising alternating steps of being bound at an adsorption site ("stop") and moving ("go") emerges. This picture is made quantitative. The bound time, frequency of stop-go steps, and tortuosity all decrease with H2O content. Fourier analysis of particle motion during bound time segments provides a measure of an attempt frequency that is connected quantitatively to the bound time and an activation energy of a hydrogen bond. For increasing H2O content, the polymer-H2O systems swell, leading to an increase in the diffusion coefficient and porosity and a decrease in activation energy.

Water Adsorption in Wood Microfibril-Hemicellulose System: Role of the Crystalline-Amorphous Interface.

A two-phase model of a wood microfibril consisting of crystalline cellulose and amorphous hemicellulose is investigated with molecular dynamics in full range of sorption to understand the molecular origin of swelling and weakening of wood. Water is adsorbed in hemicellulose, and an excess of sorption is found at the interface, while no sorption occurs within cellulose. Water molecules adsorbed on the interface push away polymer chains, forcing the two phases to separate and causing breaking of h-bonds, particularly pronounced on the interface. Existence of two different regions in moisture response is demonstrated. At low moisture content, water is uniformly adsorbed within hemicellulose, breaking a small amount of hydrogen bonds. Microfibril does not swell, and the porosity does not change. As moisture content increases, water is adsorbed preferentially at the interface, which leads to additional swelling and porosity increase at the interface. Young's and shear moduli decrease importantly due to breaking of h-bonds and screening of the long-range interactions.

Quantitative neutron imaging of water distribution, venation network and sap flow in leaves.

MAIN CONCLUSION: Quantitative neutron imaging is a promising technique to investigate leaf water flow and transpiration in real time and has perspectives towards studies of plant response to environmental conditions and plant water stress. The leaf hydraulic architecture is a key determinant of plant sap transport and plant-atmosphere exchange processes. Non-destructive imaging with neutrons shows large potential for unveiling the complex internal features of the venation network and the transport therein. However, it was only used for two-dimensional imaging without addressing flow dynamics and was still unsuccessful in accurate quantification of the amount of water. Quantitative neutron imaging was used to investigate, for the first time, the water distribution in veins and lamina, the three-dimensional venation architecture and sap flow dynamics in leaves. The latter was visualised using D2O as a contrast liquid. A high dynamic resolution was obtained by using cold neutrons and imaging relied on radiography (2D) as well as tomography (3D). The principle of the technique was shown for detached leaves, but can be applied to in vivo leaves as well. The venation network architecture and the water distribution in the veins and lamina unveiled clear differences between plant species. The leaf water content could be successfully quantified, though still included the contribution of the leaf dry matter. The flow measurements exposed the hierarchical structure of the water transport pathways, and an accurate quantification of the absolute amount of water uptake in the leaf was possible. Particular advantages of neutron imaging, as compared to X-ray imaging, were identified. Quantitative neutron imaging is a promising technique to investigate leaf water flow and transpiration in real time and has perspectives towards studies of plant response to environmental conditions and plant water stress.

Cross-scale modelling of transpiration from stomata via the leaf boundary layer.

BACKGROUND AND AIMS: Leaf transpiration is a key parameter for understanding land surface-climate interactions, plant stress and plant structure­function relationships. Transpiration takes place at the microscale level, namely via stomata that are distributed discretely over the leaf surface with a very low surface coverage (approx. 0·2-5%). The present study aims to shed more light on the dependency of the leaf boundary-layer conductance (BLC) on stomatal surface coverage and air speed. METHODS: An innovative three-dimensional cross-scale modelling approach was applied to investigate convective mass transport from leaves, using computational fluid dynamics. The gap between stomatal and leaf scale was bridged by including all these scales in the same computational model (10⁻5-10⁻¹ m), which implies explicitly modelling individual stomata. KEY RESULTS: BLC was strongly dependent on stomatal surface coverage and air speed. Leaf BLC at low surface coverage ratios (CR), typical for stomata, was still relatively high, compared with BLC of a fully wet leaf (hypothetical CR of 100%). Nevertheless, these conventional BLCs (CR of 100%), as obtained from experiments or simulations on leaf models, were found to overpredict the convective exchange. In addition, small variations in stomatal CR were found to result in large variations in BLCs. Furthermore, stomata of a certain size exhibited a higher mass transfer rate at lower CRs. CONCLUSIONS: The proposed cross-scale modelling approach allows us to increase our understanding of transpiration at the sub-leaf level as well as the boundary-layer microclimate in a way currently not feasible experimentally. The influence of stomatal size, aperture and surface density, and also flow-field parameters can be studied using the model, and prospects for further improvement of the model are presented. An important conclusion of the study is that existing measures of conductances (e.g. from artificial leaves) can be significantly erroneous because they do not account for microscopic stomata, but instead assume a uniform distribution of evaporation such as found for a fully-wet leaf. The model output can be used to correct or upgrade existing BLCs or to feed into higher-scale models, for example within a multiscale framework.

A plant cell division algorithm based on cell biomechanics and ellipse-fitting.

BACKGROUND AND AIMS: The importance of cell division models in cellular pattern studies has been acknowledged since the 19th century. Most of the available models developed to date are limited to symmetric cell division with isotropic growth. Often, the actual growth of the cell wall is either not considered or is updated intermittently on a separate time scale to the mechanics. This study presents a generic algorithm that accounts for both symmetrically and asymmetrically dividing cells with isotropic and anisotropic growth. Actual growth of the cell wall is simulated simultaneously with the mechanics. METHODS: The cell is considered as a closed, thin-walled structure, maintained in tension by turgor pressure. The cell walls are represented as linear elastic elements that obey Hooke's law. Cell expansion is induced by turgor pressure acting on the yielding cell-wall material. A system of differential equations for the positions and velocities of the cell vertices as well as for the actual growth of the cell wall is established. Readiness to divide is determined based on cell size. An ellipse-fitting algorithm is used to determine the position and orientation of the dividing wall. The cell vertices, walls and cell connectivity are then updated and cell expansion resumes. Comparisons are made with experimental data from the literature. KEY RESULTS: The generic plant cell division algorithm has been implemented successfully. It can handle both symmetrically and asymmetrically dividing cells coupled with isotropic and anisotropic growth modes. Development of the algorithm highlighted the importance of ellipse-fitting to produce randomness (biological variability) even in symmetrically dividing cells. Unlike previous models, a differential equation is formulated for the resting length of the cell wall to simulate actual biological growth and is solved simultaneously with the position and velocity of the vertices. CONCLUSIONS: The algorithm presented can produce different tissues varying in topological and geometrical properties. This flexibility to produce different tissue types gives the model great potential for use in investigations of plant cell division and growth in silico.

Cyclist drag in team pursuit: influence of cyclist sequence, stature, and arm spacing.

In team pursuit, the drag of a group of cyclists riding in a pace line is dependent on several factors, such as anthropometric characteristics (stature) and position of each cyclist as well as the sequence in which they ride. To increase insight in drag reduction mechanisms, the aerodynamic drag of four cyclists riding in a pace line was investigated, using four different cyclists, and for four different sequences. In addition, each sequence was evaluated for two arm spacings. Instead of conventional field or wind tunnel experiments, a validated numerical approach (computational fluid dynamics) was used to evaluate cyclist drag, where the bicycles were not included in the model. The cyclist drag was clearly dependent on his position in the pace line, where second and subsequent positions experienced a drag reduction up to 40%, compared to an individual cyclist. Individual differences in stature and position on the bicycle led to an intercyclist variation of this drag reduction at a specific position in the sequence, but also to a variation of the total drag of the group for different sequences. A larger drag area for the group was found when riding with wider arm spacing. Such numerical studies on cyclists in a pace line are useful for determining the optimal cyclist sequence for team pursuit.