We present a systematic study of capillary filling for a binary fluid by using a mesoscopic lattice Boltzmann model for immiscible fluids describing a diffusive interface moving at a given contact angle with respect to the walls. The phenomenological way to impose a given contact angle is analysed. Particular attention is given to the case of complete wetting, that is contact angle equal to zero. Numerical results yield quantitative agreement with the theoretical Washburn law, provided that the correct ratio of the dynamic viscosities between the two fluids is used. Finally, the presence of precursor films is experienced and it is shown that these films advance in time with a square-root law but with a different prefactor with respect to the bulk interface.
We study the impact of wall corrugations in microchannels on the process of capillary filling by means of three broadly used methods - Computational Fluid Dynamics (CFD), Lattice-Boltzmann Equations (LBE) and Molecular Dynamics (MD). The numerical results of these approaches are compared and tested against the Concus-Finn (CF) criterion, which predicts pinning of the contact line at rectangular ridges perpendicular to flow for contact angles theta > 45. While for theta = 30, theta = 40 (no flow) and theta = 60 (flow) all methods are found to produce data consistent with the CF criterion, at th…
We theoretically examine the widespread hypothesis of an electro-viscous origin of the increase in apparent viscosity observed in recent experiments on capillary filling of nanochannels. Including Debye-layer corrections to the hydraulic resistance we find that the apparent viscosity reaches a maximum in the mesoscopic regime where the channel height (or more generally the hydraulic radius) is comparable to the screening length. However, for realistic estimates of central parameters, we find that the electro-viscous contribution to the apparent viscosity is at most a 1% effect.
The motion of an air-fluid interface through an irregularly coated capillary is studied by analysing the Lucas-Washburn equation with a random capillary force. The pinning probability goes from zero to a maximum value, as the interface slows down. Under a critical velocity, the distribution of waiting times $τ$ displays a power-law tail $\sim τ^{-2}$ which corresponds to a strongly intermittent dynamics, also observed in experiments. We elaborate a procedure to predict quantities of experimental interest, such as the average interface trajectory and the distribution of pinning lengths.
The agglomeration of particles caused by the formation of capillary bridges has a decisive impact on the transport properties of a variety of at a first sight very different systems such as capillary suspensions, fluidized beds in chemical reactors, or even sand castles. Here, we study the connection between the microstructure of the agglomerates and the rheology of fluidized suspensions using a coupled lattice Boltzmann and discrete element method approach. We address the influence of the shear rate, the secondary fluid surface tension, and the suspending liquid viscosity. The presence of cap…
We present hydrokinetic Lattice Boltzmann and Molecular Dynamics simulations of capillary filling of high-wetting fluids in nano-channels, which provide clear evidence of the formation of thin precursor films, moving ahead of the main capillary front. The dynamics of the precursor films is found to obey the Lucas-Washburn law as the main capillary front, z2(t) proportional to t, although with a larger prefactor, which we find to take the same value for both geometries under inspection. Both hydrokinetic and Molecular Dynamics approaches indicate a precursor film thickness of the order of one t…
We present a regularized version of the color gradient lattice Boltzmann (LB) scheme for the simulation of droplet formation in microfluidic devices of experimental relevance. The regularized version is shown to provide computationally efficient access to Capillary number regimes relevant to droplet generation via microfluidic devices, such as flow-focusers and the more recent microfluidic step emulsifier devices.
This article discusses the way the standard description of capillary filling dynamics has to be modified to account for liquid/solid slip in nanometric pores. It focuses in particular on the case of a large slip length compared to the pore size. It is shown that the liquid viscosity does not play a role, and that the flow is only controlled by the friction coefficient of the liquid at the wall. Moreover in the Washburn regime, the filling velocity does not depend on the tube radius. Finally, molecular dynamics simulations suggest that this standard description fails to describe the early stage…
We investigate the dynamics of capillary filling using two lattice Boltzmann schemes: a liquid-gas model and a binary model. The simulation results are compared to the well-known Washburn's law, which predicts that the filled length of the capillary scales with time as $l \propto t^{1/2}$. We find that the liquid-gas model does not reproduce Washburn's law due to condensation of the gas phase at the interface, which causes the asymptotic behaviour of the capillary penetration to be faster than $t^{1/2}. The binary model, on the other hand, captures the correct scaling behaviour when the viscos…
Liquid capillary-bridge formation between solid particles has a critical influence on the rheological properties of granular materials and, in particular, on the efficiency of fluidized bed reactors. The available analytical and semi-analytical methods have inherent limitations, and often do not cover important aspects, like the presence of non-axisymmetric bridges. Here, we conduct numerical simulations of the capillary bridge formation between equally and unequally-sized solid particles using the lattice Boltzmann method, and provide an assessment of the accuracy of different families of ana…
The dynamics of capillary filling in the presence of chemically coated heterogeneous boundaries is investigated, both theoretically and numerically. In particular, by mapping the equations of front motion onto the dynamics of a dissipative driven oscillator, an analytical criterion for front pinning is derived, under the condition of diluteness of the coating spots. The criterion is tested against two dimensional Lattice Boltzmann simulations, and found to provide satisfactory agreement as long as the width of the front interface remains much thinner than the typical heterogeneity scale of the…
We propose a combined computational approach based on the multi-phase-field and the lattice Boltzmann method for the motion of solid particles under the action of capillary forces. The accuracy of the method is analyzed by comparison with the analytic solutions for the motion of two parallel plates of finite extension connected by a capillary bridge. The method is then used to investigate the dynamics of multiple spherical solid bodies connected via capillary bridges. The amount of liquid connecting the spheres is varied, and the influence of the resulting liquid-morphology on their dynamics i…
We show how the capillary filling of microchannels is affected by posts or ridges on the sides of the channels. Ridges perpendicular to the flow direction introduce contact line pinning which slows, or sometimes prevents, filling; whereas ridges parallel to the flow provide extra surface which may enhances filling. Patterning the microchannel surface with square posts has little effect on the ability of a channel to fill for equilibrium contact angle $θ_e \lesssim 30^{\mathrm{o}}$. For $θ_e \gtrsim 60^{\mathrm{o}}$, however, even a small number of posts can pin the advancing liquid front.
This work revisits capillary filling dynamics in the regime of nanometric to subnanometric channels. Using molecular dynamics simulations of water in carbon nanotubes, we show that for tube radii below one nanometer, both the filling velocity and the Jurin rise vary non-monotonically with the tube radius. Strikingly, with fixed chemical surface properties, this leads to confinement-induced reversal of the tube wettability from hydrophilic to hydrophobic for specific values of the radius. By comparing with a model liquid metal, we show that these effects are not specific to water. Using complem…
When a very thin capillary is inserted into a liquid, the liquid is sucked into it: this imbibition process is controlled by a balance of capillary and drag forces, which are hard to quantify experimentally, in particularly considering flow on the nanoscale. By computer experiments using a generic coarse-grained model, it is shown that an analysis of imbibition forced by a controllable external pressure quantifies relevant physical parameter such as the Laplace pressure, Darcy's permeability, effective pore radius, effective viscosity, dynamic contact angle and slip length of the fluid flowing…
The merging of immiscible drops differs significantly from the merging of miscible drops due to the formation of a liquid-liquid interface between drops. The immiscibility requires the formation of a four-phase contact point, where the drops, the gas and the substrate meet. We show that this point has its own unique dynamics, never studied beforehand. For very different scenarios, the propagation distance of this point follows scales with time like t^{0.5}. A model balancing the driving and dissipative forces agrees with our experiments.
We investigate the interplay of thermophoretic force and interfacial tension on the capillary filling dynamics of a Newtonian nanofluid in a microchannel. In our model, we also consider an intricate thermofluidic coupling by taking the temperature dependence of viscosity aptly into account. This, in turn, determines the evolution of the viscous resistive force as the capillary front progresses, and presents an involved inter-connection between the driving thermophoretic force and the viscous resistive force. The two distinct regimes of particle transport in a fluid medium, delineated by partic…
In this work we want to simulate with the Lattice-Boltzmann method in 2D the capillary infiltration into porous structures obtained from the packing of particles. The experimental problem motivating our work is the densification of carbon preforms by reactive melt infiltration. The aim is to determine optimization principles for the manufacturing of high-performance ceramics. Simulations are performed for packings with varying structural properties. Our analysis suggests that the observed slow infiltrations can be ascribed to interface dynamics. Pinning represents the primary factor retarding …
The Washburn law has always played a critical role for ceramics. In the microscale, surface forces take over volume forces and the phenomenon of spontaneous infiltration in narrow interstices becomes of particular relevance. The Lattice Boltzmann method is applied in order to ascertain the role of surface reaction and subsequent deformation of a single capillary in 2D for the linear Washburn behavior. The proposed investigation is motivated by the problem of reactive infiltration of molten silicon into carbon preforms. This is a complex phenomenon arising from the interplay between fluid flow,…
An improved wetting boundary implementation strategy is proposed based on lattice Boltzmann color-gradient model in this paper. In this strategy, an extra interface force condition is demonstrated based on the diffuse interface assumption and is employed in contact line region. It has been validated by three benchmark problems: static droplet wetting on a flat surface and a curved surface, and dynamic capillary filling. Good performances are shown in all three cases. Relied on the strict validation to our scheme, the viscous fingering phenomenon of immiscible fluids displacement in a two-dimen…
In this article, we show a novel approach to implementing valving action in a dynamically evolving capillary filling process, by exploiting alternating current electrothermal (ACET) mechanism. The surfaces of the top and bottom walls of the capillary are asymmetrically patched with two different wettabilities. Our observations reveal that by exploiting an intricate interplay of the electrothermal effects and interfacial tension modulation, the acceleration-deceleration motion of the interface and interface pinning at specific locations may be delicately tuned. This, in turn, modulates the flow…
It is widely recognized that the structure of porous media is of relevance for a variety of mechanical and physical phenomena. The focus of the present work is on capillarity, a pore-scale process occurring at the micron scale. We attempt to characterize the influence of pore shape for capillary infiltration by means of Lattice Boltzmann simulations in 2D with reactive boundaries leading to surface growth and ultimately to pore closure. The systems under investigation consist of single channels with different simplified morphologies: namely, periodic profiles with sinusoidal, step-shaped and z…
Gas and ion transport in the capillary-skimmer subatmospheric interface of a mass spectrometer, which is typically utilized to separate unevaporated micro-droplets from ions, was studied numerically using a two-step approach spanning multiple gas dynamic regimes. The gas flow in the heated capillary and in the interface was determined by solving numerically the Navier-Stokes equation. The capillary-to-skimmer gas/ion flow was modeled through the solution of the full Boltzmann equation with a force term. The force term, together with calculated aerodynamic drag, determined the ion motion in the…
The moving contact-line problem is of both theoretical and practical interest. The dynamic contact angle changes with the capillary number defined by the contact-line speed, and the correlation also depends on the equilibrium contact angle measured at the static state. This correlation is usually required as an input to the traditional solvers based on the Navier-Stokes-like equations, but it is simulated as an output in the current study using the lattice Boltzmann method (LBM) in a displacement process of two-immiscible fluids. The macroscopic theory and the molecular dynamics (MD) simulatio…
We report on simulations of capillary filling of high-wetting fluids in nano-channels with and without obstacles. We use atomistic (molecular dynamics) and hydrokinetic (lattice-Boltzmann) approaches which point out clear evidence of the formation of thin precursor films, moving ahead of the main capillary front. The dynamics of the precursor films is found to obey a square-root law as the main capillary front, z^2(t) ~ t, although with a larger prefactor, which we find to take the same value for the different geometries (2D-3D) under inspection. The two methods show a quantitative agreement w…
Based on mesoscale lattice Boltzmann (LB) numerical simulations, we investigate the effects of viscoelasticity on the break-up of liquid threads in microfluidic cross-junctions, where droplets are formed by focusing a liquid thread of a dispersed (d) phase into another co-flowing continuous (c) immiscible phase. Working at small Capillary numbers, we investigate the effects of non-Newtonian phases in the transition from droplet formation at the cross-junction (DCJ) to droplet formation downstream of the cross-junction (DC) (Liu $\&$ Zhang, ${\it Phys. ~Fluids.}$ ${\bf 23}$, 082101 (2011)). We …
Electrolyte filling is a time-critical step during battery manufacturing that also affects the battery performance. The underlying physical phenomena during filling mainly occur on the pore scale and are hard to study experimentally. In this paper, a computational approach, i.e.\ the lattice Boltzmann method, is used to study the filling process and corresponding pore-scale phenomena in 3D lithium-ion battery cathodes. The electrolyte flow through the nanoporous binder is simulated using a homogenization approach. Besides the process time, the influence of structural and physico-chemical prope…
We study the forced displacement of a fluid-fluid interface in a three-dimensional channel formed by two parallel solid plates. Using a Lattice-Boltzmann method, we study situations in which a slip velocity arises from diffusion effects near the contact line. The difference between the slip and channel velocities determines whether the interface advances as a meniscus or a thin film of fluid is left adhered to the plates. We find that this effect is controlled by the capillary and Peclet numbers. We estimate the crossover from a meniscus to a thin film and find good agreement with numerical re…
We show that, when a single relaxation time lattice Boltzmann algorithm is used to solve the hydrodynamic equations of a binary fluid for which the two components have different viscosities, strong spurious velocities in the steady state lead to incorrect results for the equilibrium contact angle. We identify the origins of these spurious currents, and demonstrate how the results can be greatly improved by using a lattice Boltzmann method based on a multiple-relaxation-time algorithm. By considering capillary filling we describe the dependence of the advancing contact angle on the interface ve…
The free surface lattice Boltzmann method (FSLBM) is a combination of the hydrodynamic lattice Boltzmann method (LBM) with a volume of fluid (VOF) interface apturing technique for the simulation of incompressible free surface flows. Capillary effects are modeled by extracting the curvature of the interface from the VOF indicator function and imposing a pressure jump at the free boundary. However, obtaining accurate curvature estimates from a VOF description can introduce significant errors. This article reports numerical results for three different surface tension models in standard test cases…
The capillary levelling of cylindrical holes in viscous polystyrene films was studied using atomic force microscopy as well as quantitative analytical scaling arguments based on thin film theory and self-similarity. The relaxation of the holes was shown to consist of two different time regimes: an early regime where opposing sides of the hole do not interact, and a late regime where the hole is filling up. For the latter, the self-similar asymptotic profile was derived analytically and shown to be in excellent agreement with experimental data. Finally, a binary system of two holes in close pro…
The infiltration of molten silicon into carbon preforms is a widespread technique employed in the industry in order to enhance the thermal and mechanical properties of the final ceramic products. A proper understanding of this phenomenon is quite challenging since it stems from the reciprocal action and reaction between fluid flow, the transition to wetting, mass transport, precipitation, surface growth as well as heat transfer. As a result, the exhaustive modeling of such problem is an involved task. Lattice Boltzmann simulations in 2D for capillary infiltration are carried out in the isother…
A numerical method for simulating three-phase flows with moving contact lines on arbitrarily complex surfaces is developed in the framework of lattice Boltzmann method. In this method, the immiscible three-phase flow is modeled through a multiple-relaxation-time color-gradient model, which not only allows for a full range of interfacial tensions but also produces stable outcomes for a wide range of viscosity ratios. A characteristic line model is introduced to implement the wetting boundary condition, which is not only easy to implement but also able to handle arbitrarily complex boundaries wi…
In this paper, a fractional step lattice Boltzmann method is proposed to model two-phase flows with large density differences by solving Cahn-Hilliard phase-field equation and the incompressible Navier-Stokes equations.In order to maintain a hyperbolic tangent property of the interface profile and conserve the volume, an interfacial profile correction term and a flux correction term are added into the original Cahn-Hilliard equation respectively. By using a fractional step scheme, the modified Cahn-Hilliard equation is split into two sub-equations. One is solved in the framework of lattice Bol…
A recent experiment showed that cylindrical segments of water filling a hydrophilic stripe on an otherwise hydrophobic surface display a capillary instability when their volume is increased beyond the critical volume at which their apparent contact angle on the surface reaches ninety degrees (Gau et al., Science, 283, 1999). Surprisingly, the fluid segments did not break up into droplets -- as would be expected for a classical Rayleigh-Plateau instability -- but instead displayed a long-wavelength instability where all excess fluid gathered in a single bulge along each stripe. We consider here…
A lattice Boltzmann method for axisymmetric multiphase flows is presented and validated. The method is capable of accurately modeling flows with variable density. We develop the classic Shan-Chen multiphase model [ Phys. Rev. E 47 1815 (1993)] for axisymmetric flows. The model can be used to efficiently simulate single and multiphase flows. The convergence to the axisymmetric Navier-Stokes equations is demonstrated analytically by means of a Chapmann-Enskog expansion and numerically through several test cases. In particular, the model is benchmarked for its accuracy in reproducing the dynamics…
Different formulations of interfacial force have been adopted in phase-field-based lattice Boltzmann method for two-phase flows. Although they are identical mathematically, their numerical performances may be different due to truncation errors in the discretization. In this paper, four-type formulations of interfacial force available in the literature, namely stress tensor form (STF), chemical potential form (CPF), pressure form (PF) and continuum surface force (CSF) form, are compared and discussed. A series of benchmark problems, including stationary droplet, two merging droplets, Capillary …
We use free energy lattice Boltzmann methods (FRE LBM) to simulate shear and extensional flow of a binary mixture in two and three dimensions. To this end, two classical configurations are digitally twinned, namely a parallel-band device for binary shear flow and a four-roller apparatus for binary extensional flow. The FRE LBM and the test cases are implemented in the open-source C++ framework OpenLB and evaluated for several non-dimensional numbers. Characteristic deformations are captured, where breakup mechanisms occur for critical capillary regimes. Though the known mass leakage for small …
When a suspension dries, the suspending fluid evaporates, leaving behind a dry film composed of the suspended particles. During the final stages of drying, the height of the fluid film on the substrate drops below the particle size, inducing local interface deformations that lead to strong capillary interactions among the particles. Although capillary interactions between rigid particles are well studied, much is still to be understood about the behaviour of soft particles and the role of their softness during the final stages of film drying. Here, we use our recently-introduced numerical meth…
Modeling the transport of deformable capsules under different flow regimens is crucial in a variety of fields, including oil rheology, blood flow and the dispersion of pollutants. The aim of this study is twofold. Firstly, a combined Lattice Boltzmann-Immersed Boundary (LBM-IB) approach is developed for predicting the transport of inertial deformable capsules. A Moving Least Squares (MLS) scheme has been implemented to correlate the pressure, velocity and force fields of the fluid domain with the capsule dynamics. This computational strategy has been named LBM Dynamic IB. Secondly, this strate…
We extend a recently proposed ternary free energy lattice Boltzmann model with high density contrast, by incorporating wetting boundaries at solid walls. The approaches are based on forcing and geometric schemes, with implementations optimised for ternary (and more generally higher order multicomponent) models. Advantages and disadvantages of each method are addressed by performing both static and dynamic tests, including the capillary filling dynamics of a liquid displacing the gas phase, and the self-propelled motion of a train of drops. Furthermore, we measure dynamic angles and show that t…
In this paper, a lattice Boltzmann (LB) model is presented for axisymmetric multiphase flows. Source terms are added to a two-dimensional standard lattice Boltzmann equation (LBE) for multiphase flows such that the emergent dynamics can be transformed into the axisymmetric cylindrical coordinate system. The source terms are temporally and spatially dependent and represent the axisymmetric contribution of the order parameter of fluid phases and inertial, viscous and surface tension forces. A model which is effectively explicit and second order is obtained. This is achieved by taking into accoun…
We present pore-scale simulations of two-phase flows in a reconstructed fibrous porous layer. The three dimensional microstructure of the material, a fuel cell gas diffusion layer, is acquired via X-ray computed tomography and used as input for lattice Boltzmann simulations. We perform a quantitative analysis of the multiphase pore-scale dynamics and we identify the dominant fluid structures governing mass transport. The results show the existence of three different regimes of transport: a fast inertial dynamics at short times, characterised by a compact uniform front, a viscous-capillary regi…
We present a lattice-Boltzmann method that can simulate the coupled hydrodynamics and electrostatics equations of motion of a two-phase fluid as a means to model electrowetting phenomena. Our method has the advantage of modelling the electrostatic fields within the lattice-Boltzmann algorithm itself, eliminating the need for a hybrid method. We validate our method by reproducing the static equilibrium configuration of a droplet subject to an applied voltage and show that the apparent contact angle of the drop depends on the voltage following the Young-Lippmann equation up to contact angles of …
The tumbling to tank-treading (TB-TT) transition for red blood cells (RBCs) has been widely investigated, with a main focus on the effects of the viscosity ratio $λ$ (i.e., the ratio between the viscosities of the fluids inside and outside the membrane) and the shear rate $\dotγ$ applied to the RBC. However, the membrane viscosity $μ_m$ plays a major role in a realistic description of RBC's dynamics, and only a few works have systematically focused on its effects on the TB-TT transition. In this work, we provide a parametric investigation on the effect of membrane viscosity $μ_m$ on the TB-TT …
We report a hybrid numerical method for the solution of the model H fluctuating hydrodynamic equations for binary mixtures. The momentum conservation equations with Landau-Lifshitz stresses are solved using the fluctuating lattice Boltzmann equation while the order parameter conservation equation with Langevin fluxes are solved using the stochastic method of lines. Two methods, based on finite difference and finite volume, are proposed for spatial discretisation of the order parameter equation. Special care is taken to ensure that the fluctuation-dissipation theorem is maintained at the lattic…
We study the dynamics of the interface between two immiscible fluids in contact with a chemically homogeneous moving solid plate. We consider the generic case of two fluids with any viscosity ratio and of a plate moving in either directions (pulled or pushed in the bath). The problem is studied by a combination of two models, namely an extension to finite viscosity ratio of the lubrication theory and a Lattice Boltzmann method. Both methods allow to resolve, in different ways, the viscous singularity at the triple contact between the two fluids and the wall. We find a good agreement between th…
We propose a kinetic framework for single-component non-ideal isothermal flows. Starting from a kinetic model for a non-ideal fluid, we show that under conventional scaling the Navier-Stokes equations with a non-ideal equation of state are recovered in the hydrodynamic limit. A scaling based on the smallness of velocity increments is then introduced, which recovers the full Navier-Stokes-Korteweg equations. The proposed model is realized on a standard lattice and validated on a variety of benchmarks. Through a detailed study of thermodynamic properties including co-existence densities, surface…
We propose a novel approach to the numerical simulation of thin film flows, based on the lattice Boltzmann method. We outline the basic features of the method, show in which limits the expected thin film equations are recovered and perform validation tests. The numerical scheme is applied to the viscous Rayleigh-Taylor instability of a thin film and to the spreading of a sessile drop towards its equilibrium contact angle configuration. We show that the Cox-Voinov law is satisfied, and that the effect of a tunable slip length on the substrate is correctly captured. We address, then, the problem…
Contact angle is an essential physical quantity that characterizes the wettability of a substrate. Although it is widely used in the studies of surface wetting, capillary phenomena and moving contact lines, measuring contact angles in experiments and simulations is still complicated and time-consuming. In this paper, we present an efficient scheme for the real-time and on-the-spot measurement of contact angles on curved wetting surfaces in lattice Boltzmann simulations. The measuring results are in excellent agreement with the theoretical predictions by the spherical cap method without conside…
Porous asphalt (PA) is an open-graded porous material with a porosity of 20%, allowing fast drainage of rain and improving driving and acoustic conditions. However, the high porosity leads to significant contact with water resulting in a shorter life expectancy. To improve the durability and performance of PA, the distribution of water and its residence time have to be understood which entails capturing diverse multiphase phenomena. For these reasons, a numerical study is performed to analyze in detail the fluid transport mechanisms at play in PA, towards estimating the liquid distribution ins…
This study compares the free-surface lattice Boltzmann method (FSLBM) with the conservative Allen-Cahn phase-field lattice Boltzmann method (PFLBM) in their ability to model two-phase flows in which the behavior of the system is dominated by the heavy phase. Both models are introduced and their individual properties, strengths and weaknesses are thoroughly discussed. Six numerical benchmark cases were simulated with both models, including (i) a standing gravity and (ii) capillary wave, (iii) an unconfined rising gas bubble in liquid, (iv) a Taylor bubble in a cylindrical tube, and (v) the vert…
