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 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 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.
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 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 pr…
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…
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…
This is a fluid dynamics video submitted to the Gallery of Fluid Motion of the 63rd Annual Meeting of the American Physical Society Division of Fluid Dynamics. We examine the Landau-Levich flow of a suspension of neutrally buoyant particles within a rotating glass cylinder. This differs from previously investigated systems in that we deal with macroscopic particles which immediately exceed the thickness of the deposited liquid film. Thus, the presence of particles on the liquid-coated wall creates excess surface area, leading to a capillary attraction between particles. In turn, this capillary…
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…
We study numerically and theoretically the gravity-driven flow of a viscous liquid film coating the inner side of a horizontal cylindrical tube and surrounding a shear-free dynamically inert gaseous core. The liquid-gas interface is prone to the Rayleigh-Plateau and Rayleigh-Taylor instabilities. Here, we focus on the limit of low and intermediate Bond numbers, Bo, where the capillary and gravitational forces are comparable and the Rayleigh-Taylor instability is known to be suppressed. We first study the evolution of the axially invariant draining flow, initiating from a uniform film thickness…
In this study we attempt to explore the consequences of surfactant coating on the electrohydrodynamic manipulation of a drop motion in a plane Poiseuielle flow. In addition we consider bulk insoluble surfactants and a linear dependency of the surface tension on the surfactant concentration. Subsequently a double asymptotic perturbation method is used in terms of small electric Reynolds number and capillary number in the limit of a diffusion-dominated surfactant transport mechanism. Also going beyond the widely employed axisymmetric framework, the coupled system of governing differential equati…
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…
In this paper, we depict interfacial electro-thermo-chemical-hydrodynamics of two immiscible fluids in a microchannel with substrates patterned by ribs. The motion of the binary fluids is set by an alternating current electrothermal (ACET) mechanism. Our investigations, based on free-energy-based phase field formalism, reveal that the capillary filling dynamics and the contact line motion are strong functions of the wetting characteristics and geometric parameters of the patterned ribs. Modulation of these parameters alters the surface energy over the rib surface, which, in turn, facilitates t…
The stability of the interface separating two immiscible incompressible fluids of different densities and viscosities is considered in the case of fluids filling a cavity which performs horizontal harmonic oscillation. There exists a simple basic state which corresponds to the unperturbed interface and plane-parallel unsteady counter flows; the properties of this state are examined. A linear stability problem for the interface is formulated and solved a) for both inviscid and b) for both viscous fluids. A transformation is found which reduces the linear stability problem under inviscid approxi…
