Conductances between confined rough walls

Two- and three-dimensional creeping flows and diffusion transport through constricted and possibly rough surfaces are studied. Asymptotic expansions of conductances are derived as functions of the constriction local geometry. The validity range of the proposed theoretical approximations is explored through a comparison either with available exact results for specific two-dimensional aperture fields or with direct numerical computations for general three-dimensional geometries. The large validity range of the analytical expressions proposed for the hydraulic conductivity (and to a lesser extent for the electrical conductivity) opens up interesting perspectives for the simulation of flows in highly complicated geometries with a large number of constrictions

Quasi-static liquid–air drainage in narrow channels with variations in the gap

This paper studies the shape of an air bubble quasi-statically flowing in the longitudinal direction of narrow channels. Two bottom topographies are treated, i.e., linear and quadratic variations of the gap along the transverse direction. This work analyses the main characteristics of the gas–liquid interface with respect to the wedge aspect ratio. From the convergence of asymptotic, numerical and experimental analyses, we found simple dependences for the finger width and total curvature as a function of channel aspect ratio. These results provide simple and general expressions for the pressure drop needed to overcome capillary forces and push the air finger inside the channel

Roles of gas in capillary filling of nanoslits

Control and understanding of flows inside fabricated nanochannels is rich in potential applications, but nanoscale physics of fluids remains to be clarified even for the simple case of spontaneous capillary filling. This paper reports an experimental and modelling investigation of the role of gas on the capillary filling kinetics slowdown in nanoslits (depth going from 20 nm to 400 nm) compared to Washburn's prediction. First, the role of gas through the usually observed trapped bubbles during a nanoslits capillary filling is analysed thanks to experiments realized with water, ethanol and silicone oil in siliconglass nanochannels. Bubbles are trapped only when slit depth is below a liquid-dependent threshold. This is interpreted as possible contact line pinning strength varying with wettability. Stagnant trapped bubbles lifetime is investigated for the three liquids used. Experimental results show that bubbles are first compressed because of the increasing local liquid pressure. Once the gas bubble pressure is sufficiently high, gas dissolution induces the final bubble collapse. Influence of the bubbles' presence on the capillary filling kinetics is analysed by estimating viscous resistance induced by the bubbles using an effective medium approach (Brinkman approximation). Surprisingly, the bubbles' presence is found to have a very minor effect on nanoslits capillary filling kinetics. Second, the transient gas pressure profile between the advancing meniscus and the channel exit is computed numerically taking into account gas compressibility. A non-negligible over-pressure ahead of the meniscus is found for nano-scale slit capillary filling. Considering the possible presence of precursor films, reducing cross-section for gas flow, leads to a capillary filling kinetics slowdown comparable to the ones measured experimentally

Nanobubbles and gas dynamics during capillary filling of nanochannels

This paper focuses on capillary filling at the nanoscale where deviations to the Washburn’s classical theory are observed. Imbibition experiments in microfabricated silicon-glass nanochannels with low aspect ratio (width >> depth and depths going from 400 nm down to 20 nm) are performed for several liquids. In all cases, as predicted by the Washburn’s law, liquid invasion front location evolves as the square root of time. However, filling kinetics slowdown compared to the Washburn’s law is measured in nanochannels for depths below ~ 100 nm. Furthermore, below a liquid-dependent depth threshold, we observe spontaneous bubbles formation behind the advancing meniscus. Bubbles dynamics (formation conditions and lifetime) are analyzed thanks to our experimental data involving several liquids and nanochannels depths. Viscous resistance induced by the bubbles presence is estimated using an effective medium approach. Conjointly, gas flow ahead of the advancing meniscus is modeled considering the gas as viscous and compressible. Influence of these effects on the filling kinetics is discussed

Migration of finite sized particles in a laminar square channel flow from low to high Reynolds numbers

The migration of neutrally buoyant finite sized particles in a Newtonian square channel flow is investigated in the limit of very low solid volumetric concentration, within a wide range of channel Reynolds numbers Re = [0.07-120]. In situ microscope measurements of particle distributions, taken far from the channel inlet (at a distance several thousand times the channel height), revealed that particles are preferentially located near the channel walls at Re > 10 and near the channel center at Re 10). In this regime, we show that (i) the particle undergoes cross-streamline migration followed by a cross-lateral migration (parallel to the wall) in agreement with previous observations, and (ii) the stable equilibrium positions are located at the midline of the channel faces while the diagonal equilibrium positions are unstable. At low flow inertia, the first instants of the numerical simulations (carried at Re = O(1)) reveal that the cross-streamline migration of a single particle is oriented towards the channel wall, suggesting that the particle preferential positions around the channel center, observed in the experiments, are rather due to multi-body interactions

Three Periods of Drying of a Single Square Capillary Tube

The drying kinetics of a porous medium is classically described in three main periods, which depend on the interplay between the external and internal mass transfers during evaporation. The first period is described as essentially depending on the external mass transfer, whereas the third period is dominated by the internal mass transfer. The second period is a crossover period. We show experimentally that a similar drying kinetics can be obtained from a much simpler system owing to the effect of corner liquid films: a capillary tube of square cross section

Locus of first crystals on the evaporative surface of a vertically textured porous medium

The evaporation of a saline solution from a heterogeneous porous medium formed by the assembly of a coarse medium column and a fine medium column is studied numerically. We concentrate on the locus of the formation of first crystals on the evaporative surface from the computation of the ion mass fraction distribution at the surface prior to the efflorescence development. Two basic situations considered in previous works, namely the evaporation–wicking situation and the drying situation are considered. The study makes clear that each situation leads to a markedly different locus of the efflorescence formation, except, however, for very high initial salt concentrations. The study emphasizes the key-role of the velocity field induced in the porous domain in the case of the evaporation–wicking situation. In the case of the drying situation, a key aspect lies in the local increase in the ion mass fraction due to the local desaturation, i.e. the local shrinking of the liquid volume containing the ions

Stagnation Points as Loci of Solute Concentration Extrema at the Evaporative Surface of a Random Porous Medium

Evaporation of a saline solution from a porous medium often leads to the precipitation of salt at the surface of the porous medium. It is commonly observed that the crystallized salt does not form everywhere at the porous medium surface but at some specific locations. This is interpreted at the signature of spatial variations in the salt concentration at the surface of the porous medium prior to the onset of crystallization. We explore numerically the link between the ion concentration spatial variations at the surface and porous medium heterogeneities considering strongly anisotropic short-range correlated permeability Gaussian fields corresponding to a vertical layering perpendicular to the top evaporative surface for the case of the evaporation–wicking situation. It is shown that the ion concentration extrema at the surfaces correspond to stagnation points with minima corresponding to divergent stagnation points and maxima to convergent stagnation points. Counter-intuitively, the ion concentration maxima are shown to correspond to permeability minima. However, the ion concentration absolute maximum does not necessarily always correspond to the permeability absolute minimum. More generally, the study emphasizes the key role played by the impact of heterogeneities on the velocity field induced in the medium by the evaporation process. It is also shown that the number of ion mass fraction maxima at the porous medium surface is generally much lower than the naive prediction based on the number of correlation lengths spanning the medium

Experimental and numerical investigation of two-phase flow in a model of nanoporous medium

1.Motivation / Context 2.Fabrication and procedure 3.Two phase flow in dead end nanochannel

Evaporation-driven growth of large crystallized salt structures in a porous medium

Subflorescence refers to crystallized salt structures that form inside a porous medium. We report a drying experiment revealing major development of subflorescence in the dry region of the porous medium away from the liquid zone. Using a combination of image analyses and numerical computations, we show that the growth is directly correlated to the evaporation flux distribution along the boundary of the growing salt structure. This indicates that the salt is transported into the domain occupied by the salt structure in the porous medium up to the structure periphery, where salt deposition takes place. This is confirmed when a growing salt structure encounters dry subflorescence formed earlier during the drying process. The dry subflorescence is reimbibed and resumes its growth. The analysis also suggests that the solution within the growing subflorescence is in equilibrium with the crystallized salt wall. These results shed light on the growth mechanisms of subflorescence, a phenomenon that can play a fundamental role in several important issues such as carbon dioxide sequestration or salt weathering