We present measurements on the spontaneous imbibition (capillary rise) of water, a linear hydrocarbon (n-C16H34) and a liquid crystal (8OCB) into the pore space of monolithic, nanoporous Vycor glass (mean pore radius 5 nm). Measurements on the mass uptake of the porous hosts as a function of time, m(t), are in good agreement with the Lucas-Washburn square root of time prediction, typical of imbibition of liquids into porous hosts. The relative capillary rise velocities scale as expected from the bulk fluid parameters.
Based on the capillary pore model (space-charge theory) for combined fluid and ion flow through cylindrical nanopores or nanotubes, we derive the continuum equations modified to include wall slip. We focus on the ionic conductance and streaming conductance, cross-coefficients of relevance for electrokinetic energy conversion and electro-osmotic pumping. We combine the theory with a Langmuir-Stern 1-pK charge regulation boundary condition resulting in a non-monotonic dependence of the cross-coefficients on salt concentration.
We report on the capillary rise of water in three-dimensional networks of hydrophilic silica pores with 3.5nm and 5nm mean radii, respectively (porous Vycor monoliths). We find classical square root of time Lucas-Washburn laws for the imbibition dynamics over the entire capillary rise times of up to 16h investigated. Provided we assume two preadsorbed strongly bound layers of water molecules resting at the silica walls, which corresponds to a negative velocity slip length of -0.5nm for water flow in silica nanopores, we can describe the filling process by a retained fluidity and capillarity of…
When a capillary is inserted into a liquid, the liquid will rapidly flow into it. This phenomenon, well studied and understood on the macroscale, is investigated by Molecular Dynamics simulations for coarse-grained models of nanotubes. Both a simple Lennard-Jones fluid and a model for a polymer melt are considered. In both cases after a transient period (of a few nanoseconds) the meniscus rises according to a $\sqrt{\textrm{time}}$-law. For the polymer melt, however, we find that the capillary flow exhibits a slip length $δ$, comparable in size with the nanotube radius $R$. We show that a cons…
Capillary filling dynamics of liquid n-tetracosane (n-C24H50) in a network of cylindrical pores with 7 and 10 nm mean diameter in monolithic silica glass (Vycor) exhibit an abrupt temperature-slope change at Ts=54 deg C, ~4 deg C above bulk and ~16 deg C, 8 deg C, respectively, above pore freezing. It can be traced to a sudden inversion of the surface tension's T slope, and thus to a decrease in surface entropy at the advancing pore menisci, characteristic of the formation of a single solid monolayer of rectified molecules, known as surface freezing from macroscopic, quiescent tetracosane melt…
The capillary flow of a ferrofluid in a single cylindrical capillary tube and through a sandy porous medium under the action of a non-uniform magnetic field is studied experimentally. The dynamics of the capillary rise and the static case have been considered. It has been shown that the non-uniform magnetic field with upward directed gradient accelerates the capillary rise; contrary, the non-uniform magnetic field with downward directed gradient decelerates the capillary rise. Time dependences of the ferrofluid height and maximum reachable height of ferrofluid have been analyzed. The method of…
Carbonates are highly heterogeneous formations with large variations in pore size distribution and pore space topology, which results in complex multiphase flow behavior. Here we investigate the spontaneous imbibition behavior of fluids in vuggy carbonates. Glass beads of 1.0 mm diameter, with dissolvable inclusions, are sintered to form multiple configurations of heterogeneous vuggy core with variations in matrix porosity, vug size, vug spatial location, and number of vugs. The core fabrication process is repeatable and allows the impact of vug textural properties to be investigated in a cont…
The anomalous dynamics of capillary rise in a porous medium discovered experimentally more than a decade ago (Delker et al., Phys. Rev. Lett. 76 (1996) 2902) is described. The developed theory is based on considering the principal modes of motion of the menisci that collectively form the wetting front on the Darcy scale. These modes, which include (i) dynamic wetting mode, (ii) threshold mode and (iii) interface de-pinning process, are incorporated into the boundary conditions for the bulk equations formulated in the regular framework of continuum mechanics of porous media, thus allowing one t…
Capillary driven flow is a famous problem in fluid dynamics which dates back to Leonardo da Vinci. In this paper, we apply an analytic approximation method for highly nonlinear problem, namely the homotopy analysis method (HAM), to a model of the meniscus movement in a uniform vertical circular tube. Convergent explicit series solution is successfully obtained. Our results agree well with the numerical results given by the symbolic computing software Mathematica using six-order Runge-Kutta methods. More importantly, our analytic solution is valid in the whole region of physical parameters, and…
Liquid flow propelled by capillary forces is one of the most important transport mechanisms in porous environments. It is governed by a fascinating interplay of interfacial, viscous drag as well as gravitational forces which liquids encounter upon invasion into geometries with often complex topologies, such as capillary networks of trees or interconnected fractures in soils and ice. Here, we present fundamentals, concepts and an experimental, gravimetric study on the capillarity-driven invasion dynamics of liquids in networks of pores a few nanometers across in monolithic, nanoporous silica gl…
Capillary invasion of a liquid into an empty tube, which is called capillary rise when the tube axis is in the vertical direction, is one of the fundamental phenomena representing capillary effects. Usually, the tube is actually filled with another pre-existing fluid, air, whose viscosity and inertia can be practically neglected. In this study, we considered the effect of the pre-existing fluid, when its viscosity is non-negligible, in a horizontally geometry. This geometry is free from gravity and thus simpler than the geometry of capillary rise. We observed the dynamics when a capillary tube…
We present gravimetrical and optical imaging experiments on the capillarity-driven imbibition of silicone oils in monolithic silica glasses traversed by 3D networks of pores (mesoporous Vycor glass with 6.5 nm or 10 nm pore diameters). As evidenced by a robust square-root-of-time Lucas-Washburn (L-W) filling kinetics, the capillary rise is governed by a balance of capillarity and viscous drag forces in the absence of inertia and gravitational effects over the entire experimental times studied, ranging from a few seconds up to 10 days. A video on the infiltration process corroborates a collecti…
The surface free energy, or surface tension, of a liquid interface gives rise to a pressure jump when the interface is curved. Here we show that a similar capillary pressure arises at the interface of soft solids. We present experimental evidence that immersion of a thin elastomeric wire into a liquid induces a substantial elastic compression due to the solid capillary pressure at the bottom. We quantitatively determine the effective surface tension from the elastic displacement field, and find a value comparable to the liquid-vapor surface tension. Most importantly, these results also reveal …
Wetting of surfaces with porous coating is relevant for a wide variety of technical applications, such as printing technologies and heat transfer enhancement. Imbibition and evaporation of liquids on surfaces covered with porous layers are responsible for significant improvement of cooling efficiency during drop impact cooling and flow boiling on such surfaces. Up to now, no reliable model exists which is able to predict the kinetics of imbibition coupled with evaporation on surfaces with porous coatings. In this work we consider one of possible mechanisms of imbibition on a substrate covered …
Liquid-Nitrogen Micropillar-Wick Cooling for Cryogenic Electronics: A Numerical Study of Thermal Performance and Capillary Dry-Out Limits
Fraunhofer Institute for Photonic Microsystems IPMS（弗劳恩霍夫光子微系统研究所）；Institute of Applied Physics, TU Dresden（德累斯顿工业大学应用物理研究所）；Keio University（庆应义塾大学）；ctd.qmat: Dresden-Würzburg Cluster of Excellence—EXC 2147, TU Dresden（德累斯顿-维尔茨堡卓越集群 ctd.qmat（TU德累斯顿））
We present gravimetrical, optical, and neutron imaging measurements of the capillarity-driven infiltration of mesoporous silica glass by hydrocarbons. Square-root-of-time Lucas-Washburn invasion kinetics are found for linear alkanes from n-decane (C10) to n-hexacontane (C60) and for squalane, a branched alkane, in porous Vycor with 6.5 nm or 10 nm pore diameter, respectively. Humidity-dependent experiments allow us to study the influence on the imbibition kinetics of water layers adsorbed on the pore walls. Except for the longest molecule studied, C60, the invasion kinetics can be described by…
The problem of two-phase flow in straight capillaries of polygonal cross section displays many of the dynamic characteristics of rapid interfacial motions associated with pore-scale displacements in porous media. Fluid inertia is known to be important in these displacements but is usually ignored in network models commonly used to predict macroscopic flow properties. This study presents a numerical model for two-phase flow which describes the spatial and temporal evolution of the interface between the fluids. The model is based on an averaged Navier-Stokes equation and is shown to be successfu…
Capillary phenomena are involved in many industrial processes, especially those dealing with composite manufacturing. However, their modelling is still challenging. Therefore, a finite element setting is proposed to better investigate this complex issue. The variational formulation of a liquid-air Stokes system is established, while the solid substrate is described through boundary conditions. Expressing the weak form of Laplace's law over liquid-air, liquid-solid and air-solid interfaces, leads to a natural enforcement of the mechanical equilibrium over the wetting line, without imposing expl…
A wetting liquid is driven through a thin gap due to surface tension and when the gap boundaries are elastic, the liquid deforms the gap as it rises. But when the fluid boundaries are also permeable (or poroelastic), the liquid can permeate the boundaries as the fluid rises and change their properties, for example by swelling and softening, thereby altering the dynamics of the rise. In this paper, we study the dynamics of capillary rise between two poroelastic sheets to understand the effects of boundary permeability and softening. We find that if the bending rigidity of sheets is reduced, due…
Spontaneous imbibition enables the elegant propelling of nano-flows because of the dominance of capillarity at small length scales. The imbibition kinetics are, however, solely determined by the static geometry of the porous host, the capillarity, and the fluidity of the imbibed liquid. This makes active control particularly challenging. Here, we show for aqueous electrolyte imbibition in nanoporous gold that the fluid flow can be reversibly switched on and off through electric potential control of the solid-liquid interfacial tension, i.e. we can accelerate the imbibition front, stop it, and …
We study the meniscus on the outside of a small spherical particle with radius $R$ at a liquid-vapor interface. The liquid is confined in a cylindrical container with a finite radius $L$ and has a contact angle $π/2$ at the container surface. The center of the particle is placed at various heights along the central axis of the container. By varying $L$, we are able to systematically study the crossover of the meniscus from nanometer to macroscopic scales. The meniscus rise or depression on the particle is found to grow as $\ln (2L/R)$ when $R\ll L\ll κ^{-1}$ with $κ^{-1}$ being the capillary l…
In this fluid dynamics video we show capillary rise experiments with diethyl ether in short tubes. The height of each short tube is less than the maximum height the liquid can achieve, and therefore the liquid reaches the top of the tube while still rising. Over a narrow range of heights, the ether bulges out from the top of the tube and spreads onto the external wall.
Liquid-infused membranes inspired by slippery liquid-infused porous surfaces (SLIPS) have been recently introduced to membrane technology. The gating mechanism of these membranes is expected to give rise to anti-fouling properties and multi-phase transport capabilities. However, the long-term retention of the infusion liquid has not yet been explored. To address this issue, we investigate the retention of the infusion liquid in slippery liquid-infused membranes (SLIMs) via liquid-liquid displacement porometry (LLDP) experiments combined with microscopic observations of the displacement mechani…
In this paper we reveal the physics underlying the conditions needed for the generation of emulsions composed of uniformly sized drops of micrometric or submicrometric diameters when two immiscible streams flow in parallel under the so-called tip streaming regime after Suryo & Basaran (2006). Indeed, when inertial effects in both liquid streams are negligible, the inner to outer flow-rate and viscosity ratios are small enough and the capillary number is above an experimentally determined threshold which is predicted by our theoretical results with small relative errors, a steady micron-sized j…
We report an experimental and theoretical study of the global stability and nonlinear dynamics of vertical jets of viscous liquid confined in the axial direction due to their impact on a bath of the same liquid. Previous works demonstrated that in the absence of axial confinement the steady liquid thread becomes unstable due to an axisymmetric global mode for values of the flow rate, $Q$, below a certain critical value, $Q_c$, giving rise to oscillations of increasing amplitude that finally lead to a dripping regime (Sauter & Buggisch, J. Fluid Mech., 2005; Rubio-Rubio et al., J. Fluid Mech., …
When a macroscopic droplet spreads, a thin precursor film of liquid moves ahead of the advancing liquid-solid-vapor contact line. Whereas this phenomenon has been explored extensively for planar solid substrates, its presence in nanostructured geometries has barely been studied so far, despite its importance for many natural and technological fluid transport processes. Here we use porous photonic crystals in silicon to resolve by light interferometry capillarity-driven spreading of liquid fronts in pores of few nanometers in radius. Upon spatiotemporal rescaling the fluid profiles collapse on …
