Capillary rise and evaporation of a liquid in a corner between a plane and a cylinder: A model of imbibition into a nanofiber mat coating
Noemi Ghillani, Michael Heinz, Tatiana Gambaryan-Roisman
备注：
16 pages, 11 figures Submitted to The European Physical Journal Special Topics, special issue devoted to the Workshop "Challenges in Nanoscale Physics of Wetting Phenomena" which took place in August 2019 in Dresden, Germany
发表信息：
The European Physical Journal Special Topics 229 (2020) 1799-1818
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 by a nanofiber mat. This is the capillary pressure-driven flow in a corner formed between a flat substrate and a fiber attached to it. The shape and the area of the cross-section occupied by the liquid as well as the capillary pressure change along the flow direction. A theoretical/numerical model of simultaneous imbibition and evaporation is developed, in which viscosity, surface tension and evaporation are taken into account. At the beginning of the process the imbibition length is proportional to the square root of time, in agreement with the Lucas-Washburn law. As the influence of evaporation becomes significant, the imbibition rate decreases. The model predictions are compared with experimental data for imbibition of water-ethanol mixtures into nanofiber mat coatings.
The paper deals with the global Kondaurov double porosity model describing a non-equilibrium two-phase immiscible flow in fractured-porous reservoirs when non-equilibrium phenomena occur in the matrix blocks, only. It is shown that the homogenized model can be represented as usual equations of two-phase incompressible immiscible flow, except for the addition of two source terms calculated by a solution to a local problem which is a boundary value problem for a non-equilibrium imbibition equation given in terms of the real saturation and a non-equilibrium parameter.
A deep understanding of two-phase displacement in porous media with permeability contrast is essential for the design and optimisation of enhanced oil recovery processes. In this paper, we investigate the forced imbibition behaviour in two dual-permeability geometries that are of equal permeability contrast. First, a mathematical model is developed for the imbibition in a pore doublet, which shows that the imbibition dynamics can be fully described by the viscosity ratio $λ$ and capillary number $Ca_m$ which creatively incorporates the influence of channel width and length. Through the finite …
During spontaneous imbibition a wetting liquid is drawn into a porous medium by capillary forces. In systems with comparable pore length and diameter, such as paper and sand, the front of the propagating liquid forms a continuous interface. Sections of this interface advance in a highly correlated manner due to an effective surface tension, which restricts front broadening. Here we investigate water imbibition in a nanoporous glass (Vycor) in which the pores are much longer than they are wide. In this case, no continuous liquid-vapor interface with coalesced menisci can form. Anomalously fast …
We describe the imbibition process from a point source into a homogeneous semi-infinite porous material. When body forces are negligible, the advance of the wetting front is driven by capillary pressure and resisted by viscous forces. With the assumption that the wetting front assumes a hemispherical shape, our analytical results show that the absorbed volume flow rate is approximately constant with respect to time, and that the radius of the wetting evolves in time as r \approx t^(1/3). This cube-root law for the long-time dynamics is confirmed by experiments using a packed cell of glass micr…
Heat transport during drop impact onto a heated wall covered with an electrospun nanofiber mat: The influence of wall superheat, impact velocity, and mat thickness
Imbibition, the displacement of a nonwetting fluid by a wetting fluid, plays a central role in diverse energy, environmental, and industrial processes. While this process is typically studied in homogeneous porous media with uniform permeabilities, in many cases, the media have multiple parallel strata of different permeabilities. How such stratification impacts the fluid dynamics of imbibition, as well as the fluid saturation after the wetting fluid breaks through to the end of a given medium, is poorly understood. We address this gap in knowledge by developing an analytical model of imbibiti…
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…
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…
Watercolor or aquarelle is one of the oldest painting methods in which pigments suspended in an aqueous liquid are deposited over a substrate, typically an absorbing material such as paper. The physical processes which lead to pattern formation have not been studied in any depth, in spite of being closely related to flows in other contexts. Identifying and understanding these processes is of imperative importance to restore and preserve watercolor paintings. Here, we report an experimental study of the effect of the pigment concentration and paper humidity on the pattern formation derived from…
We present a mathematical approach to optimize the material distribution for fluid transport in unsaturated porous media. Our benchmark problem is a simplified diaper model as an exemplary liquid absorber. Our model has up to three materials with vastly different properties, which in the reference configuration are arranged in parallel layers. Here, swelling is neglected and the geometry of a swollen diaper is assumed and treated as a porous medium of high porosity. The imbibition process is then simulated by solving an unsaturated flow problem based on Richards' equation. Our aim is to maximi…
Spatial confinement in nanoporous media affects the structure, thermodynamics and mobility of molecular soft matter often markedly. This article reviews thermodynamic equilibrium phenomena, such as physisorption, capillary condensation, crystallisation, self-diffusion, and structural phase transitions as well as selected aspects of the emerging field of spatially confined, non-equilibrium physics, i.e. the rheology of liquids, capillarity-driven flow phenomena, and imbibition front broadening in nanoporous materials. The observations in the nanoscale systems are related to the corresponding bu…
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…
