Droplet spreading and capillary imbibition in a porous medium: A coupled IB-VOF method based numerical study

Abstract

We investigate the dynamics of a liquid droplet in contact with a surface of a porous structure by means of the pore-scale level, fully resolved numerical simulations. The geometrical details of the solid porous matrix are resolved by a sharp interface immersed boundary method on a Cartesian computational grid, whereas the motion of the gas-liquid interface is tracked by a mass conservative volume of fluid method. The numerical simulations are performed considering a model porous structure that is approximated by a 3D cubical scaffold with cylindrical struts. The effect of the porosity and the equilibrium contact angle (between the gas-liquid interface and the solid struts) on the spreading behavior, liquid imbibition, and apparent contact angle (between the gas-liquid interface and the porous base) are studied. We also perform several simulations for droplet spreading on a flat surface as a reference case. Gas-liquid systems of the Laplace number, La = 45 and La = 144 × 103 are considered neglecting the effect of gravity. We report the time exponent (n) and pre-factor (C) of the power law describing the evolution of the spreading diameter (S = Ctn) for different equilibrium contact angles and porosity. Our simulations reveal that the apparent or macroscopic contact angle varies linearly with the equilibrium contact angle and increases with porosity. Not necessarily for all the wetting porous structures, a continuous capillary drainage occurs, and we find that the rate of the capillary drainage very much depends on the fluid inertia. At La = 144 × 103, numerically we capture the capillary wave induced pinch-off and daughter droplet ejection. We observe that on the porous structure the pinch-off is weak compared to that on a flat plate.

Free vibration predicted using forced oscillation in the lock-in region

“…34 IBM has been used extensively to study the interaction between the structure and fluid flow, and a latest application is, for example, that on the fluid-solid "sharp" interface. 35 IBM treats structure-fluid boundary by replacing the body surface with a layer of distributed force g into Eq. 6 36 or…”

Radial Imbibition in Paper under Temperature Differences

“…Using the linear relations (8) and (9) in Equation (7) allows us to find the motion equation in the form:…”

“…In the context of the imbibition under temperature gradients, the physical parameters of the problem t c (Equation (11)) and A and B (Equation (12)) have specific meanings: t c is the viscous-capillary time indicating that the initial imbibition radius at τ = 0 is finite [8], and it also involves the structure of the porous medium through d; A is the non-dimensional relative variation of viscosity with temperature, and B is the dimensionless relative variation of the surface tension with temperature. Later on, we will notice the dynamical changes produced by A and B.…”

“…The aim of this work is to study imbibition, i.e., the spontaneous capillary penetration of a viscous liquid into a homogeneous, thin, circular, dry porous medium to which has been imposed previously a temperature difference ∆T along the radial direction, r. Isothermal imbibition from an unlimited liquid reservoir has received attention due its important applications in paper chromatography [1,2], printing ink [3], paper absorption [1,[4][5][6], and aerosol research [5,7]. In the latter case, the spreading of liquid drops into a porous substrate is of much interest because it corresponds to radial imbibition from finite liquid volumes [5,7,8].…”

“…Isothermal radial imbibition in horizontal porous samples has been studied, for example, in samples of paper [1,5,6], in 3D cubical scaffold with cylindrical struts [8], and in thin Hele-Shaw cells filled with granular material [9]. Moreover, studies of radial imbibition in Hele-Shaw cells following a one-dimensional approach (without granular material) yield a similar equation for the advance front, as a function of time [4,10], as those reported for thin radial porous samples.…”