Numerical solution of wetting fluid spread into porous media

Abstract

Purpose -The purpose of this paper is to develop a general numerical solution for the wetting fluid spread into porous media that can be used in solving of droplet spread into soils, printing applications, fuel cells, composite processing. Design/methodology/approach -A discrete capillary network model based on micro-force balance is numerically implemented and the flow for an arbitrary capillary number can be solved. At the fluid interface, the boundary condition that accounts for the capillary pressure jump is used. Findings -The wetting fluid spread into porous medium starts as a single-phase flow, and after some particular number of the porous medium characteristic length scales, the multi-phase flow pattern occurs. Hence, in the principal flow direction, the phase content (saturation) decreases, and in the lower limit for the capillary number sufficiently small, the saturation should become constant. This qualitative saturation behavior is observed irrespective of the flow dimensionality, whereas the quantitative results vary for different flow systems.Research limitations/implications -The numerical solution has to be expanded to solve the spread of the fluid in the porous medium after there is no free fluid left at the porous medium surface. Practical implications -It is shown that the multi-phase flow can develop even on a small domain due to the porous medium heterogeneity. Neglecting the medium heterogeneity and flow type can lead to a large error as shown for the droplet spread time in the porous medium. Originality/value -This is believe to be the only paper relating to solving the droplet spread into porous medium as a multi-phase flow problem.

On spread extent of sessile droplet into porous medium: Numerical solution and comparisons with experiments

“…For very large droplets and highly heterogeneous media, the multiphase flow can be developed later on during the primary spread. 24 During the secondary spread, the liquid from the large pores flows into small pores due to the capillary force. At the beginning of the secondary spread, the large pores filled by liquid that are closer to the free interface are emptied; as the secondary spread proceeds, the overall number of large pores filled by liquid decreases.…”

“…At the end of primary spread, the imprint wetted area is around A w Ϸ 23 mm 2 which is different ͑it is larger͒ from the droplet base area that is calculated from the droplet base radius r 0 = 1.4 mm, ͑r 0 2 p = 6.2 mm 2 ͒. Measuring A w and d p at the end of the primary spread and assuming the droplet imprint is a spheroid in shape due to the pore cross links and droplet base finite size, 11,[24][25][26] it is found that the liquid mass balance for a single-phase flow is satisfied and the void volume in wetted sand ͑droplet imprint͒ is fully saturated by the liquid phase. Hence, V 0 can be expressed as…”

“…3, the liquid phase mass and momentum balances are coupled together with capillary pressure jump and flow rate at the free interface. 24 For the liquid phase in porous medium, two different boundaries can be identified: inlet ͑S inl ͒ and free interface ͑S int ͒, where the liquid flow rate in one pore ͑q i ͒ that belongs to the boundary is equal to…”

“…It has been observed that the primary spread into a heterogeneous medium always starts as a single phase, and later it may transform into a multiphase flow. 24 This transition is influenced by viscous and capillary forces, and since the numerical solution uses a rigid force balance at the free interface, the transition point is captured without any further constraints on the numerical implementation. The secondary spread is always multiphase flow as there is an increase in wetted volume of porous medium for a constant volume of liquid.…”

Infiltration time and imprint shape of a sessile droplet imbibing porous medium

“…Furthermore, adopting the spheroid geometry [13], the imprint shape is given with two half-axes lengths a and b…”