Spontaneous Penetration of Liquids into Capillaries and Porous Membranes Revisited

Spreading of Liquid Drops over Saturated Porous Layers

“…If boundary conditions [13] and [18] are compared, then it is easy to see that the latter one can be directly obtained from condition [18] if we adopt…”

“…Hence, this interface always coincides with the surface z = 0. It is worth mentioning that everything is going on time scales much bigger than the initial period considered in (18). The liquid motion inside the porous layer with thickness is assumed to obey Brinkman's equations.…”

Dynamic capillary impact on longitudinal micro-flow in vacuum assisted impregnation and the unsaturated permeability of inner fiber tows

“…By combination with Eq. (13), quasi-static capillary pressure P s c may be theoretically estimated using the Young-Laplace equation [25], as follows:…”

Capillary rise of a meniscus with phase change

“…In particular, when a capillary of a sufficiently small radius is brought in contact with a "wetting" fluid, the fluid spontaneously enters the capillary and flows, displacing the fluid already occupying the capillary. According to a recent review [1], the problem of capillary rise in a cylindrical tube dates back to the mid-18th century, addressed to Euler as an example of Newtonian dynamics with a variable mass. Euler's response is unknown, and it was not until the pioneering works of Lucas [2], Washburn [3] and Bosanquet [4], that a mathematical model was formulated and analysis of various limiting cases of the problem was presented.…”