Foam drainage placed on a porous substrate

Abstract

A model for drainage/imbibition of a foam placed on the top of a porous substrate is presented. The equation of liquid imbibition into the porous substrate is coupled with a foam drainage equation at the foam/porous substrate interface. The deduced dimensionless equations are solved using a finite element method. It was found that the kinetics of foam drainage/imbibition depends on three dimensionless numbers and the initial liquid volume fraction. The result shows that there are three different regimes of the process. Each regime starts after initial rapid decrease of a liquid volume fraction at the foam/porous substrate interface: (i) rapid imbibition: the liquid volume fraction inside the foam at the foam/porous substrate interface remains constant close to a final liquid volume fraction; (ii) intermediate imbibition: the liquid volume fraction at the interface with the porous substrate experiences a peak point and imbibition into the porous substrate is slower as compared with the drainage; (iii) slow imbibition: the liquid volume fraction at the foam/porous substrate interface increases to a maximum limiting value and a free liquid layer is formed between the foam and the porous substrate. However, the free liquid layer disappears after some time. The transition points between these three different drainage/imbibition regimes were delineated by introducing two dimensionless numbers.

Foams built up by non-Newtonian polymeric solutions: Free drainage

“…11 and Table 1, f n~4 9 for a Newtonian liquid (n= 1) and immobile interface which is in complete agreement with the values reported earlier [8,18,35].…”

“…The drainage equations in the case of Newtonian liquids have been solved numerically and/or analytically in different prototype situations including free drainage [4][5][6][7][8][9], where liquid drains out of a foam due to the influence of gravity and capillarity; wetting of a dry foam [10,11], where a dry foam is in contact with a liquid at its base; forced drainage [8,9,[12][13][14], where liquid is added to the top of foam column producing a traveling wave; and pulsed drainage [8,[15][16][17], where a small volume of liquid is injected to the top of a foam and left to evolve. A new type of these situations is the case of foam drainage placed on a porous substrate [18,19], where foam is deposited on a porous substrate and the presence of unsaturated pores inside the porous substrate results in an imbibition of liquid from the foam into the unsaturated pores.…”

Electroosmotic Flow in Free Liquid Films: Understanding Flow in Foam Plateau Borders

“…Foam is a multiphase colloidal system made from entrapment of gas in a continuous liquid phase. Drainage refers to gravity-and/or capillary-driven flow of liquid between the gas bubbles through Plateau borders, nodes, and films, and is well documented [1][2][3]. Plateau borders in foams have higher liquid content, and a free liquid film (~180 µm thick) can be used to model the electrokinetic flow inside Plateau borders.…”

Wetting properties of cosmetic polymeric solutions on hair tresses

“…There was some expected variation in the arrangement of individual hair fibres on the frame in the course of repeated experiments, leading to a considerable standard Colloids and Interface Science Communications 9 (2015) [12][13][14][15] error of measurements. The porosity of tress of hair was estimated as 0.43 and the distance between the fibres was~17.4 μm.…”

“…Even more than that, it has two-type porous structure: (i) pores built by an array of individual fibres (slightly different in each measurement) and (ii) a fine porous structure of each individual hair fibre (see Fig. 2(b)) [12][13][14]. A hair tress demonstrates hydrophobic properties not only because of the hydrophobic nature of the hair surface, but also because of air pockets in between the fibres.…”