Quasi-static liquid–air drainage in narrow channels with variations in the gap

Abstract

This paper studies the shape of an air bubble quasi-statically flowing in the longitudinal direction of narrow channels. Two bottom topographies are treated, i.e., linear and quadratic variations of the gap along the transverse direction. This work analyses the main characteristics of the gas-liquid interface with respect to the wedge aspect ratio. From the convergence of asymptotic, numerical and experimental analyses, we found simple dependences for the finger width and total curvature as a function of channel aspect ratio. These results provide simple and general expressions for the pressure drop needed to overcome capillary forces and push the air finger inside the channel.

Critical point network for drainage between rough surfaces

“…Again, because of small surface slopes, the liquid/gas interface within the saddle-point constriction remains close to the saddle-point central position as illustrated in Figs. 2a and c. The shape of the interface that is found for those constricted channels is very similar to those obtained in a straight channel by Geoffroy et al (2006) (such as the one depicted in Fig. 2a) having the same cross-section as the saddle-point cross-section.…”

“…In the latter, an asymptotic analytical expressions for the pressure difference across a meniscus traveling in the channel in the quasi-static limit is derived. The saddle-points considered in the present study have locally a geometry similar to one of the channel shapes considered in Geoffroy et al (2006). Hence, the invasion criteria previously obtained for straight channels is extended through an asymptotic analysis to saddle-points of interest for the present study.…”

“…Quasi-static drainage in narrow straight channels has been investigated by Geoffroy et al (2006) in both linearly and quadratically varying channel cross-sections. These narrow channels have small aspect ratio.…”

“…This means that the ratio between the maximum gap h 0 at the saddle-point and the channel's width , is a small parameter = h 0 / 1. We would like to discuss here how the results that have been obtained by Geoffroy et al (2006) can be transposed to find the saddle-point percolation geometrical criteria. Let us first consider the vicinity of a saddle-point.…”

“…Thus, in addition to obtain an appropriate representation for the aperture field in terms of network, this approach relies on a correct estimation of bond capillary pressure thresholds. In this respect, the present paper relies on a previous work, by Geoffroy et al (2006), devoted to the study of drainage in elementary flat straight channels. In the latter, an asymptotic analytical expressions for the pressure difference across a meniscus traveling in the channel in the quasi-static limit is derived.…”