Particle-bubble interaction inside a Hele-Shaw cell

Abstract

Hydrodynamic interactions between air bubbles and particles have wide applications in multiphase separation and reaction processes. In the present work, we explore the fundamental mechanism of such complex processes by studying the collision of a single bubble with a fixed solid particle inside a Hele-Shaw cell. Physical experiments show that an air bubble either splits or slides around the particle depending on the initial transverse distance between the bubble and particle centroids. An air bubble splits into two daughter bubbles at small transverse distances, and slides around the particle at large distances. In order to predict the critical transverse distance that separates these two behaviors, we also develop a theoretical model by estimating the rate of the bubble volume transfer from one side of the particle to the other based on Darcy's law, which is in good agreement with experiments.

The interaction of multiple bubbles in a Hele-Shaw channel

“…2014; Zhang et al. 2016; Madec 2021; Sirino, Mancilla & Morales 2021). A key result from these studies is that there is only one stable single-bubble solution for a channel of constant rectangular cross-section.…”

“…The propagation of finite air bubbles in a Hele-Shaw channel of uniform depth is a classical problem in fluid dynamics with a long and rich history. Transient behaviour and steady propagation modes have been investigated extensively in the case of a single bubble using a mixture of analytical and numerical techniques (see, for example Taylor & Saffman 1959;Tanveer 1987;Tanveer & Saffman 1987;Khalid, McDonald & Vanden-Broeck 2015;Green, Lustri & McCue 2017;Lustri, Green & McCue 2020) and experiments (see, for example Maxworthy 1986;Kopf-Sill & Homsy 1988;Wang et al 2014;Zhang et al 2016;Madec 2021;Sirino, Mancilla & Morales 2021). A key result from these studies is that there is only one stable single-bubble solution for a channel of constant rectangular cross-section.…”

Interfacial Dynamics in Dual Channels: Inspired by Cuttlebone

“…Furthermore, the role of solid vertical walls in affecting interface movement is significant. Several studies have examined how bubbles interact with rigid obstacles within a Hele-Shaw cell [19][20][21][22]. In microfluidic channels, the introduction of geometric obstacles has been employed to induce and regulate droplet breakups [23][24][25].…”

The interaction of multiple bubbles in a Hele-Shaw channel

“…The propagation of finite-air bubbles in a Hele-Shaw channel of uniform depth is a classical problem in fluid dynamics with a long and rich history. Transient behaviour and steady propagation modes have been investigated extensively in the case of a single-bubble using a mixture of analytical and numerical techniques [see, for example 10,17,20,[32][33][34] and experiments [see, for example 18,21,22,31,38,39]. If a depth-perturbation is added to the bottom of the channel as shown in figure 1, the range of existence and stability of steady propagation modes changes dramatically, as mapped out by Franco-Gómez et al [7,8], Gaillard et al [9], Keeler et al [14].…”