TY - JOUR

T1 - Stable bubble formations in a depth-perturbed Hele-Shaw channel

AU - Lawless, Jack

AU - Keeler, Jack

AU - Hazel, Andrew L.

AU - Juel, Anne

PY - 2024/9/25

Y1 - 2024/9/25

N2 - The propagation of polydisperse bubbles inside a rectangular Hele-Shaw channel by the constant volumetric flux flow of an ambient viscous liquid is generally unsteady; pairs of neighboring bubbles will either separate or coalesce because their propagation speeds increase monotonically with their sizes. Thus, any group of bubbles will eventually rearrange itself in order of decreasing size, individual bubbles will separate, and, crucially, there are no stable multiple-bubble states. Remarkably, the introduction of a small axially uniform elevation to the channel's lower boundary (on the order of a percent of the channel's depth) leads to the creation of stable multiple-bubble states and, thus, disrupts the usual reordering by bubble sizes. The constituent bubbles of such states lie in alternation on opposite sides of the elevation. The elevation provides a mechanism for the trailing bubbles to reduce their propagation speeds when approaching their preceding nearest neighbors. The stable multiple-bubble states are always led by the smallest bubble while the trailing bubbles can be arranged in any order and, thus, their number grows factorially as the number of bubbles increases.

AB - The propagation of polydisperse bubbles inside a rectangular Hele-Shaw channel by the constant volumetric flux flow of an ambient viscous liquid is generally unsteady; pairs of neighboring bubbles will either separate or coalesce because their propagation speeds increase monotonically with their sizes. Thus, any group of bubbles will eventually rearrange itself in order of decreasing size, individual bubbles will separate, and, crucially, there are no stable multiple-bubble states. Remarkably, the introduction of a small axially uniform elevation to the channel's lower boundary (on the order of a percent of the channel's depth) leads to the creation of stable multiple-bubble states and, thus, disrupts the usual reordering by bubble sizes. The constituent bubbles of such states lie in alternation on opposite sides of the elevation. The elevation provides a mechanism for the trailing bubbles to reduce their propagation speeds when approaching their preceding nearest neighbors. The stable multiple-bubble states are always led by the smallest bubble while the trailing bubbles can be arranged in any order and, thus, their number grows factorially as the number of bubbles increases.

U2 - 10.1103/PhysRevFluids.9.093605

DO - 10.1103/PhysRevFluids.9.093605

M3 - Article

VL - 9

JO - Physical Review Fluids

JF - Physical Review Fluids

SN - 2469-990X

IS - 093605

M1 - 093605

ER -