The evolution of a three-dimensional microbubble at a corner in a Maxwell fluid

Abstract

Bubbles often appear in non-Newtonian liquids from nature, engineering to biomedical applications, but their study has been under research compared to their Newtonian counterpart. Here, we extend the axisymmetric modeling of Lind and Phillips to three-dimensional modeling. The approach is based on the boundary integral method coupled with the Maxwell constitutive equation. The flow is assumed to have moderate to high Reynolds numbers and, thus, is irrotational in the bulk domain. The viscoelastic effects are incorporated approximately in the normal stress balance at the bubble surface. The numerical model has excellent agreement with the corresponding Rayleigh–Plesset equation for spherical bubbles in a non-Newtonian liquid. Computations are carried out for a bubble near a corner at various angles. The numerical results agree very well with the experiments for bubbles in a Newtonian fluid in a corner. As the Deborah number increases, the amplitude and period of the bubble oscillation increase, the bubble migration to the corner enhances, and the bubble jet is broader, flatter, and inclined more to the further boundary. This implies an improvement to surface cleaning of all surrounding boundaries for ultrasonic cavitation cleaning and results in greater administration of noninvasive therapy and drug delivery.