Thomasina Ball

Viscoplastic blisters

Many problems involve the spreading of a viscous fluid underneath a surface skin or crust, such as the intrusion of magma into the crust, the formation of ordered wrinkle patterns for the production of microfluidic devices, and the reopening of airways in biological fluid mechanics. A characteristic of these types of problems is that the spreading is controlled by the physics at the fluid front rather than a bulk similarity solution due to the singular nature of the contact line. This leads to a matching problem between a quasi-static interior blister and the behaviour of the peeling region at the front.

Typically, these studies have considered the skin to be elastic, however in many cases a more viscous or plastic description might be a more relevant model. In this talk, I will consider the spreading of a viscous fluid underneath a viscoplastic plate (a Herschel-Bulkley rheology). I will look at the regimes when the plate is a very viscous fluid or an ideal plastic material, in either a two-dimensional or circular geometry. As I will show, unlike other peeling problems, the viscoplastic plate model gives rise to an integral constant which reduces the need for a detailed solution over the peeling region. In the case of a viscous plate, this simplifies the analysis dramatically compared with the elastic case. For the viscoplastic plate, the simplification also occurs. However, understanding the structure of the peeling region is complicated by the presence of a yield stress as the peeling wave ahead of the blister includes an infinite series of plugs and yielded zones, akin to other viscoplastic shallow films.