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 to produce 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. 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), in either a two-dimensional or circular geometry. 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. 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.