Non-local Effects in Shear Banding of Polymeric Flows

Many fluids undergo shear banding, in which two states of different apparent viscosity coexist for a given shear rate (or for a given stress). In the idealized case of an infinite gap between shearing plates the selection of the conditions for shear banding has been shown to depend on the spatial structure and shape of the interface between shear bands. With the advent of microfluidic design for processing and additive manufacturing, the processing of many complex fluids often occurs in situations where this idealized limit doesn't apply, and the gap between walls, in either shearing flow or more often for pressure driven flow, is no longer "infinite" compared to the structural scales. It is increasingly clear that the effective rheology and structure of flowing fluids in these conditions requires information about the entire sample size, i.e., that the rheology is intrinsically non-local. In this review we discuss some recent attempts (both theoretical and experimental) to address non-local rheology and its implications for shear-banding flows of polymeric fluids. This manifests itself in rheology extracted from velocity profiles, as well as the dependence of shear-banding conditions on the position of the interface between shear bands, as well as the system size.