Flow of a Bingham-like fluid in a finite channel of varying width: A two-scale approach

► We provide a new model for Bingham flow in a channel with small aspect ratio ε. ► We consider a deformable core. ► We show that when deformations are allowed the “lubrication” paradox is avoided. ► We provide an asymptotic expansion around ε (aspect ratio). ► We perform numerical simulation to show the behavior of the stationary solution.