Cessation of Couette and Poiseuille flows of a Bingham plastic and finite stopping times

Two-dimensional dam break flows of Herschel–Bulkley fluids: The approach to the arrested state

“…In both these cases, when the driving pressure gradient or boundary velocity is reduced to zero the fluid arrests in finite time [23][24][25]. The reason for the different behaviour is that for our case of gravity driven flow, the force driving the motion never vanishes, but asymptotically approaches zero.…”

Channel flow of a tensorial shear-thinning Maxwell model: Lattice Boltzmann simulations

“…2 as a dotted line). One can view finite 1/θ as a regularization parameter as it is often employed in numerical calculations involving Bingham or other yield-stress fluids 59 . In fact, the case θ → ∞ is an idealization that is not achieved in reality, as even in the glass, some residual relaxation processes persist.…”

Application of the augmented Lagrangian method to steady pipe flows of Bingham, Casson and Herschel–Bulkley fluids

“…For example, it can be shown theoretically that the pipe flow of a viscous fluid comes to rest in an infinitely long time [18], while the flow of Bingham fluid and more general viscoplastic fluids (including Casson and Herschel-Bulkley fluids) takes a finite amount of time to do so [19,20,23], if the pressure gradient falls below the critical value needed to overcome the yield stress effect. Indeed, the numerical modelling of cessation of the Poiseuille flow of the Papanastasiou fluid shows that when the imposed pressure gradient is non-zero and below the critical value, a steady non-trivial Poiseuille flow still persists [21]. When one uses a regularised method to develop a stopping criteria in steady flows, the situation is similar; see Fig.…”