Finite stopping time problems and rheometry of Bingham fluids

On kinematic conditions affecting the existence and non-existence of a moving yield surface in unsteady unidirectional flows of Bingham fluids

“…Given that the Bingham fluid ceases to move in a pipe after a finite amount of time when the pressure gradient is lowered below a critical value [2,15], one may look at the cessation of the flow in its counterpart, i.e., in a channel [18]. Similarly, the decay of velocity driven flows such as steady simple shear and the Couette flow in a viscometer when the moving boundaries are brought to rest [18], or when the angular acceleration of the inner bob in a Couette viscometer becomes negative [19] have been examined.…”

“…Similarly, the decay of velocity driven flows such as steady simple shear and the Couette flow in a viscometer when the moving boundaries are brought to rest [18], or when the angular acceleration of the inner bob in a Couette viscometer becomes negative [19] have been examined. In these cases, the extinction time is finite.…”

“…However, the decay of a steady flow in the above category to a state of rest is a simpler matter. While the location of the yield surface is unknown, the Bingham fluid attains a state of rest very quickly, with upper bounds for the extinction times being available in many instances [15,18], or a proof that this time is finite through the maximum principle [19,20].…”

Slumps of viscoplastic fluids on slopes

“…It has some important consequences in the interpretation of data from devices such as the Bostwick consistometer or other slump-like test, in which material is set into motion and allowed to flow towards a yield-stress arrested state. The algebraic decay means that unlike the cessation of flows of yield stress materials in pipes and channels, for which when the driving pressure gradient is abruptly removed and the flow stops in a finite time [28], the free-surface slumps only approach the arrested state asymptotically.…”

Cessation Flows of Bingham Plastics With Slip at the Wall

“…Bingham plastics. In fact, theoretical upper bounds on the stopping time have been derived [2,3]. These bounds depend on the density, the viscosity, the yield stress, a new geometric constant, and the leading eigenvalue of the second-order linear differential operator for the interval under consideration.…”