Squeeze flow of Bingham plastic with stick-slip at the wall

Axisymmetric squeeze flow of a Herschel–Bulkley medium

“…Smyrnaios and Tsamopoulos [9] showed that unyielded material could only exist around the two stagnation points of flow. The numerical modeling for Bingham fluid [9], [16], [23], experiments [10] and asymptotic solution [22] confirmed the results [9]. It is interesting to investigate the obtained asymptotic solution for Herschel-Bulkley fluid near the stagnation point.…”

“…2 shows the graphs of the pseudo-yield surfaces z = z 0 (r), for different values of B and n. We see that z = z 0 (r) is the decreasing function of radius. This property is easy to confirm analytically, differentiating z 0 (23) with respect to r (0 < z 0 ≤ 1)…”

“…Figure2: The pseudo-yield surface z 0 (r)(23) for n = 1 (solid lines), n = 0.5 (dashed lines), n = 0.25 (dash-dotted lines).…”

Sliding flows of yield-stress fluids

“…In the present study, we formulate the well known ‘stick–slip’ law for yield-stress fluids beyond one-dimensional (1-D) rheometric flows and then generalize the previously proposed numerical algorithm (Roquet & Saramito 2008; Muravleva 2018) based on the augmented Lagrangian method for attacking this kind of problem. Theoretical tools are developed in the presence of slip.…”

An embedded boundary approach for efficient simulations of viscoplastic fluids in three dimensions

“…Equation (3a) is Cauchy's momentum balance, (3b) is the incompressibility constraint, and (3c) relates the stress to the specific rheological equation for a generalised Newtonian fluid model through the apparent viscosity η ( γ ). The perfect no-slip boundary condition which we employ in (3d) is the simplest and most common way to deal with wall effects for viscous flow, although many cases require more advanced treatments of the solid-fluid interactions, such as the stick-slip condition for Bingham fluids20,21 .…”