Axial annular flow of plastic fluids: Dead zones and plug-free flow

In axial annular flow, the shear stress decreases from its value τ(κR) at the inner cylinder to 0 at r = λR and increases from then on to τ(R) at the outer cylinder. For plastic fluids with a yield stress τ_c, λ will be such that flow commences when τ(κR) = τ(R) = τ_c. For fluids with position-dependent yield stresses (electro- and magnetorheological fluids are examples), the situation is more complex. While it is possible that yielding and flow occur everywhere, it is also possible that flow occurs only in parts of the fluid-filled space, and a dead zone (region in which the fluid is at rest) close to one of the walls exists. In that case, the fluid will flow no matter how small the applied pressure difference P = Δp/L is. If P is large enough, the dead zone ceases to exist and flow without any plug is possible. The fluid flows as if no yield stress exists.