Flow of micropolar and viscoplastic fluids in a Hele-Shaw cell

Rotational Particle Separation in Solutions: Micropolar Fluid Theory Approach

“…Similarly, the constitutive law ( 32) is equivalent to the inclusion N ∈ ∂V n (A) with V n (D) = γ|D| 2 + τ n |D|, ∀D ∈ R 3×3 . The meaning of the plug zone |N(x, t)| ≤ τ n is discussed in [35].…”

“…It is proved in [35] that the rotation yield stress τ n causes the appearance of clusters of particles, with each cluster being a plug zone which rotates as a rigid body. Conglomerates of particles were not observed in [9] for the Couette flows of suspensions between two rotating cylinders; this is why τ n and τ n1 can be neglected.…”

Steady flows of Cosserat–Bingham fluids

“…As for local deformations, they are characterized also by two tensors that allow to calculate the velocity gradient and the spin gradient; both these tensors should vanish in the zone of stiffness, the strong plug zone. In contrast to the classical Bingham fluid, the micropolar Bingham fluid may have a weak plug zone where the spin gradient vanishes, whereas the velocity gradient does not vanish [1,2].…”

“…Examples are animal blood, cutting transport by drilling mud, and granular flows. Recent examples concern the proppant flow within the hydrofracture . On one hand, such a fluid exhibits microrotational effects and microrotational inertia; the fluid can support the couple stress, the body couples, and the nonsymmetric stress tensor.…”

Forced Convective of Micropolar Fluid on a Stretching Surface of Another Quiescent Fluid

“…Micropolar fluid theory also able to explain some fluid phenomena that contain suspended fluid additives such as animal blood, liquid crystal, paint, body fluid, colloidal fluid, magnetic fluids, cloud with dust, muddy fluids and polymer that cannot be explained by Navier-Stokes equation. Due to the wide applications, many researchers concentrate on micropolar as subject of study such as Rees and Bassom [1], Ahmadi [2], Chawla [3], Guram and Smith [4], Peddieson [5], Takhar and Soundalgekar [6], Ishak et al [7], Ariffin et al [8] and Shelukhin and Neverov [9]. 398 Details about micropolar fluid can be found on Ariman et al [10], Ariman et al [11], Willson [12], Lukaszewicz [13] and Eremeyev et al [14].…”