Confined viscoplastic flows with heterogeneous wall slip

Abstract

The steady, pressure-driven flow of a Herschel-Bulkley fluid in a microchannel is considered assuming that different power-law slip equations apply at the two walls due to slip heterogeneities, allowing the velocity profile to be asymmetric. Three different flow regimes are observed as the pressure gradient is increased. Below a first critical pressure gradient 1 G , the fluid moves unyielded with a uniform velocity and thus the two slip velocities are equal. In an intermediate regime between 1 G and a second critical pressure gradient 2 G , the fluid yields in a zone near the weak-slip wall and flows with uniform velocity near the stronger-slip wall. Beyond this regime, the fluid yields near both walls and the velocity is uniform only in the central unyielded core. It is demonstrated that the central unyielded region tends towards the midplane only if the power-law exponent is less than unity; otherwise, this region rends towards the weak-slip wall, and asymmetry is enhanced. The extension of the different flow regimes depends on the channel gap; in particular the intermediate asymmetric flow regime dominates when the gap becomes smaller than a characteristic length which incorporates the wall slip coefficients and the fluid properties. The theoretical results compare well with available experimental data on soft glassy suspensions. These results open new routes in manipulating the flow of viscoplastic materials in applications where the flow behavior depends not only on the bulk rheology of the material but also on the wall properties.

On the Enhancement of Heat Transfer and Reduction of Entropy Generation by Asymmetric Slip in Pressure-Driven Non-Newtonian Microflows

“…The Nusselt number is obtained by substituting the dimensionless mean temperature into Eq. (39). The dimensionless velocity and temperature profiles are finally also substituted into Eqs.…”

“…(23)- (25)], wherein the power-law fluid is a special case of a derivation for HB fluids. Of course, in showing an equivalence, one has to take into account the different characteristic scales employed in [39].…”

“…We also understand that the Nusselt number is completely defined only by specifying a reference temperature, see Eq. (39), which itself depends on the rate of heat transfer-a quantity that we are trying to predict in the first place! This makes the definition of the Nusselt number a circular one.…”

“…Vayssade et al [38] performed an experimental study of suspension flow in a microchannel, providing evidence for asymmetric slip velocities along the channel walls. Panaseti et al [39] extended the latter approach, which was based on the Herschel-Bulkley (HB) fluid model, to account for slip via Navier's nonlinear slip condition. How-ever, thermal effects in such flows have not been considered.…”

A finite volume method for the simulation of elastoviscoplastic flows and its application to the lid-driven cavity case

“…Viscoplastic and viscoelastic fluids can exhibit complex slip behaviour, e.g. power-law slip [79,80], pressure dependence [81], or "slip yield stress" [82,83]. However, experiments with Carbopol in [78] (0.2% by weight) and [74] w , respectively, where u s is the slip velocity (the left-hand side of Eq.…”