Flow of a yield stress fluid over a rotating surface

Abstract

We study the flow of yield stress fluids over a rotating surface when both the viscoelastic solid behavior below a critical deformation (γ c) and liquid properties beyond γ c can play a significant role. We review the detailed characteristics of the flow in the solid regime in the specific case of a pure elongational strain (large height to radius ratio). We, in particular, show that there exists a critical rotation velocity (ω c) associated with the transition from the solid to the liquid regime. We then consider the specific case of lubricational regime (small height to radius ratio) in the liquid regime. In that case we describe the different possible evolutions of the equilibrium shape of the material as a function of the rotation velocity (ω), from which we extrapolate the transient shape evolutions as ω increases. We show that for a sufficiently large rotation velocity the sample separates into two parts, one remaining at rest around the rotation axis, the other going on moving radially. These predictions are then compared with systematic spin-coating tests under increasing rotation velocity ramps followed by a plateau at ω f with typical yield stress fluids. It appears that there exists a critical velocity below which the material undergoes a limited elongation and beyond which it starts to spread significantly over the solid surface. For a larger ω f value the sample forms a thick peripheral roll, leaving behind it a thin layer of fluid at rest relatively to the disc. These characteristics are in qualitative agreement with the theoretical predictions. Beyond a sufficiently large ω f value this roll eventually spreads radially in the form of thin fingers. Moreover, in agreement with the theory in the lubricational regime, the different curves of deformation vs ω fall along a master curve when the rotation velocity is scaled by ω c for different accelerations, different sample radii, or different material yield stress. The final thickness of the deposit seems to be mainly governed by the displacement of the roll, the characteristics of which take their origin in the initial stage of the spreading, including the solid-liquid transition.

Elastoplastic behavior of yield stress fluids

“…Nevertheless, theoretical approaches for the basic aspects of the behavior in this regime, i.e. the stress vs deformation relationship, have been proposed [14][15][16][17][18], but these models are essentially aimed at good prediction of the transitional characteristics, i.e. the characteristics of the solid to liquid transition, and the proposed behavior in the solid regime is generally rather simplistic.…”

Pair-particle trajectories in a shear flow of a Bingham fluid

“…Particles in non-Newtonian fluids have been much less studied, although the case of particles suspended in viscoelastic fluids have received a lot of attention recently, in particular because of the tendency of particles to form chains under flow [15] . Since yield stress fluids are used in the industry to stabilize the particles against gravity, the sedimentation problem has been the subject of most studies on particles suspended in yield stress fluids [4,22,46,53] , with a focus on a single particle and on the onset of flow. The rheological properties of model suspensions have also been studied recently experimentally [13,39,45] and theoretically [3,8] .…”

Simulation of viscoplastic flow past cylinders in tubes

“…Also, in [3] the authors determine their yield values via extrapolation with no talk of error and very smooth data presented. The recent works [7][8][9][10][11][12] show that for Carbopol the yield values are not so easily specified.…”

“…Although Jossic and Magnin [3] have been careful in determining the rheology, there may be some doubt that the experiments represent the computations. In particular, recent papers by Coussot and co-workers [8][9][10] and by Putz et al [12] have looked at low shear rheology of Carbopol (the latter group during sedimentation). Coussot and co-workers find a transition between creep and viscous behaviour; Putz et al [12] show particle-image-velocimetry (PIV) data indicating that the flow field is non-symmetric.…”

“…New experiments and simulations in the last decade have made major contributions to the field. Experimentally, studies by de Bruyn, Coussot, and co-workers [6][7][8][9][10] and others [11,12] have shown the difficulty of measuring accurately the yield-stress properties of viscoplastic fluids and of determining the limiting criterion for flow around a sphere found numerically by Beris et al [4]. A successful agreement between theory and experiments was achieved only recently [9].…”