Flow of a yield stress fluid over a rotating surface

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.