The shape of a small liquid drop on a cone and plate rheometer

We construct asymptotic solutions for the shape of a small liquid sessile drop in a cone and plate rheometer. The approximation is based on small Bond number or, equivalently, on a characteristic length scale which is much smaller than the capillary length. The drop has a complicated asymptotic structure, consisting of five separate scalings, which is resolved using the method of matched asymptotic expansions. We find that the presence of a substrate above (and below) the drop gives rise to qualitatively new drop configurations

Asymptotics of a small liquid drop on a cone and plate rheometer

A cone and a plate rheometer is a laboratory apparatus used to measure the viscosity and other related parameters of a non-Newtonian liquid subject to an applied force. A small drop, of order millimetres, of the liquid is located between the horizontal plate and the shallow cone of the rheometer. Rotation of the cone ensues, the liquid begins to flow and the plate starts to rotate. Liquid parameters are inferred based on the difference in the applied rotational force and the resulting rotational force of the plate. To describe the flow of the drop, the initial drop configuration, before rotation commences, must be determined. The equilibrium drop profile is given by the solution to the well-known nonlinear Young-Laplace equation. We formulate asymptotic solutions for the drop profile based on the small Bond number. The modelling of the drop exhibits a rich asymptotic structure consisting of five distinct scalings which are resolved via the method matched asymptotics

Shear induced normal stress differences in aqueous foams

A finite simple shear deformation of an elastic solid induces unequal normal stresses. This nonlinear phenomenon, known as the Poynting effect, is governed by a universal relation between shear strain and first normal stresses difference, valid for non-dissipative elastic materials. We provide the first experimental evidence that an analog of the Poynting effect exists in aqueous foams where besides the elastic stress, there are significant viscous or plastic stresses. These results are interpreted in the framework of a constitutive model, derived from a physical description of foam rheology

A new look at blood shear-thinning

Blood viscosity decreases with shear stress, a property essential for an efficient perfusion of the vascular tree. Shear-thinning is intimately related to the dynamics and mutual interactions of red blood cells (RBCs), the major constituents of blood. Our work explores RBCs dynamics under physiologically relevant conditions of flow strength, outer fluid viscosity and volume fraction. Our results contradict the current paradigm stating that RBCs should align and elongate in the flow direction thanks to their membrane circulation around their center of mass, reducing flow-lines disturbances. On the contrary, we observe both experimentally and with simulations, rich morphological transitions that relate to global blood rheology. For increasing shear stresses, RBCs successively tumble, roll, deform into rolling stomatocytes and finally adopt highly deformed and polylobed shapes even for semi-dilute volume fractions analogous to microcirculatory values. Our study suggests that any pathological change in plasma composition, RBCs cytosol viscosity or membrane mechanical properties will impact the onset of shape transitions and should play a central role in pathological blood rheology and flow behavior

Elastic turbulence in curvilinear flows of polymer solutions

Following our first report (A. Groisman and V. Steinberg, \sl Nature $\bf 405$, 53 (2000)) we present an extended account of experimental observations of elasticity induced turbulence in three different systems: a swirling flow between two plates, a Couette-Taylor (CT) flow between two cylinders, and a flow in a curvilinear channel (Dean flow). All three set-ups had high ratio of width of the region available for flow to radius of curvature of the streamlines. The experiments were carried out with dilute solutions of high molecular weight polyacrylamide in concentrated sugar syrups. High polymer relaxation time and solution viscosity ensured prevalence of non-linear elastic effects over inertial non-linearity, and development of purely elastic instabilities at low Reynolds number (Re) in all three flows. Above the elastic instability threshold, flows in all three systems exhibit features of developed turbulence. Those include: (i)randomly fluctuating fluid motion excited in a broad range of spatial and temporal scales; (ii) significant increase in the rates of momentum and mass transfer (compared to those expected for a steady flow with a smooth velocity profile). Phenomenology, driving mechanisms, and parameter dependence of the elastic turbulence are compared with those of the conventional high Re hydrodynamic turbulence in Newtonian fluids.Comment: 23 pages, 26 figure