An account is given of the development of the idea of a yield stress for solids, soft solids and structured liquids from the beginning of this century to the present time. Originally, it was accepted that the yield stress of a solid was essentially the point at which, when the applied stress was increased, the deforming solid first began to show liquid-like behaviour, i.e. continual deformation. In the same way, the yield stress of a structured liquid was originally seen as the point at which, when decreasing the applied stress, solid-like behaviour was first noticed, i.e. no continual deformation. However as time went on, and experimental capabilities increased, it became clear, first for solids and lately for soft solids and structured liquids, that although there is usually a small range of stress over which the mechanical properties change dramatically (an apparent yield stress), these materials nevertheless show slow but continual steady deformation when stressed for a long time below this level, having shown an initial linear elastic response to the applied stress. At the lowest stresses, this creep behaviour for solids, soft solids and structured liquids can be described by a Newtonian-plateau viscosity. As the stress is increased the flow behaviour usually changes into a power-law dependence of steady-state shear rate on shear stress. For structured liquids and soft solids, this behaviour generally gives way to Newtonian behaviour at the highest stresses. For structured liquids this transition from very high (creep) viscosity (>106 Pa.s) to mobile liquid (

The yield stress—a review or ‘παντα ρει’—everything flows?

Slip occurs in the flow of two-phase systems because of the displacement of the disperse phase away from solid boundaries. This arises from steric, hydrodynamic, viscoelastic and chemical forces and constraints acting on the disperse phase immediately adjacent to the walls. The enrichment of the boundary near the wall with the continuous (and usually low-viscosity) phase means that any flow of the fluid over the boundary is easier because of the lubrication effect. Because this effect is usually confined to a very narrow layer — with typical thickness of 0.1–10 μm—it so resembles the slip of solids over surfaces that it has historically been given the same terminology. The restoring force for all the forces that cause an increase in concentration is usually osmotic, and this will always limit the effective slip. In dilute systems, concentration gradients can be present over relatively large distances out from walls, giving what might be interpreted on an overall basis as a thick solvent-only layer. However, as the concentration of the system increases, the layer gets thinner and thinner because it is more difficult to create with the large reverse osmotic force present. However, the enormous increase in the bulk viscosity with increase in concentration means that although thinner, the layer becomes, paradoxically, even more important. Slip manifests itself in such a way that viscosity measured in different size geometries gives different answers if calculated the normal way — in particular the apparent viscosity decreases with decrease in geometry size (e.g. tube radius). Also, in single flow curves unexpected lower Newtonian plateaus are sometimes seen, with an apparent yield stress at even lower stresses. Sudden breaks in the flow curve can also be seen. Large particles as the disperse phase (remember flocs are large particles), with a large dependence of viscosity on the concentration of the dispersed phase are the circumstances which can give slip, especially if coupled with smooth walls and small flow dimensions. The effect is usually greatest at low speeds/flow rates. When the viscometer walls and particles carry like electrostatic charges and the continuous phase is electrically conducted, slip can be assumed. In many cases we need to characterise the slip effects seen in viscometers because they will also be seen in flow in smooth pipes and condults in manufacturing plants. This is usually done by relating the wall shear stress to a slip velocity using a power-law relationship. When the bulk flow has also been characterized, the flow in real situations can be calculated. To characterise slip, it is necessary to change the size of the geometry, and the results extrapolated to very large size to extract unambigouos bulk-flow and slip data respectively. A number of mathematical manipulations are necessary to retrieve these data. We can make attempts to eliminate slip by altering the physical or chemical character of the walls. This is usually done physically by roughening or profiling, but in the extreme, a vane can be used. This latter geometry has the advantage of being easy to make and clean. In either case—by extrapolation or elimination—we end up with the bulk flow properties. This is important in situations where we are trying to understand the microstructure/flow interactions.

A review of the slip (wall depletion) of polymer solutions, emulsions and particle suspensions in viscometers: its cause, character, and cure

Measuring the Flow Properties of Yield Stress Fluids

Rheology 863 Experimental Methods. 865 Artifacts and Blood Rheology. 868 Pure water. 868 Physiological saline, Ringer solution. 868 Saline solutions of fractionated plasma proteins. 869 Plasma andserum. 869 Formed elements and physiological saline or equivalent. 870 Whole blood and suspensions of red cells in plasma. 871 Rheology of Normal Human Blood. 874 Basicdata 874 Hematocrit. 876 Fibrinogen. 876 Temperature. 877 Abnormal Human Blood. 877 Polycythemia, anemia. 877 Afibrinogenemia, hyperfibrinogenemia. 878 Diabetes mellitus. 879 Hyperlipemias 879 Plasma protein abnormalities other than fibrinogen. 879 Blood after extracorporeal circulation. 880 Effect of Additives on Blood Rheology. 881 Anticoagulants 88 1 Saline solution. 88 1 Plasma expanders, substitute plasma. 881 Mammalian Blood Other Than Human. 883 Indirect Rheological Tests or Simplified Testing. 884 Physiological Significance of Blood Rheology. 884

Rheology of blood

Chapter 26 – Biophysical Behavior of Red Cells in Suspensions

The Rheology of Human Blood—Measurement Near and at Zero Shear Rate

Rheological properties of normal human blood as a homogeneous substance: its yield stress and the stress-shear rate function under creeping shear rates, were directly measured for the first time in...

G. R. Cokelet

Papers

The Rheology of Human Blood—Measurement Near and at Zero Shear Rate

Rheology of blood and flow in the microcirculation

Influence of plasma proteins on the rheology of human blood