Shear-thickening liquids

If the measured viscosity rj is constant with respect to shear rate, then the liquid is said to be Newtonian as described above. However, as is usually the case for structured liquids such as polymer solutions and suspensions, the viscosity decreases with increasing shear rate such liquids are described as shear thinning. Occasionally, situations arise where the opposite is true, and the viscosity increases with increasing shear rate these are called shear-thickening liquids, see chapter 15. 

Shear-thickening liquids are liquids whose apparent viscosity increases with increased shear rate. The old name for this is "dila-tant" because the fluid appears to swell as it is sheared. The best way 1 can describe this is to ask you to think of a bucket of sand and water with about an inch of water above the settled sand. (Think back to your childhood visits to the seaside or sand pit.) Suppose you now rock the bucket from side to side the sand and water mix together to form a rather unstable suspension. However, if you take a stick and try to stir the contents of the bucket with any appreciable amount of force it is virtually impossible. The suspension actually begins to look like a fractured solid. This is an extreme example of shear thickening. The voidage between the sand particles and the amount of water present when the mixture behaves like a suspension is just enough to... 

The smaller the value of n, the more shear thinning the liquid will be. The opposite is true for a shear-thickening liquid. 

Figure 8.9 Shear stress-streun rate plots of various fluids. For shear-shinning liquids (e.g. paint), viscosity is reduced with increasing shear rate and vice versa for shear thickening liquids (e.g. quicksemd). Water and petrol are Newtonian liquids. Bingham plastics, where a yield stress is required for flow, can be, for example, toothpaste and butter...

Non-llocculated suspensions can exist at very much higher concentrations and, at all but file highest volumetric concentrations, are often Newtonian. When such suspensions are sheared, some dilation occurs as a result of particles trying to "climb over each other . If the amount of liquid present is then insufficient fully to till the void spaces, particle-particle solid friction can come into play and the resistance to shear increases. This is just one way in which shear-thickening can occur. 

Nienow and Elson (1988) have reviewed work done mainly by them and their co-workers on the mixing of non-Newtonian liquids in tanks. The above approach for inelastic, shearing thinning liquids has been largely substantiated but considerable doubt has been cast over using this method for dilatant, shear thickening materials. 

For a liquid under shear the rate of deformation or shear rate is a function of the shearing stress. The original exposition of this relationship is Newton s law, which states that the ratio of the stress to the shear rate is a constant, ie, the viscosity. Under Newton s law, viscosity is independent of shear rate. This is tme for ideal or Newtonian liquids, but the viscosities of many liquids, particularly a number of those of interest to industry, are not independent of shear rate. These non-Newtonian liquids may be classified according to their viscosity behavior as a function of shear rate. Many exhibit shear thinning, whereas others give shear thickening. Some liquids at rest appear to behave like solids until the shear stress exceeds a certain value, called the yield stress, after which they flow readily. 

Shear-thickening is shown in particular, as a dilatant effect, by pastes of densely packed peptised particles in which there is only sufficient liquid to fill the voids. As the shear rate is increased, this dense packing must be broken down to permit the particles to flow past one another. The resulting expansion leaves insufficient liquid to fill the voids and is opposed by surface tension forces. This explains why wet sand apparently becomes dry and firm when walked upon. 

As the shear rate increases, the viscosity of some dispersions actually increases. This is called dilatancy, or shear-thickening. Dilatancy can be due to the dense packing of particles in very concentrated dispersions for which at low shear, the particles can just move past each other but at high shear they become wedged together such that the fluid cannot fill (lubricate) the increased void volume, and the viscosity increases. An example of this effect is the apparent drying of wet beach sand when walked on, the sand in the footprint initially appears very dry and then moistens a few seconds later. Other examples include concentrated suspensions (plastisols) of polyvinyl chloride (PVC) particles in plasticizer liquid and the commercial novelty product Silly Putty (which is a silicone material). 

Equation 3.5 contains a constant factor K and a varying factor n, which specifies the slope of the viscosity function. For Newtonian fluids, K corresponds to the shear viscosity r) and n=l. For 0 < n < 1, the fluid is a shear thinning fluid. For shear-thickening fluids, i.e. liquids, whose viscosity increases with shearing, 1 < n < °°. 

In processes with very small liquid dimensions and high speeds, such as spraying or coating processes, shear rates can reach up to 105 1/s. If shear thinning or shear thickening materials are used, the viscosity can therefore vary greatly depending on shear rate. 

An understanding of the rheological behaviour is necessary as PVC pastes are classified as non-Newtonian liquids and can be dilatent (shear thickening), pseudoplastic (shear thinning) or thixotropic (viscosity reduces with time under constant shear). Each process requires specific rheological characteristics and this is achieved by formulation of appropriate PVC grades and knowledge of the influence of shear rate and time under constant shear. 

This space-filling network of percolating and interacting fumed silica particles may result in an enormous high viscosity or even a yield point. The thickened liquid gets a gel-like consistence and will resists shear stress until the shear stress overcomes the strength of the particle-particle interactions and... 

If)/ is independent of shear history, the material is said to be time independent. Such liquids can exhibit different behavior patterns, however, if, as is frequently the case with polymers, )/ varies with shear rate. A material whose viscosity is independent of shear rate, e.g., water, is a Newtonian fluid. Figure 11-26 illustrates shear-thickening, Newtonian and shear-thinning rj-y relations. Most polymer melts and solutions are shear-thinning. (Low-molecular-weight polymers and dilute solutions often exhibit Newtonian characteristics.) Wet sand is a familiar example of a shear-thickening substance. It feels hard if you run on it, but you can sink down while standing still. 

Barnes, H. A. 1989. Shear thickening Dilatancy in suspensions of non aggregating solid particles dispersed in Newtonian liquids. J. Rheol. 33 329-366. 

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