Shear stress, suspensions

Colloidal dispersions often display non-Newtonian behaviour, where the proportionality in equation (02.6.2) does not hold. This is particularly important for concentrated dispersions, which tend to be used in practice. Equation (02.6.2) can be used to define an apparent viscosity, happ, at a given shear rate. If q pp decreases witli increasing shear rate, tire dispersion is called shear tliinning (pseudoplastic) if it increases, tliis is known as shear tliickening (dilatant). The latter behaviour is typical of concentrated suspensions. If a finite shear stress has to be applied before tire suspension begins to flow, tliis is known as tire yield stress. The apparent viscosity may also change as a function of time, upon application of a fixed shear rate, related to tire fonnation or breakup of particle networks. Thixotropic dispersions show a decrease in q, pp with time, whereas an increase witli time is called rheopexy. 

Time-dependent fluids are those for which structural rearrangements occur during deformation at a rate too slow to maintain equilibrium configurations. As a result, shear stress changes with duration of shear. Thixotropic fluids, such as mayonnaise, clay suspensions used as drilling muds, and some paints and inks, show decreasing shear stress with time at constant shear rate. A detailed description of thixotropic behavior and a list of thixotropic systems is found in Bauer and Colhns (ibid.). 

Rheopectic behavior is the opposite of thixotropy. Shear stress increases with time at constant shear rate. Rheopeclic behavior has been obsei ved in bentonite sols, vanadium pentoxide sols, and gypsum suspensions in water (Bauer and Colhns, ibid.) as well as in some... 

For any given process, one takes a qualitative look at the possible role of fluid shear stresses. Then one tries to consider pathways related to fluid shear stress that may affect the process. If there are none, then this extremely complex phenomenon can be dismissed and the process design can be based on such things as uniformity, circulation time, blend time, or velocity specifications. This is often the case in the blending of miscible fluids and the suspension of sohds. 

Each stage of particle formation is controlled variously by the type of reactor, i.e. gas-liquid contacting apparatus. Gas-liquid mass transfer phenomena determine the level of solute supersaturation and its spatial distribution in the liquid phase the counterpart role in liquid-liquid reaction systems may be played by micromixing phenomena. The agglomeration and subsequent ageing processes are likely to be affected by the flow dynamics such as motion of the suspension of solids and the fluid shear stress distribution. Thus, the choice of reactor is of substantial importance for the tailoring of product quality as well as for production efficiency. 

Values of n and k for the suspensions used are given in Table 5.2. Experimental results are shown in Figure 5.8 as wall shear stress R as a function of wall shear rate (dn /dyfr o using logarithmic coordinates. 

Similar kinetics have been observed for some [91] but not all [116] animal/insect lines. Trials conducted over a range of average shear stresses (Fig. 2) clearly indicate a higher degree of suspension sensitivity to turbulent, rather than laminar, flow conditions. Similar effects have been reported by other workers for plant [57] and mammalian [86,114,122] systems. From these... 

BalHca and Ryu [158] correlated reductions in cell yield in Datura stramonium suspensions with the increased Reynolds stresses associated with higher aeration rates in a 1.2-1 ALR. A more recent study [159] of C. roseus suspensions cultivated in a 1.5-1 bubble column showed that the increased bubble sizes associated with both larger sparger pores and higher aeration rates caused a reduction in system performance. Here, also, it was postulated that the effects were due to increased Reynolds shear stresses in the flow field. However, it was not possible to rule out gas-stripping effects. 

The hydrodynamic forces acting on the suspended colloids determine the rate of cake buildup and therefore the fluid loss rate. A simple model has been proposed in literature [907] that predicts a power law relationship between the filtration rate and the shear stress at the cake surface. The model shows that the cake formed will be inhomogeneous with smaller and smaller particles being deposited as the filtration proceeds. An equilibrium cake thickness is achieved when no particles small enough to be deposited are available in the suspension. The cake thickness as a function of time can be computed from the model. 

As is evident from Eq. (3-20) or (3-21), the Bingham plastic exhibits a shear thinning viscosity i.e., the larger the shear stress or shear rate, the lower the viscosity. This behavior is typical of many concentrated slurries and suspensions such as muds, paints, foams, emulsions (e.g., mayonnaise), ketchup, or blood. 

Mooney s method has been modified in various ways to allow for the observation that, with many suspensions, the slip velocity depends on the tube diameter as well as the wall shear stress. Jastrzebski (1967) deduced that, for certain kaolinite-water suspensions, vs was inversely proportional to d Thus a modified slip coefficient Cj may be defined by... 

Hydrocyclones are 20-500 mm in diameter, with the smaller units giving a much better separation. Typical values of length to diameter ratios range from about 5 to 20. Because of the very high shearing stresses which are set up, floes will be broken down and the suspension in the secondary vortex will be completely deflocculated, irrespective of its condition on entry. Generally, hydrocylones are not effective in removing particles smaller than about 2-3 rm. 

When a shear stress is applied to a suspension or liquid exhibiting laminar flow, a velocity gradient (the rate of shear) is established. When the rate of shear varies linearly with the applied shear stress, the system is termed Newtonian and the proportionality constant is termed the viscosity. Newtonian flow is usually observed in dilute... 

In addition to temperature, the viscosity of these mixtures can change dramatically over time, or even with applied shear. Liquids or solutions whose viscosity changes with time or shear rate are said to be non-Newtonian, that is, viscosity can no longer be considered a proportionality constant between the shear stress and the shear rate. In solutions containing large molecules and suspensions contain nonattracting aniso-metric particles, flow can orient the molecules or particles. This orientation reduces the resistance to shear, and the stress required to increase the shear rate diminishes with increasing shear rate. This behavior is often described by an empirical power law equation that is simply a variation of Eq. (4.3), and the fluid is said to be a power law fluid ... 

Concentrated particle suspensions may also show a yield point which must be exceeded before flow will occur. This may result from interaction between irregularly shaped particles, or the presence of water bridges at the interface between particles which effectively bind them together. Physical and chemical attractive forces between suspended particles can also promote flocculation and development of particle network structures, which can be broken down by an applied shear stress [2]. 

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