Shear fields

The largest drop that can exist in a shear field is related to the maximum value of the shear rate by... 

Smoluehowski also presented a simple theory of aggregation kineties assuming eollisions of perfeet eolleetion effieieney to prediet spherieal partiele size distributions in a uniform liquid shear field of eonstant veloeity gradient. The aggregation kernel is then expressed as... 

As early as 1916, Smoluehowski showed that aggregation of spherieal partieles in a laminar shear field ean be expressed as... 

Thus in a mixed system, as e.g. in a stirred tank, the rate of agglomeration additionally depends on the shear field and therefore on the energy dissipation e in the vessel. Furthermore, in precipitation systems solution supersaturation plays an important role, as the higher the supersaturation, the stickier the particles and the easier they agglomerate (Mullin, 2001). This leads to a general formulation of the agglomeration rate... 

Figure 9 We - 8 plot comparison of effect of viscosity ratio 8 on critical shear We.cn in rotational and irrotational shear fields [18].

Many microbial polysaccharides show pseudoplastic flow, also known as shear thinning. When solutions of these polysaccharides are sheared, the molecules align in the shear field and the effective viscosity is reduced. This reduction of viscosity is not a consequence of degradation (unless the shear rate exceeds 105 s 1) since the viscosity recovers immediately when die shear rate is decreased. This combination of viscous and elastic behaviour, known as viscoelasticity, distinguishes microbial viscosifiers from solutions of other thickeners. Examples of microbial viscosifiers are ... 

A true fluid flows when it is subjected to a shear field and motion ceases as soon as the stress is removed. In contrast, an ideal solid which has been subjected to a stress recovers its original state as soon as the stress is removed, The two extremes of behaviour are therefore represented by ... 

Many polymers form shear-thinning solutions in water. The molecules are generally long and tend to be aligned and to straighten out in a shear field, and thus to offer less resistance to flow. Such solutions are sometimes viscoelastic and this effect may be attributable to a tendency of the molecules to recover their previous configuration once the stress is removed. Molten polymers are usually viscoelastic. 

The electroviscous effect present with solid particles suspended in ionic liquids, to increase the viscosity over that of the bulk liquid. The primary effect caused by the shear field distorting the electrical double layer surrounding the solid particles in suspension. The secondary effect results from the overlap of the electrical double layers of neighboring particles. The tertiary effect arises from changes in size and shape of the particles caused by the shear field. The primary electroviscous effect has been the subject of much study and has been shown to depend on (a) the size of the Debye length of the electrical double layer compared to the size of the suspended particle (b) the potential at the slipping plane between the particle and the bulk fluid (c) the Peclet number, i.e., diffusive to hydrodynamic forces (d) the Hartmarm number, i.e. electrical to hydrodynamic forces and (e) variations in the Stern layer around the particle (Garcia-Salinas et al. 2000). 

The primary electroviscous effect occurs, for a dilute system, when the complex fluid is sheared and the electrical double layers around the particles are distorted by the shear field. The viscosity increases as a result of an extra dissipation of energy, which is taken into account as a correction factor pi" to the Einstein equation ... 

In a steady rotational shear field a spherical micro-organism with a soft wall will be deformed to an ellipsoidal shape. The deformation, M, is defined in... 

Fig. 22. Spherical drop deformed into an ellipsoidal shape in a rotational shear field [76]...

Fig. 24. Comparison of effect of viscosity ratio on reduced burst time for rotational and irro-tational shear fields [76]...

The velocity, viscosity, density, and channel-height values are all similar to UF, but the diffusivity of large particles (MF) is orders-of-magnitude lower than the diffusivity of macromolecules (UF). It is thus quite surprising to find the fluxes of cross-flow MF processes to be similar to, and often higher than, UF fluxes. Two primary theories for the enhanced diffusion of particles in a shear field, the inertial-lift theory and the shear-induced theory, are explained by Davis [in Ho and Sirkar (eds.), op. cit., pp. 480-505], and Belfort, Davis, and Zydney [/. Membrane. Sci., 96, 1-58 (1994)]. While not clear-cut, shear-induced diffusion is quite large compared to Brownian diffusion except for those cases with very small particles or very low cross-flow velocity. The enhancement of mass transfer in turbulent-flow microfiltration, a major effect, remains completely empirical. 

V. Mishra, S. M. Kresta, J. H. Masliyah 1998, (Self-preservation of the drop size distribution function and variation in the stability ratio for rapid coalescence of a polydisperse emulsion in a simple shear field), J. Colloid Interface Sci. 197, 57. 

Aggregation of particles may occur, in general, due to Brownian motion, buoyancy-induced motion (creaming), and relative motion between particles due to an applied flow. Flow-induced aggregation dominates in polymer processing applications because of the high viscosities of polymer melts. Controlled studies—the conterpart of the fragmentation studies described in the previous section—may be carried out in simple flows, such as in the shear field produced in a cone and plate device (Chimmili, 1996). The number of such studies appears to be small. 

Barth s-Biesel, D., and Acrivos, A., Deformation and burst of a liquid droplet freely suspended in a linear shear field. J. Fluid Mech. 61,1-21 (1973). 

Schowalter, W. R., Stability and coagulation of colloids in shear fields. Ann. Rev. Fluid Mech. 16, 245-261 (1984). 

The methodology discussed previously can be applied to the study of colloidal suspensions where a number of different molecular forces and hydrodynamic effects come into play to determine the dynamics. As an illustration, we briefly describe one example of an MPC simulation of a colloidal suspension of claylike particles where comparisons between simulation and experiment have been made [42, 60]. Experiments were carried out on a suspension of AI2O3 particles. For this system electrostatic repulsive and van der Waals attractive forces are important, as are lubrication and contact forces. All of these forces were included in the simulations. A mapping of the MPC simulation parameters onto the space and time scales of the real system is given in Hecht et al. [42], The calculations were carried out with an imposed shear field. 

By loading is meant an application of force through the neighbors to the contact point between the two granules which are in contact with each other. Since not all couples can survive the shearing field in an agglomerating charge, there is a finite probability of coalescence, which is ... 

This model was introduced by Neville and Hunter (13,14) for the case of sterically stabilized dispersions which have undergone reversible flocculation. It is assumed that the major contribution to the excess energy dissipation in such pseudoplastic systems comes from the need to provide energy from the shear field to separate contacting particles. Under these conditions, the extrapolated yield value is given by the expression (13,32,33),... 

Particle collision in an idealized shear field of velocity gradient du/dz. 

Figure 3.10 The dilation of the flow field around a spherical particle. The shear field has a vorticity equal to y/2 and the particle rotates with this constant angular velocity...

Figure 3.19 The collision trajectories of particles in a shear field, r0 = hQ + 2a...

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