Shear-induced dispersions

M. R. King, D. T. Leighton 2001, (Measurement of shear-induced dispersion in a dilute emulsion), Phys. Fluids 13, 397. 

Despite the small dimensions, conventional models for dispersion have been applied to microreactors. Since flow is laminar, a Taylor-Aris or shear-induced dispersion model generally describes dispersion. Beard has applied the Taylor-Aris dispersion model to... 

For l-/im particles, the inertial force is quite small relative to the drag force, and rapid formation of a particle or gel layer is predicted. However, the particle layer does not grow steadily until it plugs the channel but seems to reach a steady-state thickness. One explanation is that the high shear rate near the wall causes a tumbling motion of individual particles, which expands the layer and leads to migration away from the wall. This shear-induced dispersion and the particle movement toward regions of lower concentration can be modeled with a particle diffusivity, which is proportional to the shear rate and the square of the particle size. More work is needed to understand the effects of particle shape and surface characteristics. 

Theoretical representation of the behaviour of a hydrocyclone requires adequate analysis of three distinct physical phenomenon taking place in these devices, viz. the understanding of fluid flow, its interactions with the dispersed solid phase and the quantification of shear induced attrition of crystals. Simplified analytical solutions to conservation of mass and momentum equations derived from the Navier-Stokes equation can be used to quantify fluid flow in the hydrocyclone. For dilute slurries, once bulk flow has been quantified in terms of spatial components of velocity, crystal motion can then be traced by balancing forces on the crystals themselves to map out their trajectories. The trajectories for different sizes can then be used to develop a separation efficiency curve, which quantifies performance of the vessel (Bloor and Ingham, 1987). In principle, population balances can be included for crystal attrition in the above description for developing a thorough mathematical model. 

Shear-induced coalescence or finer dispersion of droplets or bubbles, changing the properties of the sample. 

The object of this study was to clarify some aspects of the mechanism of shear-induced flocculation in colloidal dispersions. Vinyl chloride homopolymer and copolymer latices were prepared by emulsion polymerization using sodium dodecyl sulphate as emulsifier. Agglomeration behavior in these latices was studied by measuring the mechanical stability using a high speed stirring test. The latex particle size was measured by an analytical centrifuge. Molecular areas of emulsifier in the saturated adsorption layer at the surface of homopolymer and copolymer latex particles were estimated from adsorption titration data. 

Structural rearrangements of the dispersion affected by Brownian motion is encoded in the transient density correlator. Shear induced affine motion, viz. the case Do = 0, is not sufficient to cause (z) to decay. Brownian motion of the quiescent correlator leads at high densities to a slow structural process which arrests at... 

Although this picture is remarkably generic, the mechanisms responsible for the formation of a particle-lean layer adjacent to the wall depend on the properties of the material under consideration. For the case of solid particle dispersions, wall depletion, particle migration, and solid-liquid separation are the most frequent sources of solvent layer lubrication. Wall depletion occurs whenever dispersions are brought into contact with smooth and solid surfaces because the suspended particles cannot penetrate rigid boundaries [147]. Particle migration is due to various forces arising from fluid inertia, fluid elasticity, and shear-induced diffusivity effects [165]. Solid-liquid separation, which frequently occurs in flocculated suspensions like... 

Gustafsson, J., Nordenswan, E., and Rosenholm, J.B., Shear-induced aggregation of anatase dispersion investigated by oscillation and low shear rate viscometry, 7. Colloid Interf. Sci., 242, 82, 2001. 

Several types of dispersions show strain rate thinning, and a quantitative explanation is not easily given. We will briefly consider two cases. The first one concerns shear flow. As discussed (above, Factor 4), anisometric particles show rotational diffusion and thereby increase viscosity. This effect will be smaller for a higher shear rate when the shear-induced rotation is much faster than the diffusional rotation, the latter will have no effect anymore. The shear rate thinning effect is completely reversible. Something comparable happens in polymer solutions (Section 6.2.2). 

Eor dilute Newtonian systems, the size of the smallest drop that can be broken is calculable from Taylor s theory. However for polymer systems, many studies have shown that the equUibrium drop size is usually larger than predicted, and the deviation increases with concentration of the dispersed phase, ( )j - ( ), where ( )j is the volume fraction of the dispersed phase, and ( ) = 0.005 is the smallest concentration for which the deviation occurs. Roland and Bohm [1984] studied the shear-induced coalescence in two-phase polymeric fluids by smaU-angle neutron scattering. The coalescence rate was high, dependent on the rheological properties of the two phases and the flow field. 

This can be explained as follows. It is known that PP and EPDM are immiscible materials and they exhibit a lower critical temperature (LCST) phase diagram (19). During mixing, especially at high shear rates, the LCST curve elevates with temperature and shear-induced mixing takes place. Thus, in the process of dynamic vulcanization, PP and EPDM can be considered as miscible materials under high shear rates. As a result, after the cross-linking reaction, the unmixed EPDM component forms the dispersed domain, while the matrix consists of mixed PP (dominant) and EPDM (minor) components connected by chemical cross-links (20). 

These surface vortices provide an efficient means for microfiuidic mixing, as shown in Fig. 10, where a dye is rapidly mixed within several seconds. The mixing can be enhanced by inducing the vortex instabilities wherein turbulent-like mixing efficiencies are observed [18]. In addition, particles dispersed in the flow are also observed to be drawn into the vortices due to positive dielectrophoresis toward a point on the interface closest to the needle where the field is most intense. Once a sufficient particle concentration is achieved within the vortex, shear-induced migration leads to crossstreamline transport such that the interior of the vortex is populated [18], as shown in Fig. 11a. 

By contrast with the flow-induced dispersion, the flow-induced coalescence is not as well described. For example, there is a critical capillarity number for breakup, but not for coalescence. Three approaches have been used, based on (i) the minimization of energy [129], (ii) the frequency of collisions assumed proportional to the shear energy, ycri2 [292], and (iii) the instability of the liquid layer trapped between two drops with an immobile or mobile interface [125, 293-297] ... 

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