Particle transport fluid shear

Heterodisperse Suspensions. The rate laws given above apply to monodisperse colloids. In polydisperse systems the particle size and the distribution of particle sizes have pronounced effects on the kinetics of agglomeration (O Melia, 1978). For the various transport mechanisms (Brownian diffusion, fluid shear, and differential settling), the rates at which particles come into contact are given in Table 7.2. 

When the voltage is critical, regime b), there is no concentration polarization because the electrophoretic transport is equal to the convective transport. Any build up of species on the membrane will be dissipated due to diffusion driven by the concentration difference. In this regime, increasing the tangential velocity is expected to have no influence on the flux because fluid shear can only improve the transport of particles down a concentration gradient. In this case, there is no concentration gradient. 

In the development above, it has been convenient to consider collisions, via particle transport, and reactions, the probability of particle attachment, as separate steps. There are a number of considerations indicating that this conceptual framework may have outlived its usefulness, as advancements in particle science, analytical capabilities, and supercomputers obviate the necessity of this artificial separation. Adler [4], Han and Lawler [3], and others have demonstrated using trajectory modeling the significant influence of hydrodynamics on particle collisions, and show how the lumped collision efficiency (inclusive of hydrodynamics) is a function of the type of collision mechanism. Thus, for a given particle pair, the collision efficiency will be different depending on whether the collision is a result of Brownian motion, fluid shear, or differential sedimentation. 

Here (3Br(ij), Psll(i,j), and PDS(ij) are the transport coefficients for interparticle contacts between particles of diameters d, and dj by Brownian diffusion, fluid shear, and differential sedimentation, respectively kB is Boltzmanns constant T is the absolute temperature p, is the viscosity of the liquid G is the mean velocity gradient of the liquid g is the gravity acceleration and pp and p, are the densities of the particles and the liquid, respectively. 

Numerical results obtained by Han and Lawler (25) for the effects of hydrodynamic interactions on particle transport by fluid shear are summarized graphically in Figure 9. These results are based on the work of Adler (26). The effects of particle size, velocity gradient, and van der Waals interaction are characterized by a dimensionless group, HA, defined as follows ... 

Figure 9. Effect of particle size on physical aspects of particle collisions by fluid shear. The ratio of rectilinear to curvilinear transport coefficients is plotted as a function of the ratio of the size of the smaller particle (dj) to a larger one (dj). The circled A, B, and C refer to cases discussed in the text. (Reproduced with permission from reference 25. Copyright 1992.)...

Zaichik, L. I. 1999 A statistical model of particle transport and heat transfer in turbulent shear flows. Physics of Fluids 11, 1521-1534. 

Three particle transport processes that bring about interparticle contacts are considered here Brownian diffusion (thermal effects), fluid shear (flow effects), and differential settling (gravity effects). Following Smoluchowski s approach, the appropriate individual transport coefficients for these three processes arc as... 

A unique interaction between fluid mechanics and transport exists for filtration processes. Such processes perform better than expected based on the predicted impact of concentration boundary layers. The improvement in performance, a rare occurrence for membrane processes, arises from a combination of hydrodynamic diffusion and inertial lift [51]. Hydrodynamic interactions between particles or colloids that accumulate in the concentration boundary layer lead to shear-induced diffusion away from the membrane surface. Shear-induced diffusion can be significantly larger than molecular diffusion and thereby reduce surface concentrations. For sufficiently large particles at high shear rates, inertial lift becomes the dominant mechanism for particle movement away from the membrane. 

Suspended particle transport is the result of dynamic equilibrium between particle detachment and deposition (sedimentation). A suspended particle will settle when the fluid shear stress drops below a critical level. Neglecting reaction, mass conservation of an insecticide associated with particles in settling velocity class i can be described by ... 

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