Aggregation orthokinetic

Figure 6.6 (a) Periidnetic aggregation, (h) Orthokinetic aggregation (schematic)... 

A semi-empirical form of orthokinetic aggregation kernel due to Thompson (1968) is adopted for illustrative purposes only, viz. 

Mumtaz, H.S., Hounslow, M.I., Seaton, N.A. and Paterson, W.R., 1997. Orthokinetic aggregation during precipitation A computational model for calcium oxalate monohydrate. Transactions of the Institution of Chemical Engineers, 75, 152-159. 

This is often referred to as the orthokinetic aggregation kernel. 

These kernels are valid for inertialess particles (i.e. Stp = 0) and can be extended to finite Stokes numbers only by employing ad hoc corrections. For example, Ammar Reeks (2009) derived for the kernel proposed by Salfman Turner (1956) a correction that is based on the local Stokes number. The relative importance of perikinetic aggregation versus orthokinetic aggregation is quantified by a Peclet number ... 

Slow stirring can indeed promote aggregation. Such aggregation under the influence of velocity gradient is known as orthokinetic aggregation. The rate of orthokinetic aggregation is given by... 

The obvious conclusion is that the resistance to breakup which should be related to the aggregate internal cohesion is greater for aggregates obtained under stirring (orthokinetic aggregation) than that of systems obtained in perikinetic processes (Eq. 29). 

Other Complications. At high volume fractions, the encounter rate will be more than proportional to cp, because the effective volume available for the particles is decreased owing to geometric exclusion. This also applies to perikinetic aggregation. For orthokinetic aggregation a high volume fraction will, moreover, affect the capture efficiency, because the stress sensed by the particles will be greater than f/f see Section 5.1.2. 

Sedimentation. If particles are subject to sedimentation, this may also lead to enhanced aggregation rate, since particles of different sizes will move with different velocities through the liquid see Section 13.3. This implies that a large particle can overtake a smaller one, and a kind of orthokinetic aggregation occurs. This will be the case if (a) there is a substantial spread in particle size and (b) particle motion over a distance equal to its diameter takes less time by sedimentation than by Brownian motion. The condition for the latter is approximately... 

It is very difficult to avoid convection currents with a velocity gradient of the order of 0.1 s 1 to occur. As soon as the particles have grown to a size for which Eq. (13.10) equals unity, orthokinetic aggregation will take over, which soon proceeds very much faster than perikinetic aggregation. 

Orthokinetic Aggregation The process of aggregation induced by hydrodynamic motions such as stirring, sedimentation, or convection. Orthokinetic aggregation is distinguished from perikinetic aggregation, the latter being caused by Brownian motions. 

Proteins in solution are also sensitive to orthokinetic aggregation, i.e., shear-induced aggregation. We have observed this phenemenon at very low shear rates in the case of BSA, ovalbumin, and BLG [28,29] in Fig. 1, one sees that the viscosity of the protein solution increases with time till it reaches a plateau the phenomenon becomes less and less pronounced as the shear rate increases, so much so that the solution displays time-independent and Newtonian flow behavior in the usual shear rate range. 

When the dispersion is stirred or when it flows, diffusion is not the only mechanism determining the collision probability. Under such conditions, the shear rate, that is, the velocity gradient, normal to the particle surface, dv(x)/dx (see Section 17.1.3) enhances the collision frequency, so that the orthokinetic aggregation rate is faster than the perikinetic aggregation rate. Under conditions of rapid aggregation, it can be derived that... 

Hollander etal. (2001) report numerical simulations of orthokinetic aggregation in a turbulent channel flow and in a stirred tank, respectively. Using a... 

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