Coagulation differential sedimentation

With this formulation, chemical effects on coagulation are included in a and physical effects in Particle contacts are usually considered to be caused by three mechanisms differential sedimentation, shear (laminar and turbulent), and Brownian motion. Differential sedimentation contact occurs when two particles fall through the water at different rates and the faster particle overtakes the slower one. Shear contact occurs when different parts of the fluid environment move at different speeds relative to each other, and thus a particle that is moving with one fluid patch overtakes and collides with a particle in a slower fluid patch. Brownian motion contact occurs when two particles move randomly through their fluid in Brownian motion and collide... 

The coagulation kernel for the rectilinear case of differential sedimentation is... 

Thus there is a lai e discrepancy between the theoretical predictions of the collision efficiency for aerosol coagulation by differential sedimentation (taking into account inter-particie fluid motion) and experimental measurements for coagulation by turbulent shear in aqueous suspensions. We do not know whether this discrepancy is due to the ba.sic difference in the coagulation mechanisms (differential sedimentation vs. turbulent shear), different phenomena operating in the different fluid media, or some other as yet unidentified effect. 

The interaction in a two-body collision in a dilute suspension has been expanded to provide a useful and quantitative understanding of the aggregation and sedimentation of particulate matter in a lake. In this view, Brownian diffusion, fluid shear, and differential sedimentation provide contact opportunities that can change sedimentation processes in a lake, particularly when solution conditions are such that the particles attach readily as they do in Lake Zurich [high cc(i,j)exp]. Coagulation provides a conceptual framework that connects model predictions with field observations of particle concentrations and size distributions in lake waters and sediment traps, laboratory determinations of attachment probabilities, and measurements of the composition and fluxes of sedimenting materials (Weilenmann et al., 1989). 

Orthokinetic coagulation and differential sedimentation play an important role in such processes as flotation, water treatment, dust entrapment and natural precipitation from the atmosphere. 

The third coagulation mechanism, differential sedimentation, occurs when a particle falling at its terminal settling velocity collides with a slower settling particle. This is represented as a cross-sectional area of collision multiplied by the difference in Stokes settling velocities of the colliding particles... 

These expressions for the collision function assume purely geometrical collisions and do not include electrostatic, van der Waals, or viscous forces. Corrections for these surface and fluid forces are available for Brownian coagulation and have been verifled experimentally by Lichten-belt et al. (12) in the absense of electrostatic forces for particles uniform in size. For shear coagulation, corrections have been computed for collisions between spheres of equal size, and experimental agreement with theory has been obtained only when electrostatic forces are absent (van de Ven and Mason (13) Zeichner and Schowalter (14)). Differential-sedimentation coagulation of hydrosols has not been examined theoretically or experimentally. 

The parameters for differential-sedimentation coagulation and settling have the same grouping of constants but different units because differential sedimentation is second order in the particle size distribution from Equation 2, while gravitational settling is first order in the size distribution as seen in Equation 1. All parameters were chosen to be independent of particle size, assuming further that particle density is also independent of particle size. 

Ab, Ash, Ads, As = dimensionless coeflBcients for Brownian, shear, and differential-sedimentation coagulation, and gravitational settling... 

The optimal concentrations were determined at which iron and silica sediments separate rapidly from a mixed sol as it coagulates, forming banded jaspilite-like layers. In these experiments, differential deposition of iron... 

Collision of colloids can be effected by Brownian motion, by velocity gradients resulting from laminar and turbulent flow and so by differential movement in the sedimentation of such particulates. If coagulation is used as technical process for the improvement of solid separation through aggregation, then velocity gradient induced collisions predominate. 

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