Coagulation gradient

In addition to the quasi-steady state assumption, the other assumptions required to arrive at equation (1) are 1. the aerosol itself does not coagulate 2. there is a fully developed concentration gradient around each aerosol particle and 3. the concentration of unattached radon progeny atoms is much greater than the concentration of aerosol particles (in order that concentration gradients of radon progeny atoms may exist). This last assumption is usually not valid since the radon progeny concentration is usually much less than the aerosol concentration. 

Coagulation a Collision efficiency volumetric concentration of suspended particles G Velocity gradient t time i... 

Smoluchowski, who worked on the rate of coagulation of colloidal particles, was a pioneer in the development of the theory of diffusion-controlled reactions. His theory is based on the assumption that the probability of reaction is equal to 1 when A and B are at the distance of closest approach (Rc) ( absorbing boundary condition ), which corresponds to an infinite value of the intrinsic rate constant kR. The rate constant k for the dissociation of the encounter pair can thus be ignored. As a result of this boundary condition, the concentration of B is equal to zero on the surface of a sphere of radius Rc, and consequently, there is a concentration gradient of B. The rate constant for reaction k (t) can be obtained from the flux of B, in the concentration gradient, through the surface of contact with A. This flux depends on the radial distribution function of B, p(r, t), which is a solution of Fick s equation... 

The rate of coagulation of particles in a liquid depends on the frequency of collisions between particles due to their relative motion. When this motion is due to Brownian movement coagulation is termed perikinetic when the relative motion is caused by velocity gradients coagulation is termed orthokinetic. 

The presence of velocity gradients in the system may also increase the rate of coagulation above the value given by Equation (24) or (42). 

The ratio of the probability of a collision induced by a fluid velocity gradient (dv/dx) (i.e., orthokinetic coagulation) to the collision probability under the influence of Brownian motion (perikinetic coagulation—what we have considered so far) has been shown to be (Probstein 1994)... 

The rate constant k0 for orthokinetic coagulation is determined by physical parameters (velocity gradient du/dz, floe volume ratio of the dispersed phase, = sum over the product of particle number and volume), and the collision efficiency factor a0 observed under orthokinetic transport conditions ... 

Chemical parameters determine the surface characteristics of the suspended colloids, the concentration of the coagulant and its effects upon the surface properties of the destabilized particles, and the influence of other constituents of the ionic medium upon the coagulant and the colloids. The extent of the chemical and physical interactions between the colloidal phase and the solution phase determines the relative stability of the suspended colloids. One speaks of stable suspensions when all collisions between the colloids induced by Brownian motion or by velocity gradients are completely elastic the colloidal particles continue their... 

The rate of coagulation depends upon the collision frequency, which is controlled by physical parameters describing perikinetic or ortho-kinetic particle transport (temperature, velocity gradient, number concentration and dimension of colloidal particles), and the collision efficiency factor a measuring the extent of the particle destabilization which is primarily controlled by chemical parameters. 

The coagulation rate depends upon physical parameters (temperature, velocity gradient, number and dimension of colloid), determining the collision frequency and upon chemical parameters (pH, Al(III) dosage, surface concentration of dispersed phase S), affecting the collision efficiency factor a... 

An important case is the interaction between two identical parallel surfaces of two infinitely extended solids. It is, for instance, important to understand the coagulation of sols. We can use the resulting symmetry of the electric potential to simplify the calculation. For identical solids the surface potential -ipo on both surfaces is equal. In between, the potential decreases (Fig. 6.9). In the middle the gradient must be zero because of the symmetry, i.e. d f(f x/ 2)/df = 0. Therefore, the disjoining pressure in the center is given only by the osmotic pressure. Towards the two surfaces, the osmotic pressure increases. This increase is, however, compensated by a decrease in the Maxwell stress term. Since in equilibrium the pressure must be the same everywhere, we have ... 

Wet scrubbing uses liquid droplets to remove fine dust in a gas stream. In all types of wet scrubbing, the basic cleaning mechanism involves the attachment of particles to the droplets. The function of the droplets in scrubbers is similar to that of spherical fibers in filtration. Likewise, the primary collection mechanisms in scrubbing are similar to those in filtration, i.e., inertial impaction, interception, and diffusion [e.g., Fan, 1989]. Secondary collection mechanisms include thermophoresis due to temperature gradients, coagulation of particles due to particle electrification, and particle growth due to liquid condensation. 

Figure 6.4 Comparison of key variables that control coagulation in natural and artificial systems G = mean water velocity gradients (s-1), = particle concentration, and a = collision efficiency. (From Stumm and Morgan, 1996, with permission.)...

As repulsive forces decrease with increasing salinity, van der Waals forces will dominate and flocculation will proceed. Strong salinity gradients in estuaries make them ideal environments for coagulation processes. 

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