Coagulation, theories

The debate as to which mechanism controls particle nucleation continues. There is strong evidence the HUFT and coagulation theories hold tme for the more water-soluble monomers. What remains at issue are the relative rates of micellar entry, homogeneous particle nucleation, and coagulative nucleation when surfactant is present at concentrations above its CMC. It is reasonable to assume each mechanism plays a role, depending on the nature and conditions of the polymerization (26). 

The coagulation, flocculation, and adsorption processes were modeled mathematically using classical coagulation theory as a starting point. The Smoluchowski equation for orthokinetic coagulation in laminar flow is written (18)... 

Various analytical solutions to the von Smoluchowski equation set have been developed over the years, originating with the solution presented by von Smoluchowski coinciding with the expression of coagulation theory in 1917 [1]. No general analytical solutions to the von Smoluchowski equation are available, but many expressions have been developed with simplifying assumptions. This section will review the available analytical solutions and discuss the uses and limitations of the solutions. 

Cunningham correction factor for, 63 settling velocity of, 81-82 Simple coagulation theory, 308 Simple diffusion, 131-143 Single-particle scattering measurements, 297-299... 

Jackson, G. A. (2005). Coagulation Theory and Models of Oceanic Plankton aggregation. CRC Press, Boca Raton, FL. 

Among the questions that coagulation theory can help answer are how organisms feed on each other and how biological production leaves the euphotic zone. Coagulation theory and the related filtration theory have, in fact, been used to understand the nature of feeding in both planktonic and benthic animals (1 1). This chapter addresses the transport of organic matter downward, out of the euphotic zone. 

There is a long history of interest in using coagulation theory to explain the nature of particulate distributions and interactions in the ocean (51-53). Most of this work focused on nonliving particles. 

The modeling also showed the importance of some of the underdeveloped aspects of coagulation theory, particularly with regard to the interaction of the hydrodynamics and the fractal structure of the aggregates on the coagulation kernels. Traditional coagulation theory emphasized understanding the interactions of two solid spheres. Some work has been done on the flow in and... 

Kiprboe, T., Lundsgaard, C., Olesen, M., Hansen, J. L. S., 1994. Aggregation and sedimentation processes during a spring phytoplankton bloom a field experiment to test coagulation theory. Journal of Marine Research, 52, 297-323. 

Figure 7. Volumetric mass transfer coefficient based on effective particle diameter using coagulation theory.

In the second edition, I have sharpened the focus on aerosol dynamics. The field has grown rapidly since its original applications to the atmospheric aerosol for which the assumption of panicle sphericity is u.sually adequate, especially for the accumulation mode. Major advances in the eighties and nineties came about when we learned how to deal with (I) the formation of solid primary panicles, the smallest individual panicles that compose agglomerates and (ii) the formation of agglomerate structures by collisions. These phenomena, which have important industrial applications, are covered in two new chapters. One chapter describes the extension of classical coagulation theory for coalescing... 

With the coagulation theory of morphine action and drug addiction substantiated, there appears to be no reason why certain morphine addicts should not be cured efficiently and completely by the use of sodium thiocyanate. 

From the theoretical point of view a similarity exists between electrostatic retardation of ion transport and coagulation retardation, known as slow coagulation (Fuchs, 1934). Both phenomena arise from electrostatic repulsion caused by the existence of the diffuse part of the DL. In the slow coagulation theory, the electric field if the DL is derived from the Gouy-Chapman model (cf. Chapter 2). This model does not consider a deviation of the diffuse layer from equilibrium. Initially, the same simplification was used by Dukhin et al. (1973) in describing the DL effect on the electrostatic retardation of adsorption. 

In the following, we comment on some peculiarities and restrictions of the slow coagulation theory since it can also be of importance for the adsorption kinetics. The elementary act of slow coagulation consists of the pairwise interaction of particles and their mutual diffusion as a nonsteady process. The concentration distribution of pairwise interacting particles is a function of distance and time and is described by the equation of non-steady electro-diffusion... 

Interstitial aerosol particles collide with cloud droplets and are removed from cloud interstitial air. The coagulation theory of Chapter 13 can be used to quantify the rate and effects of such removal. If n(Dp,t) is the aerosol number distribution and nd(Dp,t) the droplet number distribution at time r, the loss rate of aerosol particles per unit volume of air due to scavenging by cloud drops is governed by... 

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