Brownian motion polymer flow studies

Aggregation of particles may occur, in general, due to Brownian motion, buoyancy-induced motion (creaming), and relative motion between particles due to an applied flow. Flow-induced aggregation dominates in polymer processing applications because of the high viscosities of polymer melts. Controlled studies—the conterpart of the fragmentation studies described in the previous section—may be carried out in simple flows, such as in the shear field produced in a cone and plate device (Chimmili, 1996). The number of such studies appears to be small. 

Studies on orthokinetic flocculation (shear flow dominating over Brownian motion) show a more ambiguous picture. Both rate increases (9,10) and decreases (11,12) compared with orthokinetic coagulation have been observed. Gregory (12) treated polymer adsorption as a collision process and used Smoluchowski theory to predict that the adsorption step may become rate limiting in orthokinetic flocculation. Qualitative evidence to this effect was found for flocculation of polystyrene latex, particle diameter 1.68 pm, in laminar tube flow. Furthermore, pretreatment of half of the latex with polymer resulted in collision efficiencies that were more than twice as high as for coagulation. 

Now that we have settled on a model, one needs to choose the appropriate algorithm. Three methods have been used to study polymers in the continuum Monte Carlo, molecular dynamics, and Brownian dynamics. Because the distance between beads is not fixed in the bead-spring model, one can use a very simple set of moves in a Monte Carlo simulation, namely choose a monomer at random and attempt to displace it a random amount in a random direction. The move is then accepted or rejected based on a Boltzmann weight. Although this method works very well for static and dynamic properties in equilibrium, it is not appropriate for studying polymers in a shear flow. This is because the method is purely stochastic and the velocity of a mer is undefined. In a molecular dynamics simulation one can follow the dynamics of each mer since one simply solves Newton s equations of motion for mer i,... 

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