Hydrodynamic interactions between bodies

Note that in some problems of heat and mass transfer and chemical hydrodynamics, the velocity fields near the body can be determined by the flow laws of ideal nonviscous fluid. This situation is typical of flows in a porous medium [75, 153, 346] and of interaction between bodies and liquid metals (see Section 4.11, where the solution of heat problem for a translational ideal flow past an elliptical cylinder is given). 

When filler spheres are close enough, hydrodynamic interactions between particles need to be considered. By factoring in the effects of two-body interactions, a modified equation was derived that is apphcable up to > = 0.1 (24). 

The effect of hydrodynamic interactions on aggregation of colloidal particles may be rather essential and simulation results show that they constrain the growth of aggregates [63]. Computational simulation predicts that many-body hydrodynamic interactions between colloidal particle are able to reduce the sohd fraction required for percolation or gelation [64, 65]. The merging of clusters into condensed aggregate was observed at particle volume fracture p as low as 0.06-0.12 [64]. 

Physicochemical hydrodynamics was first set out as a discipline by the late Benjamin Levich in his classic book of the same name. The subject, which deals with the interaction between fluid flow and physical, chemical, and biochemical processes, forms a well-connected body of study, albeit a highly interdisciplinary one. It has applications in many areas of science and technology and is a rapidly expanding field. The aim of this textbook is to provide an introduction to the subject, which I shall refer to here by its acronym PCH. 

Up to this point we have considered distributed dilute dispersions of colloidal size particles and macromolecules in continuous liquid media. Where the particles are uncharged and of finite size, they are always separated by a fluid layer irrespective of the nature of the hydrodynamic interactions that take place. In the absence of external body forces such as gravity or a centrifugal field or some type of pressure filtration process, the uncharged particles therefore remain essentially uniformly distributed throughout the solution sample. We have also considered the repulsive electrostatic forces that act between the dispersed particles in those instances where the particles are charged. These repulsive forces will tend to maintain the particles in a uniform distribution. The extent to which a dispersion remains uniformly distributed in the absence of applied external forces, such as those noted above, is described in colloid science by the term stability, whereas colloidal systems in which the dispersed material is virtually insoluble in the solvent are termed lyophobic colloids. 

As a result of multiparticle hydrodynamic interactions, the fiij all depend on the positions of all particles in the system, in a way that is usefully split into pair interactions, three-body interactions, and higher terms. Note that and therefore Dij are divided between their self and distinct parts, including for i = j... 

The Hydrodynamic Factor. In order to determine the reasons for the dependence of adhesion on contact time, let us consider the hydrodynamic phenomena taking place as bodies approach or recede from each other. For this purpose it is customary to use adhesion-simulating techniques (see Section 13), particularly techniques involving plane-parallel disks. The hydrodynamic factor, which is governed by movement of the liquid in the gap between the contiguous bodies and which determines the variation of adhesion with contact time in the interaction of plane-parallel disks, can be taken into account by means of the Stefan-Reynolds equation [96],... 

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