Microhydrodynamics of Particles

This chapter is essentially concerned with the hydrodynamics of mixtures containing non-charged particles and macromolecules, that is, molecules with molecular mass exceeding 10 and particles with sizes in the range 0.1-100 pm. For the branch of hydrodynamics concerned with the study of motion of liquids containing macromolecules and small particles, G.K. Batchelor [1] coined the term microhydrodynamics . The distinctive features of microhydrodynamics may be summarized as follows  

As a rule, the force of inertia is small in comparison with the viscous force, and therefore the hydrodynamic equations may be reduced to Stokes equations appropriate to hydrodynamics at small Reynolds numbers. 

Consideration of the Brownian motion of the particles in a liquid is essential. 

The sedimentation rate of particles in a liquid in a gravitational field is small, and so the particles can be considered to be freely buoyant in the liquid. The volume concentration of particles affects the rheological properties of the liquid. 

The force of surface tension plays a greater role than the volume force because the surface force is proportional to the particle surface area, that is, to the square of the linear particle size, whereas the volume force is proportional to the cube of the linear particle size. 

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As can be noted, Eq. (83), often ealled the ereeping flow or Stokes equation [74], is linear, which facilitates its analytical solution. Equation (83) is therefore often used for describing the microhydrodynamic behavior of particles (e.g., their motion in the vicinity of interfaces). 

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