The Capture of Particles Due to Surface and Hydrodynamic Forces

The discussion of the particles capture in the previous section was based on the assumption, that the particles are not subject to the forces from the system liquid - collector. Actually a particle near the surface of collector, is subject to the surface forces of (molecular and electrostatic) interactions, as well as the hydrodynamic force of viscous resistance from the liquid film between the particle and collector. The account of these forces considerably complicates the problem of determining the particles capture efficiency for the given obstacle. 

Consider the collision of particles of size more than 1 pm with a collector, taking into account only forces of molecular attraction and the hydrodynamic resistance force. The particles are assumed to be uncharged, and their deposition due to gravity is neglected. Consider deposition of particles on the cylinder, whose radius is much greater than radius of particles. The last condition allows us to assume that the particles practically do not disturb the velocity field far from the 

We also assume that the undisturbed velocity field corresponds to the Oseen solution, which is, near the cylinder s surface, described by the Eq. (10.80). The motion of particle in the vicinity of the cylinder s surface is schematically shown in Fig. 10.8 [65]. 

The radial component of the hydrodynamic force is denoted as Fsu The net hydrodynamic force is a sum of the external force acting on the particle from the liquid flowing around the obstacle, and the force of viscous resistance of the liquid film dividing surfaces of particle and cylinder. The external force can push the particle closer to or pull it away from the obstacle s surface. Note that the force of viscous resistance is negative. Next, denote as Fad the molecular force of the Van der Waals attraction. This force is directed along the perpendicular line from the particle to the symmetry axis of the cylinder. Since the Navier-Stokes equations in the Oseen s approximation are linear, the forces and velocity fields induced by them are additive. 

Consider undisturbed velocity held (10.80) near the cylinder s surface. It can be represented as the sum of two flows. The first is a flat flow such as the flow in the vicinity of stagnation point (Fig. 10.8, b). The velocity in the vicinity of this point is associated with the velocity component directed along the centerline. The other 

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