Particles Collisions with an Obstacle

When size of the particles is 1 pm, the Brownian diffusion does not play a noticeable role, and deposition of the particles suspended in the flow of liquid can be studied by a method of trajectory analysis of the flow-streamlines in the carrying liquid near the obstacle. The particles collisions with an obstacle occur at contact with its surface. The case of the particles collision with a cylinder at cross flow of suspension is illustrated in Fig. 10.6. 

Consider collision of a particle with an obstacle, neglecting the surface forces and the viscous resistance force arising from squeezing out the layer of liquid film between the particle s surface and the obstacle. 

Consider first collision of particles with a sphere. We assume the motion of particles to be inertialess. Then the particles trajectories coincide with the streamlines. The stream function of the Stokes flow past the sphere is given by 

Introduce a local system of coordinates (y, 9), where r/a = 1 y/a. Then near the surface we have y/a 1 and 

By its physical meaning, the difference 2n y/- - y/2) is equal to the volume flow rate of liquid between two stream surfaces y/ = y/i and y/ = y/2. If the particles distribution far from the sphere is homogeneous, with mass concentration / q, the mass flux of the particles to the sphere is equal to 

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