Length of recoil

As in Section 11.1, we consider the reflection of a particle from a flat boundary at normal sedimentation. This assumption can be used for a bubble when we are interested in impacts close to the pole, at < ,. Thus, we can simplify the expression for the normal flow of liquid setting cosine to unity and assuming that over whole section of the surface at < j the length of recoil is characterized by a constant value. In dimensionless form, the equation for calculating the inertia path change due to the opposite motion of the liquid which has a velocity distribution expressed by a linear relationship (differs from a linear second-order differential equation with constant coefficients only due to a variation of Reynolds number for a retarded particle). It reads... 

In the other limiting case when the length of recoil is commensurable with the radius of the particle, the third term in (11.55) can be considered as a constant quantity equal to Eq. This allows us to decrease the order of the equation and to obtain a simpler solution. 

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