A general hydrodynamic theory for mixed-phase microphysics. Part II: collision kernels for coalescence

A semiempirical solution is presented to the collision efficiencies and kernels for coalescence which is based on boundary-layer theory. Extensive simplifications to the collisional problem, based on empirical arguments, and the powerful linear boundary layer approach lead to an analytical solution which is justified primarily by the quality of its results: the present theory is in good agreement with measured coalescence efficiencies and with numerical results on collision efficiencies from Stokes' theory, modified Oseen theory, and the superposition method. In the size range of particles relevant to drop coalescence the deviations between the present theory and the results from the literature are within the accuracy of the latter, from droplets with about 5 pm radius to precipitation-size drops. For drops of equal size and fall speed the present theory predicts non-vanishing collision kernels and it is capable of explaining the marked disagreement between various studies on wake capture effects. The dependence of the collision efficiency on pressure and temperature is discussed and it is found that both variations are considerable but, to a certain degree, tend to compensate each other for varying altitude.