Wake shedding and circulatory flow in bubble and droplet-type contactors

A review of published work on continuous phase circulation in spray columns, and on attached wake volumes for single droplets, revealed an apparent paradox in that reported values of the former were an order of magnitude greater than the latter when expressed as a ratio of the dispersed phase flow. These results were confirmed in experiments using a photochromic tracer to reveal the entrainment and circulatory flow.Theoretical considerations show that droplets translate an amount of continuous phase relative to their own volume of 1.5C_D/d per unit distance traversed. Droplets carry with them an attached wake (“cap”) which for Re_d< about 200 is effectively permanent, the translated continuous phase passing around droplet and “cap” leaving a wake trail. At Re_d > 200 a fraction j of the translated continuous phase accumulates in the “cap”, which becomes unstable and sheds a fraction s_av as toroids at regular intervals of height z_s. Estimated values are given for j, s_av, and z_s.This result is extended to the case of a continuous droplet flow, leading to an expression for the rate of increase in circulatory flow of continuous phase in the central core with height above the droplet distributor. This flow is balanced by an increasing momentum loss to the wall until a steady state is reached. The implications of this result on the performance of spray columns is discussed.