On the Sauter mean diameter and size distributions in turbulent liquid/liquid dispersions in a stirred vessel

Abstract It has been customary to relate the Sauter mean drop size, d 32 , to Weber number, We , by the relationship d 32 D∝We -0.6 . This relationship comes from the assumptions that d 32 is a constant fraction of d max , where d max is the maximum stable drop size and that d max can be predicted from theoretical considerations if Kolmogoroffs theory of isotropic turbulence is used for estimating the disruptive forces. Here it is shown, firstly on theoretical grounds, that the assumption d 32 ∝ d max is not justified; and secondly that experimental results from 18 different runs neither support d 32 = Ad max where A is system and agitation conditions independent nor that the exponent on We is −0.6. Further, though cumulative volume size distributions indicate self-similarity, as suggested previously, the number probability density distributions show strong bi-modality at low speed and low dispersed-phase concentration which lessens with increasing concentration and becomes uni-modal at high speeds. This study suggests that in spite of the great deal of work which has already been done, more is required in which the relationship between mean drop size and drop size distributions and agitation conditions over a wider range of concentrations are further investigated.