title: A theory on bubble-size dependence of the critical electrolyte concentration for inhibition of coalescence.
abstract: The interaction of pairs of bubbles with equal diameters grown on adjacent capillaries in aqueous magnesium sulfate solutions is studied by varying electrolyte concentration and bubble diameter by Tsang, Koh and Koch [Y.H. Tsang, Y.-H. Koh, D.L. Koch, J. Colloid Interface Sci. 275 (2004) 290] (referred to as TKK hereafter). They find that the critical concentration to prevent coalescence, Ct, increases as the equivalent diameter, deq, decreases. In fact, Ct is found to scale as deq(-1.2). This dependence is stronger than that predicted by Prince and Blanch (Ct approximately deq(-0.5)) (referred to as PB [M.J. Prince, H.W. Blanch, AIChE J. 36 (1990) 1425] hereafter) on the basis of a postulation that lubrication pressure due to Marangoni stresses inhibit coalescence. TKK postulate instead that bubbles are stabilized by hydration structures. We further illustrate here that when hydration force term is added to the equation of motion of the film thinning process, predicted values of critical concentration are found to scale as deq(-1). The current prediction shows a much better agreement with the experimental results than that proposed by PB. This suggests previous assumption that immobility of the interface by Marangoni effect as the dominant mechanism of inhibition of coalescence in an electrolytic solution is inaccurate [M.J. Prince, H.W. Blanch, AIChE J. 36 (1990) 1425, G. Marrucci, Chem. Eng. Sci. 24 (1969) 975].
authors.affiliation: Department of Mathematics, Cornell University, Ithaca, NY 14853, USA. bsc28@cornell.edu
authors.forename: Benjamin S
authors.initials: BS
authors.lastname: Chan
authors.forename: Ying Hang
authors.initials: YH
authors.lastname: Tsang