Coalescence of bubbles in liquid

Abstract

Coalescence of bubbles is important for the destabilisation of gas-liquid dispersions. The theories of coalescence used at present are reviewed. The film drainage theory and the stochastic theory of coalescence have been discussed with their merits and drawbacks. The influence of van der Waals, electrostatic double layer, steric and solvation forces on the coalescence process has been discussed. The importance of adsorption of surfactant molecules at the air/water interface in presence and in absence of salt on coalescence time has been explained. Difference between the experimental conditions under which the foam films collapse and the bubble coalescence experiments has been pointed out. Possible reasons behind the failure of the film drainage models in predicting the coalescence time have been explained. Some directions for future research have also been discussed. List of symbolsa bubble radius, m a f area of the film, m 2 A surface area, m 2 A H Hamaker constant, J A min minimum surface area per adsorbed surfactant molecule, m 2 B modified Hamaker constant, J m c concentration of surfactant in the bulk solution, mol m 23 c s concentration of salt in the bulk solution, mol m 23 c ? i concentration of ions of type i in the bulk solution, mol m 23 C 1 ,C 2 constants in equation (14), N m 21 D C surface diffusivity, m 2 s 21 e electronic charge, C f r repulsive force generated by one mole of the surfactant at the barrier ring, N mol 21 F(t R ) cumulative probability distribution of coalescence time F h hydration force, N g acceleration due to gravity, m s 22 h film thickness, m h c critical film thickness, m k Boltzmann's constant, J K 21 K L equilibrium constant in Langmuir isotherm, m 3 mol 21 l length of a polymer segment, m L thickness of the polymer brush layer, m n ' number of ions per unit volume in the bulk solution, m 23 n s number of segments of the polymer molecule N total number of ruptured films N A Avogadro's number, mol 21 p pressure, Pa P C dimensionless coalescence threshold R gas constant, J mol 21 K 21 R b radius of barrier ring, m R m radius of curved surface, m s mean distance between the attachment points, m S C normalised standard deviation t time, s t c coalescence time, s t characteristic diffusion time, s T temperature, K w b width of the barrier ring, m z valence a fraction of C that remains at the barrier ring after the displacement of the surfactant molecules to the barrier ring c surface tension, N m 21 C surface excess, mol m 22 C mean value of the distribution of surface excess C, mol m 22 C number of adsorbed chains per unit area, m 22 C ' adsorption capacity, mol m 22 C m minimum value of the surfactant concentration at the barrier ring required to prevent coalescence, mol m 22 d separation between the surfaces, m Dp excess pressure in the film, Pa Dr density difference between the two phases, kg m 23 e dielectric constant of the medium e 0 permittivity of free space, C 2 J 21 m 21 k Debye-Hü ckel parameter, m 21 l i zeros of the Bessel function of the first kind and order one J ...

Factors affecting the coalescence stability of microbubbles

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