Oscillating phase separation in microemulsions. II. Description by a bending free energy

Abstract

We propose a mechanism to describe the phase separation of a single phase of water-in-oil microemulsion droplets towards a phase of smaller water droplets coexisting with a water-rich excess phase. The phase separation shows oscillatory behavior when induced by a continuous temperature increase. A periodic clouding and clearing is observed in the extinction of transmitted light which is also reflected in the specific heat. To model this behavior the bending free energy describing the equilibrium phase transition is applied to identify the energy barriers in the dynamics of this transition. They are due to conservation laws preventing the relaxation to a close to equilibrium size distribution of droplets unless volume and surface is redistributed simultaneously for a large number of droplets. By numerical integration of an expression for the time evolution of the size distribution of droplets it is verified that constant heating gives rise to oscillations. Besides clarifying the origin of the oscillations this approach also gives good estimates for heat absorbed during a single oscillation.

A test-tube model for rainfall

“…The cell is placed in a computer controlled thermostat, and its temperature is varied smoothly away from the phase coalescence temperature T c , at a rate de-scribed by a variable ξ which has dimensions of inverse time (defined by equation (4) below). Several examples of this type of experiment have been reported: [5][6][7][8][9]. The experiments show similar quantitative results: both layers show a variation in turbidity, which is approximately periodic, with period ∆t.…”

“…Discussion. -It has been argued that the periodic precipitation phenomenon which has been described in several works [5][6][7][8][9][10][11] is analogous to an atmospheric precipiation cycle in a stable atmosphere. Consider whether the same mechanisms are relevant to the growth of real rain droplets.…”

Oscillatory instabilities in phase separation of binary mixtures: Fixing the thermodynamic driving

“…In contrast to experiments with constant temperature ramps [26][27][28][29] we observed • a large number of oscillations ͑typically more than 15͒, We used this setup to study phase separation of binary liquid mixtures under constant driving forces Eqs.…”

“…They separate into two liquid phases. 19,20,[24][25][26][27][28][29][30][31][32] Irrespective of the ramp rate only a small number of oscillations is observed when linearly cooling a sample. Phase separation leads to a polymer-poor liquid phase and a polymerrich gel phase.…”

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“…In a very broad sense, these molecules can be viewed as being composed of two species (which we shall denote by A and B), whose interactions are such that they would show a strong tendency towards phase separation. Beyond the equilibrium structure, the systems also show extremely interesting and not fully understood non-equilibrium phenomena, like shear alignment of lamellar structures [2,3], the formation of "onion" structures [4], or "cascade nucleation" of A droplets in a B phase shielded by amphiphiles under the influence of continuous driving [5][6][7]. Systems of amphiphiles can form complex morphologies, in order to bring the alike species close to each other.…”