Abstract
We report measurements on fluid–fluid phase separation in a colloid–polymer mixture, which can be followed in great detail due to the ultralow interfacial tension. The use of the real-space technique, laser-scanning confocal microscopy, leads to clear, well-defined images making quantitative comparisons to theory possible and being highly instructive. Simple scaling arguments are given why, in experiment, three steps of the phase separation can be observed: an interfacial-tension-driven coarsening, gravity-driven flow and finally the interface formation. All these processes are observed in a single experiment. The first stage can be quantitatively described by viscous hydrodynamics. Coarsening occurs through pinch-off events. The second stage begins at a typical size of ∼2π times the capillary length reminiscent of the Rayleigh–Taylor instability. The liquid phase breaks up and becomes discontinuous. There is strong directional flow in the system, but the Reynold's number remains much smaller than unity. Finally, the macroscopic interface is formed, growing upwards, with a velocity comparable to the coarsening velocity in the initial stage. Again, viscous hydrodynamics apply with a characteristic velocity of the interfacial tension over the viscosity.
Highlights
In the unstable region of the phase diagram each density fluctuation in an intially homogeneous system is energetically favourable, but fluctuations with large wavelengths and shallowdensity gradients are thermodynamically more favourable, whereas for short wavelengths particles only have to diffuse over short distances
The wavelength L ≡ 2π/qm that follows from (1) is a few times the particle diameter d for colloid–polymer mixtures away from the critical point, of similar magnitude as for example estimated by van Aartsen for demixing polymer–polymer mixtures [19] and which we here estimated by using the theory presented in [20]
Using the capillary velocity (6) as the characteristic velocity we find that at a cross-over length of ργ the inertial hydrodynamic regime is entered
Summary
In the unstable region of the phase diagram each density fluctuation in an intially homogeneous system is energetically favourable, but fluctuations with large wavelengths and shallowdensity gradients are thermodynamically more favourable, whereas for short wavelengths particles only have to diffuse over short distances. In extensive computer simulations of two incompressible fluids of maximal symmetry, i.e. identical viscosity, density and volume fraction of the two fluids, this prefactor has been determined for the first time and was found to be 0.072 [24, 25] The magnitude of this interface velocity becomes comparable to the diffusive coarsening velocity of (3) at a cross-over length of [22]. In molecular systems, where the interfacial tension is relatively large, inertial terms may be expected to become important at lengths smaller than the capillary length (for estimates of the lengths in both molecular and colloid–polymer mixtures, see for example [10]). In that case the length scales are much larger as well, of the order of the capillary length, and gravity comes into play, which provides a further explanation of the lack of experimental evidence for the occurrence of the inertial regime. During the interface formation inertial terms do not play a role in the case of colloid–polymer mixtures
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