VOLUME 84, NUMBER 9 PHYSICAL REVIEW LETTERS 28 FEBRUARY 2000 Viscous Sintering Phenomena in Liquid-Liquid Dispersions John Philip,* L. Bonakdar, P. Poulin, J. Bibette, and F. Leal-Calderon Centre de Recherche Paul Pascal, Centre National de la Recherche Scientifique, Avenue Albert Schweitzer, 33600, Pessac, France (Received 16 September 1999) We present experimental evidence for viscous sintering phenomena in a gel formed by highly viscous emulsion droplets. When a rupturing agent is added to the initially stable emulsion, a gel forms, which further contracts by preserving the geometry of the container. The initial stages of densification (up to 60%) follow very well the “cylindrical model” for viscous sintering, but deviate at the final stages of densification. The observed inverse dependence of the contraction rate on viscosity is consistent with the viscous sintering theory. PACS numbers: 82.70.Dd Liquid-liquid dispersions are observed in numerous sys- tems such as emulsions or phase separating binary fluid mixtures. These systems tend to coarsen in time via two limiting mechanisms, namely Ostwald ripening [1] and co- alescence [2]. Coalescence consists of a nucleation step followed by a shape relaxation driven by surface tension, which causes two droplets to fuse into a unique one. The characteristic time for shape relaxation is governed by the competition between surface tension and viscous dissipa- tion and is given by T r ~hRg, where h is the viscosity of the droplets, R is their characteristic radius, and g is their surface tension [3]. When there is no energy bar- rier for coalescence, the droplets coalesce as soon as they collide. This nonactivated coarsening has been identified in the late stages of phase separations or in strongly un- stable emulsions. The main limit that was most exten- sively studied to date corresponds to systems in which the characteristic shape relaxation time T r is much shorter compared to the time T b separating two droplet collisions (under the effect of Brownian motion). In this limit, it was found both theoretically and experimentally that the aver- age droplet size scales with time as t 13 in 3D systems [4]. A very different scenario is expected in the limit where T r ¿ T b . In this limit, the coarsening is limited by shape relaxation leading to very different structures and kinetics than in the previous case. Though this limit is frequently encountered in systems like emulsions of highly viscous substances (asphalt, colophon) or phase separations in bi- nary mixtures of polymers, it has not been systematically explored so far. Here we aim to complete the descrip- tion of coarsening mechanisms in fluid-fluid mixtures by exploring the limit where T r ¿ T b . We use model emul- sions of highly viscous oils (asphalt) which can be made suddenly unstable towards coalescence upon addition of a suitable chemical. Once the emulsion is made unstable, the droplets form a macroscopic gel made of an array of fused droplets, which continuously contracts with time in order to reduce its surface area. This contraction phenomenon is reminiscent of the sintering process observed in ceram- ics and aerogels [5,6]. This observation demonstrates that the viscous sintering can occur in organic materials having much lower viscosity than inorganic particles (6 to 8 orders of magnitude smaller than ceramics and glasses). By con- trast to previous studies, the viscosity is directly measured and varied, allowing thus a more quantitative comparison with models for viscous sintering. We used two different asphalts (from NYNAS Com- pany) with penetration grades 180220 and 80100 (the penetration grade is an indication of the fluidity obtained from the sinking of a needle in asphalt in normalized con- ditions). The low shear viscosity of asphalt was obtained at different temperatures ranging from 20 to 90 ± C. A crude emulsion was prepared by gently shearing surfactant and asphalt at a temperature of 95 ± C. Tetradecyl trimethyl ammonium bromide [TTAB, critical micellar concentra- tion CMC  3.5 3 10 23 M] was used as a cationic sur- factant. The composition of the asphalt, TTAB, and water was 80:6:14 by weight. From the crude initial emulsion, we obtained monodisperse samples of different sizes by using a fractionation technique [7]. The droplet size and polydispersity (approx. 12%) were measured using a Malvern particle sizer (Mastersizer S). In order to study gelation and the following contraction phenomena, we introduce the emulsion of known initial volume fraction in a rectangular cuvette and we add NaOH of known concentration. Since the emulsion is stabilized using a cationic surfactant, the droplet interface is posi- tively charged. This induces an electrostatic repulsion that prevents the droplets from coalescing. Naturally, asphalt contains some acidic molecules which are also present at the asphalt-water interface. By adding NaOH in the con- tinuous phase, the pH is raised and the acidic dissociation gives rise to some negative charges that may totally neu- tralize the interface. In the absence of electrostatic repul- sion, the droplets become unstable and coalesce. Just after the addition of NaOH, the emulsion is agitated for a few seconds and stored at a given temperature. Initially, the system remains liquidlike, but after some time, the emul- sion does not flow any more. At this stage, observation un- der microscope reveals that the droplets stick together and form a three-dimensional gel network. Once this network is formed, the gel starts to contract by reducing its surface area. In this process water is expelled from the space filling network. The contraction remains remarkably homothetic, 2018 0031-9007 00  84(9)  2018(4)$15.00 © 2000 The American Physical Society