![]() ![]() The histograms can be well-approximated by normal distributions (similarity to normality >99.8%, as measured by Kolmogorov–Smirnov statistic) 28, 29, confirming that the normal distribution is conserved through coalescence. 4a, along with the normally distributed 0th population. The histograms of simulated d n's ( n>0) are shown in Fig. To obtain the distribution of the nth droplet population, we resort to the Monte Carlo method, which computes one million d n values from randomly selected d 0's using equation (6). 1) 22, 23, 24, suggesting that the emulsions have only experienced limited coalescence 21.Īccording to equation (6), we can prove that the probability density function of d n is the T n-fold convolution power of the probability density function of (see Supplementary Note 1 for derivation), which cannot be evaluated analytically. Pickering droplets prepared following this protocol have low uniformity indices between 0.2 and 0.4 ( Supplementary Fig. 1g–i), forming a closely packed ensemble ( Fig. Then, emulsions are left standing undisturbed on top of a bench for 10 min, allowing droplets to precipitate ( Fig. 1d–f), forming Pickering emulsions containing stabilizer-wrapped droplets 21. First, water, oil and stabilizers are mixed and then shaken vigorously by hand for 10 min ( Fig. Pickering emulsions stabilized by latex particles, silica particles and CNTs are prepared following a conventional protocol 20, involving two consecutive steps. 1c) are several micrometers long and have a diameter of ca. CNTs decorated with surface tension-tuning magnetite (Fe 3O 4) nanoparticles ( Fig. 1a,b) are spheres with diameters of 0.8 μm and 1 μm, respectively. The three stabilizers and typical Pickering emulsions made from them are shown in Fig. Emulsion preparation and droplet size analysis Our results are organized in four sections as follows, including emulsion preparation and droplet size analysis, evolution of droplet size through multi-body coalescence, polydispersity and size evolution and coalescence probability and interparticle force. Subsequent comparisons with the CNT system will reveal differences between stabilizers lacking and having attractive interactions. Comparisons between the first two systems will show that multi-body coalescence occurs in both water-in-oil and oil-in-water emulsions. To investigate coalescence of Pickering droplets in an ensemble, we select three representative emulsion systems, including latex particle-stabilized water droplets in dodecane, silica particle-stabilized 1,2-dichlorobenzene (DCB) droplets in water and CNT-stabilized water droplets in dodecane. Using model stabilizers including latex particles, silica particles and carbon nanotubes (CNTs), we show that coalescence is promoted by interparticle repulsion but inhibited by interparticle attraction. Futhermore, interactions between stabilizers are found to affect the probability of coalescence by varying interfacial tension. As a result, a magic size distribition is produced with distinctive maxima related to each other through the cubic root of four times the tetrahedral numbers. More interestingly, the number of droplets involved in coalescence equals four times the corresponding number of the tetrahedral sequence, indicating the inclusion of all closely packed nearest neighbours in a single coalescene event. Here we report for the first time that the presence of stabilizers at the oil–water interface can lead to multi-body coalescence in an ensemble of Pickering droplets-a phenomenon that has not been reported for either Pickering or ordinary emulsions. This is particularly important when particle stabilizers are used to produce near-monodispersed droplets 17, during which the distribution of droplet size can be significantly broadened by coalescence under gravity, floatation and shear 18, 19. Little is known, however, about the coalescence of a collection of hundreds and thousands of Pickering droplets as in real emulsions. When individual Pickering droplets are forced to coalesce, the extraordinary stability brought about by interfacial particles can lead to the formation of non-spherical droplets 12, 13, 14 and the arrest of droplet coalescence 15, 16. Compared with ordinary emulsions, Pickering emulsions are distinctively stable because the removal of interfacial particles requires a large amount of energy 11. They are important soft matter systems that form naturally in crude oils 3 and food products 4 and have been engineered for drug delivery 5, water purification 6 and material processing 7, 8, 9, 10. Pickering emulsions are made of particle-stabilized droplets suspended in an immiscible continuous liquid phase 1, 2. ![]()
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