Wetting controls of droplet formation in step emulsification.

The formation of droplets is ubiquitous in many natural and industrial processes and has reached an unprecedented level of control with the emergence of milli- and microfluidics. Although important insight into the mechanisms of droplet formation has been gained over the past decades, a sound understanding of the physics underlying this phenomenon and the effect of the fluid's flow and wetting properties on the droplet size and production rate is still missing, especially for the widely applied method of step emulsification. In this work, we elucidate the physical controls of microdroplet formation in step emulsification by using the wetting of fluidic channels as a tunable parameter to explore a broad set of emulsification conditions. With the help of high-speed measurements, we unequivocally show that the final droplet pinch-off is triggered by a Rayleigh-Plateau-type instability. The droplet size, however, is not determined by the Rayleigh-Plateau breakup, but by the initial wetting regime, where the fluid's contact angle plays a crucial role. We develop a physical theory for the wetting process, which closely describes our experimental measurements without invoking any free fit parameter. Our theory predicts the initiation of the Rayleigh-Plateau breakup and the transition from dripping to jetting as a function of the fluid's contact angle. Additionally, the theory solves the conundrum why there is a minimal contact angle of α = 2π/3 = 120° for which droplets can form.

Coagulation-agglomeration of fractal-like particles: structure and self-preserving size distribution.

Agglomeration occurs in environmental and industrial processes, especially at low temperatures where particle sintering or coalescence is rather slow. Here, the growth and structure of particles undergoing agglomeration (coagulation in the absence of coalescence, condensation, or surface growth) are investigated from the free molecular to the continuum regime by discrete element modeling (DEM). Particles coagulating in the free molecular regime follow ballistic trajectories described by an event-driven method, whereas in the near-continuum (gas-slip) and continuum regimes, Langevin dynamics describe their diffusive motion. Agglomerates containing about 10-30 primary particles, on the average, attain their asymptotic fractal dimension, D(f), of 1.91 or 1.78 by ballistic or diffusion-limited cluster-cluster agglomeration, corresponding to coagulation in the free molecular or continuum regimes, respectively. A correlation is proposed for the asymptotic evolution of agglomerate D(f) as a function of the average number of constituent primary particles, n̅(p). Agglomerates exhibit considerably broader self-preserving size distribution (SPSD) by coagulation than spherical particles: the number-based geometric standard deviations of the SPSD agglomerate radius of gyration in the free molecular and continuum regimes are 2.27 and 1.95, respectively, compared to ∼1.45 for spheres. In the transition regime, agglomerates exhibit a quasi-SPSD whose geometric standard deviation passes through a minimum at Knudsen number Kn ≈ 0.2. In contrast, the asymptotic D(f) shifts linearly from 1.91 in the free molecular regime to 1.78 in the continuum regime. Population balance models using the radius of gyration as collision radius underestimate (up to about 80%) the small tail of the SPSD and slightly overpredict the overall agglomerate coagulation rate, as they do not account for cluster interpenetration during coagulation. In the continuum regime, when a recently developed agglomeration rate is used in population balance equations, the resulting SPSD is in excellent agreement with that obtained by DEM.