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This paper develops a model for fast filament stretching, thinning, and break-up for Newtonian and non-Newtonian fluids, and the results are compared against experimental data where fast filament relaxation occurs. A 1D approximation was coupled with the arbitrary Lagrangian Eulerian (ALE) formulation to perform simulations that captured both filament thinning and break-up. The modeling accounts for both the initial polymer stretching processes from the precise movement of the two moving pistons and also the subsequent thinning when the pistons are at rest. The simulations were first validated for a low viscosity Newtonian fluid matched to experimental data obtained from a recently developed apparatus, the Cambridge Trimaster. A non-Newtonian polymer fluid, with high frequency linear viscoelastic behavior characterized using a piezoaxial vibrator rheometer, was modeled using both an Oldroyd-B and FENE-CR single-mode constitutive models. The simulations of the filament deformation were compared with experiment. The simulations showed a generally reasonable agreement with both the stretch and subsequent relaxation experimental responses, although the mono mode models used in this paper were unable to capture all of the details for the experimental time evolution relaxation profile of the central filament diameter. V

Water droplet freezing affects many aspects of our daily lives, although there is no comprehensive model which retrieves all of the experimentally observed features when a liquid water droplet deposited on a cold substrate turns to ice. In this paper, we present general governing equations to describe water droplet freezing on a solid substrate by accounting for the physical properties of each phase present, namely the liquid and ice, in addition to the solid substrate. The approach, which takes advantage of the full mean curvature expression of both the droplet–air and liquid–ice interfaces, disjoining pressure, the Gibbs–Thomson effect, natural convection and the substrate thermal and physico-chemical properties, enables us to model a more realistic frozen droplet shape, without a prior assumption for the freezing growth angle. In addition to correctly predicting the freezing time, we capture both qualitatively and quantitatively the key experimentally observed features during water droplet freezing such as volume expansion, concave ice front and the cusp singularity. Furthermore, the proposed equation for the tip angle seems to explain its experimentally observed variability.

Turbulence and skin friction modification in channel flow with streamwise-aligned superhydrophobic surface texture Phys. Fluids 26, 095102 (2014); 10.1063/1.4894064 Numerical exploration of the origin of aerodynamic enhancements in [low-Reynolds number] corrugated airfoils A mechanism for unsteady separation in over-expanded nozzle flowThe interest on shedding and coalescence of sessile droplets arises from the importance of these phenomena in various scientific problems and industrial applications such as ice formation on wind turbine blades, power lines, nacelles, and aircraft wings. It is shown recently that one of the ways to reduce the probability of ice accretion on industrial components is using superhydrophobic coatings due to their low adhesion to water droplets. In this study, a combined experimental and numerical approach is used to investigate droplet shedding and coalescence phenomena under the influence of air shear flow on a superhydrophobic surface. Droplets with a size of 2 mm are subjected to various air speeds ranging from 5 to 90 m/s. A numerical simulation based on the Volume of Fluid method coupled with the Large Eddy Simulation turbulent model is carried out in conjunction with the validating experiments to shed more light on the coalescence of droplets and detachment phenomena through a detailed analysis of the aerodynamics forces and velocity vectors on the droplet and the streamlines around it. The results indicate a contrast in the mechanism of two-droplet coalescence and subsequent detachment with those related to the case of a single droplet shedding. At lower speeds, the two droplets coalesce by attracting each other with successive rebounds of the merged droplet on the substrate, while at higher speeds, the detachment occurs almost instantly after coalescence, with a detachment time decreasing exponentially with the air speed. It is shown that coalescence phenomenon assists droplet detachment from the superhydrophobic substrate at lower air speeds. C 2015 AIP Publishing LLC.