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Register a new userNon-axisymmetric flow characteristics in Head-on Collision of Spinning Droplets
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Effects of spinning motion on the bouncing and coalescence between a spinning droplet and a non-spinning droplet undergoing the head-on collision were numerically studied by using a Volume-of-Fluid method. A prominent discovery is that the spinning droplet can induce significant non-axisymmetric flow features for the head-on collision of equal-size droplets composed of the same liquid. Specifically, a non-axisymmetric bouncing was observed, and it is caused by the conversion of the spinning angular momentum into the orbital angular momentum. This process is accompanied by the rotational kinetic energy loss due to the interaction between the rotational and radial flows of the droplets. A non-axisymmetric internal flow and a delayed separation after temporary coalescence were also observed, and they are caused by the enhanced interface oscillation and internal-flow-induced viscous dissipation. The spinning motion can also promote the mass interminglement of droplets because the locally non-uniform mass exchange occurs at the early collision stage by non-axisymmetric flow and is further stretched along the filament at later collision stages. In addition, it is found that the non-axisymmetric flow features increase with increasing the orthogonality of the initial translational motion and the spinning motion of droplets.
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We investigate the internal flow pattern of an evaporating droplet using tomographic particle image velocimetry (PIV) when the contact line non-uniformly recedes. We observe a three-dimensional azimuthal vortex pair while the contact line non-uniformly recedes and the symmetry-breaking flow field is maintained during the evaporation. Based on the experimental results, we show that the vorticity magnitude of the internal flow is related to the relative contact line motion. Furthermore, to explain how the azimuthal vortex pair flow is created, we develop a theoretical model by taking into account the relation between the contact line motion and evaporating flux. Finally, we show that the theoretical model has a good agreement with experimental results.
The aim of this study is to derive accurate models for quantities characterizing the dynamics of droplets of non-vanishing viscosity in capillaries. In particular, we propose models for the uniform-film thickness separating the droplet from the tube walls, for the droplet front and rear curvatures and pressure jumps, and for the droplet velocity in a range of capillary numbers, $Ca$, from $10^{-4}$ to $1$ and inner-to-outer viscosity ratios, $lambda$, from $0$, i.e. a bubble, to high viscosity droplets. Theoretical asymptotic results obtained in the limit of small capillary number are combined with accurate numerical simulations at larger $Ca$. With these models at hand, we can compute the pressure drop induced by the droplet. The film thickness at low capillary numbers ($Ca<10^{-3}$) agrees well with Brethertons scaling for bubbles as long as $lambda<1$. For larger viscosity ratios, the film thickness increases monotonically, before saturating for $lambda>10^3$ to a value $2^{2/3}$ times larger than the film thickness of a bubble. At larger capillary numbers, the film thickness follows the rational function proposed by Aussillous & Quere (2000) for bubbles, with a fitting coefficient which is viscosity-ratio dependent. This coefficient modifies the value to which the film thickness saturates at large capillary numbers. The velocity of the droplet is found to be strongly dependent on the capillary number and viscosity ratio. We also show that the normal viscous stresses at the front and rear caps of the droplets cannot be neglected when calculating the pressure drop for $Ca>10^{-3}$.
We study the flow forced by precession in rigid non-axisymmetric ellipsoidal containers. To do so, we revisit the inviscid and viscous analytical models that have been previously developed for the spheroidal geometry by, respectively, Poincare (Bull. Astronomique, vol. XXVIII, 1910, pp. 1-36) and Busse (J. Fluid Mech., vol. 33, 1968, pp. 739-751), and we report the first numerical simulations of flows in such a geometry. In strong contrast with axisymmetric spheroids, where the forced flow is systematically stationary in the precessing frame, we show that the forced flow is unsteady and periodic. Comparisons of the numerical simulations with the proposed theoretical model show excellent agreement for both axisymmetric and non-axisymmetric containers. Finally, since the studied configuration corresponds to a tidally locked celestial body such as the Earths Moon, we use our model to investigate the challenging but planetary-relevant limit of very small Ekman numbers and the particular case of our Moon.
The off-center collision of binary bouncing droplets of equal size was studied numerically by a volume-of-fluid (VOF) method with two marker functions, which has been validated by comparing with available experimental results. A non-monotonic kinetic energy recovery with varying impact parameters was found based on the energy budget analysis. This can be explained by the prolonged entanglement time and the enhanced internal-flow-induced viscous dissipation for bouncing droplets at intermediate impact parameters, compared with those at smaller or larger impact parameters. The universality of this non-monotonicity was numerically verified, and thereby an approximate fitting formula was proposed to correlate the kinetic energy dissipation factor with the impact parameter for various Weber numbers and Ohnesorge numbers. From the vortex dynamics perspective, a helicity analysis of droplet internal flow identifies a strong three-dimensional interaction between the ring-shaped vortices and the line-shaped shear layers for off-center collisions. Furthermore, we demonstrated theoretically and verified numerically that the equivalence between the total enstrophy and the total viscous dissipation, which holds for a single-phase flow system confined by stationary boundaries, is not generally satisfied for the two-phase flow system containing gas-liquid interfaces. This is attributed to the work done by the unbalanced viscous stresses, which results from the interfacial flow and the vorticity associated with the movement of the oscillating interface.
This paper numerically investigates the shear flow between double concentric spherical boundaries rotating differentially, so-called spherical Couette flow, under unstable thermal stratification, focusing on the boundary of the axisymmetric/non-axisymmetric transition in wide gap cases where the inner radius is comparable to the clearance width. While the transition of SCF has been confirmed experimentally in cases without thermal factor, insufficient knowledge on SCF subject to thermal instability, related to geophysical problems especially in wide gap cases, has been accumulated mainly based on numerical analysis; our motivation is to bridge the knowledge gap by a parameter extension. We reconfirm that the transition under no thermal effect is initiated by a disturbance visualised as a spiral pattern with n arms extending from the equatorial zone to the pole in each hemisphere, at the critical Reynolds number, Recr, as previously reported. With increasing thermal factor, the buoyancy effect assists the system rotation to trigger a transition towards non-axisymmetric states, resulting in a relative decrease of Recr. This is in contrast with the result that the system rotation apparently suppresses via Coriolis effect the transition to the thermally convective states at low Reynolds numbers. The present study elucidates that the existence of the axisymmetric state is restricted within a closed area in the extended parameter space, along the boundary of which the spiral patterns observed experimentally in SCF continually connect to the classical spherical Benard convective states.
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