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Register a new userNon-uniformly receding contact line breaks axisymmetric flow patterns
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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.
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The dynamics of wetting and dewetting is largely determined by the velocity field near the contact lines. For water drops it has been observed that adding surfactant decreases the dynamic receding contact angle even at a concentration much lower than the critical micelle concentration (CMC). To better understand why surfactants have such a drastic effect on drop dynamics, we constructed a dedicated a setup on an inverted microscope, in which an aqueous drop is held stationary while the transparent substrate is moved horizontally. Using astigmatism particle tracking velocimetry, we track the 3D displacement of the tracer particles in the flow. We study how surfactants alter the flow dynamics near the receding contact line of a moving drop for capillary numbers in the order of $10^{-6}$. Even for surfactant concentrations $c$ far below the critical micelle concentration ($c ll$ CMC) Marangoni stresses change the flow drastically. We discuss our results first in a 2D model that considers advective and diffusive surfactant transport and deduce estimates of the magnitude and scaling of the Marangoni stress from this. Modeling and experiment agree that a tiny gradient in surface tension of a few $mu N , m^{-1}$ is enough to alter the flow profile significantly. The variation of the Marangoni stress with the distance from the contact line suggests that the 2D advection-diffusion model has to be extended to a full 3D model. The effect is ubiquitous, since surfactant is present in many technical and natural dewetting processes either deliberately or as contamination.
When a solid plate is withdrawn from a liquid bath, a receding contact line is formed where solid, liquid, and gas meet. Above a critical speed $U_{cr}$, a stationary contact line can no longer exist and the solid will eventually be covered completely by a liquid film. Here we show that the bifurcation diagram of this coating transition changes qualitatively, from discontinuous to continuous, when decreasing the inclination angle of the plate. We show that this effect is governed by the presence of capillary waves, illustrating that the large scale flow strongly effects the maximum speed of dewetting.
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.
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.
Building on the recent theoretical work of Wray, Duffy and Wilson [J. Fluid Mech. 884, A45 (2020)] concerning the competitive diffusion-limited evaporation of multiple thin sessile droplets in proximity to each other, we obtain theoretical predictions for the spatially non-uniform densities of the contact-line deposits (often referred to as coffee stains or ring stains) left on the substrate after such droplets containing suspended solid particles have completely evaporated. Neighbouring droplets interact via their vapour fields, which results in a spatially non-uniform shielding effect. We give predictions for the deposits from a pair of identical droplets, which show that the deposit is reduced the most where the droplets are closest together, and demonstrate excellent quantitative agreement with experimental results of Pradhan and Panigrahi [Coll. Surf. A 482, 562-567 (2015)]. We also give corresponding predictions for a triplet of identical droplets arranged in an equilateral triangle, which show that the effect of shielding on the deposit is more subtle in this case.
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