Search arXivSearch

arXiv · 2106.05033

Collision of elastic drop with thin cylinder

Abstract

The collision of water and elastic liquid drops with a thin cylinder (thread) is studied. The droplet flight trajectory and the cylinder axis are mutually perpendicular. Attention is focused on the difference between collisions of water drops and drops of elastic fluids. In the experiments, the drop diameter was 3 mm, the diameter of horizontal stainless steel cylinders was 0.4 and 0.8 mm. The drops were formed by slowly pumping liquid through a vertical stainless steel capillary with an outer diameter of 0.8 mm, from which droplets were periodically detached under the action of gravity. The droplet velocity before collision was defined by the distance between the capillary cut and the target (cylinder); in experiments, this distance was approximately 5, 10, and 20 mm. The drop velocities before impact are estimated in the range of 0.2-0.5 m/s. The collision process was monitored by high-speed video recording methods with a frame rate of 240 and 960 Hz. The test liquids were water and aqueous solutions of polyacrylamide of molecular weight 11 million and concentrations of 100 and 1000 ppm (PAM-100 and PAM-1k). Experiments have shown that, depending on the drop impact height and polymer concentration, different scenarios of a drop collision with a thin cylinder are possible: a short-term recoil of a drop from an obstacle, a drop flowing around a cylindrical obstacle while maintaining the continuity of the drop, the breakup of a drop into two secondary drops, one of which can continue flight and the other one is captured by the cylinder, or both secondary droplets continue to fly, the drop also can be captured by the cylinder, until the impact of the next drop(s) forces the accumulated drop detach from the cylinder. Numerical modeling satisfactorily reproduces the phenomena observed in the experiment.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Alla O. Rudenko, Alexey I. Fedyushkin, Aleksey N. Rozhkov. 2021-06-09. Collision of elastic drop with thin cylinder. https://arxiv.org/abs/2106.05033

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Data-driven low-dimensional model for the onset of turbulence in plane Couette flow

We construct low-dimensional dynamical systems for low-Reynolds-number turbulence in plane Couette flow using Kernel Quantile Regression. Exploiting the finite-dimensional structure of attractors in dissipative systems, reduced-order models are learned from direct numerical simulation data using a small set of physically meaningful observables. The resulting discrete-time models accurately reproduce periodic and chaotic dynamics near the onset of turbulence. The minimum number of variables required for accurate prediction is found to be consistent with embedding theory based on the attractor dimension. For chaotic regimes, the models capture both short-term trajectory evolution and long-term statistical properties, including probability density functions. By incorporating the Reynolds number as an additional input variable, we further develop a parameter-dependent model that successfully reproduces the bifurcation structure over a range of Reynolds numbers, including bifurcations between training points. These results demonstrate the effectiveness of machine-learning-based reduced-order modeling for capturing the essential dynamics and statistics of weakly turbulent flows.

physics.flu-dyn

Rapidly rotating internally heated convection: bounds on long-time averages

Convection on geophysical and astrophysical scales is subject to rapid rotation and strong heating from within the domain. In studying the long-time behaviour of the solutions for such a system, energy identities fail to capture the effects of rotation because the Coriolis force does no work, and rapid rotation can be prohibitive for direct numerical simulations. Instead, we derive an asymptotically reduced model for rapidly rotating convection driven by uniform internal heating between isothermal stress-free boundaries in a plane periodic layer. The main contribution is the proof of bounds on the mean temperature, and the mean vertical convective heat transport, in terms of the Rayleigh and Ekman numbers, in the limit of infinite Prandtl number. The first quantity represents the mixing of the flow, and the second the asymmetry in heat leaving the bottom and top boundaries due to convection, and unlike Rayleigh-Bénard convection, the two are not a priori related. We employ alternative estimation techniques to those used in previous studies (Grooms \& Whitehead, 2014 \textit{Nonlinearity}, 28, 29) and identify two distinct scaling behaviours for both quantities. Finally, our bounds are optimised, within the methodology, and provide a rigorous constraint for future studies of rotation-dominated internally heated convection.

physics.flu-dyn

Baroclinic wave dynamics in the Ekman-free rotating rectangular annulus with localized forced plume

We report numerical simulations of a rotating rectangular annulus that isolates the Ekman-free bulk of the cylindrical baroclinic annulus, subjected to bi-directional temperature gradients imposed by a uniformly cooled inner wall and a localized forced heated plume at the outer bottom. The finite-volume OpenFOAM solver is employed across combinations of source Richardson number $Ri_0 = 99, 4, 1$ and Rossby number $Ro = 0.3, 0.1, 0.07$. A non-dimensional scaling of the governing equations identifies geostrophic-hydrostatic balance as the leading-order bulk state, a result confirmed a posteriori by the $x$ and $z-$momentum budgets. Baroclinic waves of mode $m=2$ at $Ro=0.3$ transition to $m=3$ as $Ro$ decreases, consistent with the contraction of the Eady deformation radius $L_ρ= NH/f$; Complex Empirical Orthogonal Function (CEOF) analysis characterizes the wave regime and detects a Hopf-bifurcated vacillating state at $Ri_0 = 99,~Ro = 0.1$. The plume morphology, classified through the Morton length scale and source flux-balance parameter, transitions from weak, laterally-swept structures at $Ri_0 = 99$ to sustained columnar plumes traversing the full baroclinic depth at $Ri_0 \leq 4$. The plume entrainment coefficient $Γ(z)$ shows opposite rotational sensitivities at low and high $Ri_0$, which we organize through a local plume Rossby number $Ro_p = w/(2Ωb)$. A mixing-length argument predicts a bulk turbulent heat flux $\overline{u'T'} \propto Ri_0^{-1/2}$, anticipating an order-of-magnitude enhancement from $Ri_0 = 99$ to $Ri_0 = 1$, in agreement with the simulations. A regime map in the $(Ri_0, Ro)$ plane reveals that, within the explored range, the plume-regime and wave-selection problems are approximately separable: $Ri_0$ sets the plume regime while $Ro$ selects the dominant baroclinic wave mode.

physics.flu-dyn