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Register a new userCapillary instability in concentric-cylindrical shell: numerical simulation and applications in composite microstructured fibers
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Recent experimental observations have demonstrated interesting instability phenomenon during thermal drawing of microstructured glass/polymer fibers, and these observations motivate us to examine surface-tension-driven instabilities in concentric cylindrical shells of viscous fluids. In this paper, we focus on a single instability mechanism: classical capillary instabilities in the form of radial fluctuations, solving the full Navier--Stokes equations numerically. In equal-viscosity cases where an analytical linear theory is available, we compare to the full numerical solution and delineate the regime in which the linear theory is valid. We also consider unequal-viscosity situations (similar to experiments) in which there is no published linear theory, and explain the numerical results with a simple asymptotic analysis. These results are then applied to experimental thermal drawing systems. We show that the observed instabilities are consistent with radial-fluctuation analysis, but cannot be predicted by radial fluctuations alone---an additional mechanism is required. We show how radial fluctuations alone, however, can be used to analyze various candidate material systems for thermal drawing, clearly ruling out some possibilities while suggesting others that have not yet been considered in experiments.
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Motivated by complex multi-fluid geometries currently being explored in fibre-device manufacturing, we study capillary instabilities in concentric cylindrical flows of $N$ fluids with arbitrary viscosities, thicknesses, densities, and surface tensions in both the Stokes regime and for the full Navier--Stokes problem. Generalizing previous work by Tomotika (N=2), Stone & Brenner (N=3, equal viscosities) and others, we present a full linear stability analysis of the growth modes and rates, reducing the system to a linear generalized eigenproblem in the Stokes case. Furthermore, we demonstrate by Plateau-style geometrical arguments that only axisymmetric instabilities need be considered. We show that the N=3 case is already sufficient to obtain several interesting phenomena: limiting cases of thin shells or low shell viscosity that reduce to N=2 problems, and a system with competing breakup processes at very different length scales. The latter is demonstrated with full 3-dimensional Stokes-flow simulations. Many $N > 3$ cases remain to be explored, and as a first step we discuss two illustrative $N to infty$ cases, an alternating-layer structure and a geometry with a continuously varying viscosity.
A new type of instability - electrokinetic instability - and an unusual transition to chaotic motion near a charge-selective surface was studied by numerical integration of the Nernst-Planck-Poisson-Stokes system and a weakly nonlinear analysis near the threshold of instability. Two kinds of initial conditions were considered: (a) white noise initial conditions to mimic room disturbances and subsequent natural evolution of the solution; (b) an artificial monochromatic ion distribution with a fixed wave number to simulate regular wave patterns. The results were studied from the viewpoint of hydrodynamic stability and bifurcation theory. The threshold of electroconvective movement was found by the linear spectral stability theory, the results of which were confirmed by numerical simulation of the entire system. The following regimes, which replace each other as the potential drop between the selective surfaces increases, were obtained: one-dimensional steady solution; two-dimensional steady electroconvective vortices (stationary point in a proper phase space); unsteady vortices aperiodically changing their parameters (homoclinic contour); periodic motion (limit cycle); and chaotic motion. The transition to chaotic motion did not include Hopf bifurcation. Numerical resolution of the thin concentration polarization layer showed spike-like charge profiles along the surface, which could be, depending on the regime, either steady or aperiodically coalescent. The numerical investigation confirmed the experimentally observed absence of regular (near-sinusoidal) oscillations for the overlimiting regimes. There is a qualitative agreement of the experimental and the theoretical values of the threshold of instability, the dominant size of the observed coherent structures, and the experimental and theoretical volt-current characteristics.
We show how the capillary filling of microchannels is affected by posts or ridges on the sides of the channels. Ridges perpendicular to the flow direction introduce contact line pinning which slows, or sometimes prevents, filling; whereas ridges parallel to the flow provide extra surface which may enhances filling. Patterning the microchannel surface with square posts has little effect on the ability of a channel to fill for equilibrium contact angle $theta_e lesssim 30^{mathrm{o}}$. For $theta_e gtrsim 60^{mathrm{o}}$, however, even a small number of posts can pin the advancing liquid front.
Recent experiments of thin films flowing down a vertical fiber with varying nozzle diameters present a wealth of new dynamics that illustrate the need for more advanced theory. We present a detailed analysis using a full lubrication model that includes slip boundary conditions, nonlinear curvature terms, and a film stabilization term. This study brings to focus the presence of a stable liquid layer playing an important role in the full dynamics. We propose a combination of these physical effects to explain the observed velocity and stability of traveling droplets in the experiments and their transition to isolated droplets. This is also supported by stability analysis of the traveling wave solution of the model.
In a cylindrical container filled with an eutectic GaInSn alloy, an electro-vortex flow (EVF) is generated by the interaction of a non-uniform current with its own magnetic field. In this paper, we investigate the EVF phenomenon numerically and experimentally. Ultrasound Doppler Velocimetry (UDV) is applied to measure the velocity field in a cylindrical vessel. Second, we enhance an old numerical solver by taking into account the effect of Joule heating, and employ it for the numerical simulation of the EVF experiment. Special focus is laid on the role of the magnetic field, which is the combination of the current induced magnetic field and the external geomagnetic field. For getting a higher computational efficiency, the so-called parent-child mesh technique is applied in OpenFOAM when computing the electric potential, the current density and the temperature in the coupled solid-liquid conductor system. The results of the experiment are in good agreement with those of the simulation. This study may help to identify the factors that are essential for the EVF phenomenon, and for quantifying its role in liquid metal batteries.
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