Dripping instability of a two-dimensional liquid film under an inclined plate

It is known that the dripping of a liquid film on the underside of a plate can be suppressed by tilting the plate so as to cause a sufficiently strong flow. This paper uses two-dimensional numerical simulations in a closed-flow framework to study several aspects of this phenomenon. It is shown that, in quasi-equilibrium conditions, the onset of dripping is closely associated with the curvature of the wave crests approaching a well-defined maximum value. When dynamic effects become significant, this connection between curvature and dripping weakens, although the critical curvature remains a useful reference point as it is intimately related to the short length scales promoted by the Rayleigh–Taylor instability. In the absence of flow, when the film is on the underside of a horizontal plate, the concept of a limit curvature is relevant only for small liquid volumes close to a critical value. Otherwise, the drops that form have a smaller curvature and a large volume. The paper also illustrates the peculiarly strong dependence of the dripping transition on the initial conditions of the simulations. This feature prevents the development of phase maps dependent only on the governing parameters (Reynolds number, Bond number, etc.) similar to those available for film flow on the upper side of an inclined plate.

On-demand Ferrofluid Droplet Formation With Non-linear Magnetic Permeability in the Presence of a Non-uniform Magnetic Field

The magnetic actuation of ferrofluid droplets offers an inspiring tool in widespread engineering and biological applications. In this study, the dynamics of ferrofluid droplet generation with a Drop-on-Demand feature under a non-uniform magnetic field is investigated by multiscale numerical modeling. Langevin equation is assumed for ferrofluid magnetic susceptibility due to the strong applied magnetic field. Large and small computational domains are considered. In the larger domain, the magnetic field is obtained by solving Maxwell equations. In the smaller domain, a coupling of continuity, Navier Stokes, two-phase flow, and Maxwell equations are solved by utilizing the magnetic field achieved by the larger domain for the boundary condition. The Finite volume method and coupling of level-set and Volume of Fluid methods are used for solving equations. The droplet formation is simulated in a two-dimensional axisymmetric domain. The method of solving fluid and magnetic equations is validated using a benchmark. Then, ferrofluid droplet formation is investigated experimentally and the numerical results are in good agreement with the experimental data. The effect of 12 dimensionless parameters including the ratio of magnetic, gravitational, and surface tension forces, the ratio of the nozzle and magnetic coil dimensions, and ferrofluid to continuous-phase properties ratios are studied. The results showed that by increasing the magnetic Bond number, gravitational Bond number, Ohnesorge number, dimensionless saturation magnetization, initial magnetic susceptibility of ferrofluid, the generated droplet diameter reduces, whereas the formation frequency increases. The same results were observed when decreasing the ferrite core diameter to outer nozzle diameter, density, and viscosity ratios.

Archimedes’ principle with surface tension effects in undergraduate fluid mechanics

The general physics of how objects float is only partly covered in most undergraduate fluid mechanics courses. Although Archimedes’ principle is a standard topic in fluid statics, the role of surface tension in floating is rarely discussed in detail. For example, very few undergraduate textbooks, if any, mention that the total buoyancy force on a floating object includes the weight of the fluid displaced by the meniscus. This leaves engineering students without an understanding of a wide range of phenomena that occur at a low Bond number (the ratio of buoyancy to interfacial tension forces), such as how heavier-than-water objects can float at a gas-liquid interface. This article makes a case for teaching a more unified version of Archimedes’ principle, which combines the effects of surface tension and hydrostatic pressure in calculating the total buoyancy on floating objects. Sample problems at the undergraduate level and two classroom demonstrations are described that reinforce the basic science concepts.

Velocity measurements of individual droplets in liquid-liquid Taylor flows in circular capillaries

This study is focused on the effect of droplet length on droplet velocity in liquid-liquid Taylor flows for microfluidic applications. An experimental set up was designed to measure droplet velocity over a wide range of droplet lengths and flow velocities while also varying viscosity ratio. Five different fluid combinations were examined by employing AR20, FC40, HFE7500 and water. Results indicate the complexity of predicting droplet velocity in such flow regimes and also show a strong influence of viscosity ratio and Bond number.

Application of the liquid bridges theory to find the melt menisci shape when growing cylindrical crystals

A vertical liquid bridge of small volume between a conical shaper and a convex crystallization front was investigated. Two variants of the front crystallization shape selection are considered: a conical and a spherical fronts. A variational statement of the original problem is given. As the boundary conditions we used the condition of engagement at the edge of the shaper and a given growth angle at the crystallization front. The Bond number was assumed to be small, and to find a solution of the problem the asymptotic approach was applied. The calculations are carried out for small diameter cylindrical sapphire crystals, grown from the melt by the Stepanov method. The results of the menisci shapes calculations are presented. The comparison of the results of calculations for conical and spherical crystallization fronts is carried out.

Flow Structure and Deformation of Two Bubbles Rising Side by Side in a Quiescent Liquid

In the motion of two spherical bubbles rising side by side, the bubbles are known to attract each other at a high Reynolds number (Re = ρUd/μ). Furthermore, spherical bubbles kiss and bounce under certain conditions; however, deformable bubbles repel each other without kissing. This paper experimentally and numerically presents the flow structures and shape of the nonkissing repulsion of deformable bubbles. For the experimental analysis, we organized bubble behaviors by Galilei number (Ga = ρg1/2d3/2/μ) and Bond number (Bo = ρgd2/σ). The bubbles repelled each other without kissing near the unstable critical curve of a single bubble. The curvature inside the gap, which is similar to the shape of a zigzag behavior bubble, was large. For the numerical analysis, the velocity of the equatorial plane inside the gap was larger due to the potential interaction, although the velocity behind was the opposite due to the strengthened vorticity generated at the surface. Furthermore, the double-threaded wake emerged behind the interacting bubbles, and it showed that the rotation direction was repulsion regardless of whether the bubbles attracted or repelled each other. The streamline behind the bubbles in the 2D plane was from the outside to the inside.

Plasma Lipidomics Identifies Unique Lipid Signatures and Potential Biomarkers for Patients With Aortic Dissection

Aortic dissection (AD) is a catastrophic cardiovascular emergency with a poor prognosis, and little preceding symptoms. Abnormal lipid metabolism is closely related to the pathogenesis of AD. However, comprehensive lipid alterations related to AD pathogenesis remain unclear. Moreover, there is an urgent need for new or better biomarkers for improved risk assessment and surveillance of AD. Therefore, an untargeted lipidomic approach based on ultra-high-performance liquid chromatograph-mass spectrometry was employed to unveil plasma lipidomic alterations and potential biomarkers for AD patients in this study. We found that 278 of 439 identified lipid species were significantly altered in AD patients (n = 35) compared to normal controls (n = 32). Notably, most lipid species, including fatty acids, acylcarnitines, cholesteryl ester, ceramides, hexosylceramides, sphingomyelins, lysophosphatidylcholines, lysophosphatidylethanolamines, phosphatidylcholines, phosphatidylinositols, diacylglycerols, and triacylglycerols with total acyl chain carbon number ≥54 and/or total double bond number ≥4 were decreased, whereas phosphatidylethanolamines and triacylglycerols with total double bond number <4 accumulated in AD patients. Besides, the length and unsaturation of acyl chains in triacylglycerols and unsaturation of 1-acyl chain in phosphatidylethanolamines were decreased in AD patients. Moreover, lysophosphatidylcholines were the lipids with the largest alterations, at the center of correlation networks of lipid alterations, and had excellent performances in identifying AD patients. The area under the curve of 1.0 and accuracy rate of 100% could be easily obtained by lysophosphatidylcholine (20:0/0:0) or its combination with lysophosphatidylcholine (17:0/0:0) or lysophosphatidylcholine (20:1/0:0). This study provides novel and comprehensive plasma lipidomic signatures of AD patients, identifies lysophosphatidylcholines as excellent potential biomarkers, and would be beneficial to the pathogenetic study, risk assessment and timely diagnosis and treatment of AD.

A model to predict the oscillation frequency for drops pinned on a vertical planar surface

Accurate prediction of the natural frequency for the lateral oscillation of a liquid drop pinned on a vertical planar surface is important to many drop applications. The natural oscillation frequency, normalized by the capillary frequency, is mainly a function of the equilibrium contact angle and the Bond number ( $Bo$ ), when the contact lines remain pinned. Parametric numerical and experimental studies have been performed to establish a comprehensive understanding of the oscillation dynamics. An inviscid model has been developed to predict the oscillation frequency for wide ranges of $Bo$ and the contact angle. The model reveals the scaling relation between the normalized frequency and $Bo$ , which is validated by the numerical simulation results. For a given equilibrium contact angle, the lateral oscillation frequency decreases with $Bo$ , implying that resonance frequencies will be magnified if the drop oscillations occur in a reduced gravity environment.

The Drag Forces on a Taylor Bubble Rising Steadily in Vertical Pipes

By the adoption of a drag-buoyancy equality model, analytical solutions were obtained for the drag coefficients (CD) of Taylor bubbles rising steadily in pipes. The obtained solutions were functions of the geometry of the Taylor bubble and the gas volume fraction. The solutions were applicable at a wide range of Capillary numbers. The solution was validated by comparison with experimental data of other investigators. All derived drag formulas were subject to the condition that Bond number >4, for air-water systems.

Linear stability analysis of a Newtonian ferrofluid cylinder surrounded by a Newtonian fluid

We performed a linear stability analysis of a Newtonian ferrofluid cylinder surrounded by a Newtonian non-magnetic fluid in an azimuthal magnetic field. A wire is used at the centre of the ferrofluid cylinder to create this magnetic field. Isothermal conditions are considered and gravity is ignored. An axisymmetric perturbation is imposed at the interface between the two fluids and a dispersion relation is obtained allowing us to predict whether the flow is stable or unstable with respect to this perturbation. This relation is dependent on the Ohnesorge number of the ferrofluid, the dynamic viscosity ratio, the density ratio, the magnetic Bond number, the relative magnetic permeability and the dimensionless wire radius. Solutions to this dispersion relation are compared with experimental data from Arkhipenko et al. (Fluid Dyn., vol. 15, issue 4, 1981, pp. 477–481) and, more recently, Bourdin et al. (Phys. Rev. Lett., vol. 104, issue 9, 2010, 094502). A better agreement than the inviscid theory and the theory that only takes into account the viscosity of the ferrofluid is shown with the data of Arkhipenko et al. (Fluid Dyn., vol. 15, issue 4, 1981, pp. 477–481) and those of Bourdin et al. (Phys. Rev. Lett., vol. 104, issue 9, 2010, 094502) for small wavenumbers.