# Latest papers in fluid mechanics

### Study on the dependence with the filling level of the sloshing wave pattern in a rectangular tank

This work presents a study of the influence of the filling level on the wave pattern during a sloshing problem. To this end, a rectangular tank of aspect ratio 2:1 is mounted on a shake table subject to controlled external motions. A frequency sweep analysis is performed nearest to the primary resonance frequency using two different amplitudes of imposed motion and different water depths. The wave evolution is registered at certain control points. In particular, this work is devoted to identifying the effect of the filling level on the dynamics of the wave patterns, emphasizing the nonlinearities of the free surface and their dependence on the water depth. The free surface measurements are compared with those obtained from a fixed mesh finite element simulation of the Navier-Stokes equations. The free surface is tracked using a Lagrangian technique. The effect of the bottom boundary conditions on the wave pattern is also evaluated from these simulations. From the experiments, it is confirmed that maximum and minimum wave heights do not change for larger water depth, i.e., when deep water conditions are fulfilled. This fact is also reflected by the numerical results. The computed wave evolution satisfactorily matches the experimental data. In addition, analytical solutions obtained using a potential flow approach are also evaluated. They fail in the description of nonlinear responses, but their coefficients can be numerically or experimentally characterized to fit more realistic solutions.

### Drag reduction by linear flexible polymers and its degradation in turbulent flow: A phenomenological explanation from chemical thermodynamics and kinetics

Based on chemical thermodynamics and kinetics analysis, this work provides a phenomenological explanation of drag reduction and its degradation by linear flexible polymers. We propose that drag reduction happens due to the unstable thermodynamic environment created by the elongation of free polymers and aggregates, and degradation of drag reduction happens due to the unstable kinetic environment with the chain scission of the free polymer and aggregate. Experimental results from microscopic and macroscopic scales further validate the proposed theory. Fourier series is employed to explain the molecular weight distribution that happens in the drag reduction.

### Vortex breakdown in the lower fluid of two-fluid swirling flow

This paper describes the first experimental evidence of the vortex breakdown development in the lower fluid in a sealed vertical cylindrical container in which two immiscible fluids circulate, driven by a rotating lid. The lower fluid is water, and the upper fluid is sunflower oil. In both fluids, the rotation generates centrifugal meridional circulations separated by a thin anticentrifugal circulation layer attached to the interface from below. An advanced technique of particle image velocimetry and proper laser illumination allows for the measurement of velocity and recognition of the patterns of flow in oil and water. As the rotation speeds up, a tornadolike swirling ascending jet forms near the axis-bottom intersection. A circulation cell (vortex-breakdown bubble, VBB) then emerges near the center of the water domain, approaches the bottom, and disappears. This scenario of the appearance and disappearance of the VBB is similar to that occurring in a single-fluid flow and in the upper fluid of a two-fluid flow.

### Efficient microextraction process exploiting spontaneous interfacial convection driven by Marangoni and electric field induced instability: A computational fluid dynamics study

The present study focuses on the component transfer from one liquid phase to another liquid phase, commonly known as the extraction process, performed in a microchannel in the presence of spontaneous interfacial convection, driven by either an interfacial tension gradient or an applied external electric field. Marangoni instability occurs as a result of a lateral gradient of interfacial tension existing along the interface of the two fluids. Nonequilibrium phenomena associated with factors such as temperature imbalance, a nonuniform distribution of surface-active components at the interface, evaporation, etc. can lead to the interfacial Marangoni instability. In the present study, first, we have explored temperature gradient driven Marangoni instability, which deforms the interface with significant acceleration and induces local convective mass transfer along with the conventional diffusion mode. Next, we have explored the same phenomenon in the presence of an external electric field, which can also deform the liquid-liquid interface almost instantaneously to a considerable extent. The relative strength of the mass transfer rate for different cases, such as temperature driven instability, in the presence of uniform and nonuniform electric fields has been reported in detail. It has also been observed that, due to the larger mass transfer area, the annular flow offers an enhanced rate of mass transfer compared to the stratified flow. Additionally, this article reports that the nonuniform electric field could influence the process of interfacial instability more strongly compared to the uniform electric field. The effect of the nonuniform electric field with different spatial periodicity on the extraction process has been studied in detail.

### Experimental investigation of turbulent Rayleigh-Bénard convection of water in a cylindrical cell: The Prandtl number effects for Pr [math] 1

We report an experimental study of turbulent Rayleigh-Bénard convection in a cylindrical cell of aspect ratio unity, focusing on the effects of the Prandtl number (Pr). Purified water was used as the convecting fluid. Five different Pr between 3.58 and 9.40 were achieved by changing the mean temperature of water, and the measurements were carried out over the Rayleigh number range 2.63 × 108 ≤ Ra ≤ 3.89 × 1010. Over the present parameter range, the measured Nusselt number Nu is found to scale as Nu ∼ Raβ with β = 0.30 and to be independent of Pr. Based on the oscillation period of the measured temperature, the Reynolds number Re scales as Re ∼ Ra0.47Pr−0.72. The local temperature fluctuations at the cell center and near the cell’s sidewall were measured, and their relations with Ra and Pr were studied. Our results further reveal that the non-Oberbeck-Boussinesq effects of water have a relatively small influence on the measured scaling relation Nu ∼ Raβ.

### Evolution of the flow structures in an elevated jet in crossflow

The characteristic flow features of an elevated square jet in crossflow (EJICF) are studied numerically using large eddy simulation. The effect of jet to crossflow velocity ratio, also called velocity ratio (VR), on the flow field of an elevated jet in crossflow (EJICF) is investigated. All the computations are carried out at a Reynolds number (Re) of 20 000, based on the outer width of the stack (d) and free stream crossflow velocity (U∞), for four different velocity ratios (VR), namely, 0.5, 1.0, 1.5 and 2.0. The stack used in this study has an aspect ratio h/d = 7. The shear-improved Smagorinsky model has been used to account for the subgrid scale stress while solving the filtered three-dimensional unsteady Navier-Stokes equations. The modes of shedding in the stack wake are analyzed using both instantaneous and phase-averaged data. It is found that at a low jet to crossflow velocity ratio (VR = 0.5), the stack wake exhibits two different modes of shedding, symmetric and antisymmetric, similar to the wake of a wall mounted finite-size cylinder. At higher velocity ratios (VR ≥ 1), the stack wake shows the presence of only antisymmetric modes of shedding. It is also found that velocity ratio (VR) has a profound effect on the source of vorticity of the jet shear layer structures near the upwind side. At VR = 0.5, the upstream sides of the jet shear layer structures are found to draw their vortices from the outer surface of the stack boundary layer. At higher VR, they seem to be fed by the vorticity of the boundary layer developed on the inner wall surface of the stack. Both jet vortices and stack wake vortices are found to be present in the jet wake, and the shedding frequency of both the jet wake and the stack wake is found to be same. The spatial evolution of the counter-rotating vortex pair in the case of an EJICF is found to be similar to that of a JICF.

### Experimental investigation of interactions between turbulent cylinder wake and spherical shock wave

Interactions between a spherical shock wave and a turbulent cylinder wake are studied with wind tunnel experiments. The shock wave is generated outside the wake and propagates across the turbulent wake. Instantaneous streamwise velocity is measured on the wake centerline while peak overpressure of the shock wave is measured outside the wake after the shock wave has passed across the wake. The experiments are performed for various conditions of the cylinder wake to investigate the influences of the root-mean-squared (rms) velocity fluctuation and of the length of the turbulent region through which the shock wave propagates. The velocity fluctuation opposite to the shock propagation direction is positively correlated with the peak-overpressure fluctuation. The mean peak overpressure decreases after the shock wave propagates in the wake. These relations between velocity and peak overpressure are explained by the shock-surface deformation, where the peak overpressure is increased and decreased, respectively, for the shock surfaces with concave and convex shapes in relation to the shock propagation direction. The correlation coefficients between the velocity and peak-overpressure fluctuations and the rms peak-overpressure fluctuation increase with the rms velocity fluctuation. The rms peak-overpressure fluctuation becomes independent of the turbulent length on the shock ray once the shock wave has propagated through a sufficiently long turbulent region. The peak-overpressure fluctuation has a probability density function (PDF) close to a Gaussian shape even though the PDF of velocity fluctuations in the wake is negatively skewed.

### Experimental study of inertia-based passive flexibility of a heaving and pitching airfoil operating in the energy harvesting regime

The effects of passive, inertia-induced surface flexibility at the leading and trailing edges of an oscillating airfoil energy harvester are investigated experimentally at reduced frequencies of k = fc/U∞ = 0.10, 0.14, and 0.18. Wind tunnel experiments are conducted using phase-resolved, two-component particle image velocimetry to understand the underlying flow physics, as well as to obtain force and pitching moment estimates using the vortex-impulse theory. Results are obtained for leading and trailing edge flexibility separately. It is shown that both forms of flexibility may alter the leading edge vortex inception and detachment time scales, as well as the growth rate of the circulation. In addition, surface flexibility may also trigger the generation of secondary vortical structures and suppress the formation of trailing edge vortices. The total energy harvesting efficiency is decomposed into contributions of heaving and pitching motions. Relative to the rigid airfoil, the flexible leading and trailing edge segments are shown to increase the energy harvesting efficiency by approximately 17% and 25%, respectively. However, both the flexible leading and trailing edge airfoils operate most efficiently at k = 0.18, whereas the peak efficiency of the rigid airfoil occurs at k = 0.14. It is shown that the flexible leading and trailing edge airfoils enhance the heaving contribution to the total efficiency at k = 0.18 and the negative contribution of the pitching motion at high reduced frequencies can be alleviated by using a flexible trailing edge.

### Turbulence modulation by settling inertial aerosols in Eulerian-Eulerian and Eulerian-Lagrangian simulations of homogeneously sheared turbulence

Author(s): M. Houssem Kasbaoui

When subject to strong shear, settling particles dispersed at semidilute concentrations may modulate the suspending flow significantly, in a way that enhances or attenuates turbulence. The modulation is enabled by the appearance of clusters and void fraction bubbles in the particle phase.

[Phys. Rev. Fluids 4, 124308] Published Tue Dec 31, 2019

### Spontaneous aggregation of bovine milk casein micelles: Ultra-small angle x-ray scattering and mathematical modeling

We have used Ultra Small Angle X-ray Scattering (USAXS) and mathematical models to study seemingly-spontaneous aggregation structures in two pasteurized bovine milks. Although extensive studies of casein micelles and their aggregation have been carried out, few have been done to numerically characterize submicron structures to micron-scale structures. We measured the USAXS intensity, I(q), as a function of the scattering vector magnitude, q, for commercial pasteurized skim milk and nonhomogenized whole milk at two temperatures, 7 °C and 45 °C. We observed broad peaks, reported previously to be related to casein micelles, centered at q ≈ 2 × 10−2 Å−1 and at q ≈ 9 × 10−2 Å−1. At lower q values, log I(q) displayed a behavior characteristic of aggregation manifested for a slope in the region 3–7 × 10−4 Å−1 < q < 4 × 10−3 Å−1. This behavior appeared in the absence of (a) chymosin, (b) any change in pH or CaCl2 concentration, and (c) temperature changes. We introduced a model of milk and used computer simulations to investigate consequences of casein micelles possessing surface areas lacking the water-soluble components of κ-casein proteins. These components exist to provide stability against aggregation to the casein micelles. We propose that bovine casein micelles spontaneously formed 1-dimensional aggregates.

### Surface rheological measurements of isolated food foam systems

Liquid foams represent a key component to a vast range of food industry products, from ice creams to the crema on coffee. Longevity of these foams is a highly desirable attribute; however, in order for foam stability to be effectively controlled, a better understanding of the interdependence of the bulk liquid and air-liquid interfacial rheologies is required. This study follows an increasing trend in experimental investigations made of isolated foam structures at the microscale, where the bulk and surface dynamics of a single foam liquid channel can be accurately assessed. Isolated foam channels with adjoining nodes were studied for aqueous solutions of four food grade surfactants. Existing observations of distortions to sodium dodecyl sulphate channel geometries were confirmed for solutions of Tween 20 (T20) and Tween 80 (T80) and were well described by the theory presented here. Moreover, previously unseen distortions to liquid channels were observed for polymeric surfactant systems (hydroxypropyl methylcellulose and hydrolyzed pea protein blend), which were proposed to result from their high surface viscosities. The apparent surface viscosities, μs, of surfactants tested here ranged from high (10 g/s < μs < 10−3 g/s) for polymeric surfactants to very low (10−10 g/s < μs < 10−8 g/s) for Tweens, clearly demarking the regimes of viscous and inertial dominant flows, respectively. It is recommended that further work seeks to investigate the finding of a strong correlation between μs and channel surface tension, γ, for soluble surfactant systems, which could explain the apparent non-Newtonian values of μs that were consistently measured here.

### Influence of flowing fluid property through an elastic tube on various deformations along the tube length

The study of fluid flow characteristics in collapsible elastic tubes is useful to understand biofluid mechanics encountered in the human body. The research work presented here is aimed at thoroughly investigating the influence of both Newtonian and/or non-Newtonian fluids (low and high shear thinning) during steady flow through an elastic tube on various tube deformations, which enables understanding of the interaction between wall motion, fluid flow, and intestinal transmembrane mass transfer as a crucial contribution to a mechanistic understanding of bioaccessibility/bioavailability. It is observed that for a given steady volume flow rate, the tube is buckled from an elliptical shape to a line or area contacted two lobes as the critical external pressure is increased. The downstream transmural pressure is found to get more negative than that at the upstream as the outlet pressure decreased due to stronger tube collapse resulting in a reduced cross-sectional area. The experimental results depict that the tube cross-sectional area decreased by only about a factor of one for PEG (polyethylene glycol) and about a factor of six for both CMC (carboxymethyl cellulose) and PAA (polyacrylamide) from the undeformed one under an applied external pressure of 105 mbar. The corresponding maximum velocity increased by a factor of two during steady flow of shear-thinning fluids. The shear-thinning behavior of both CMC and PAA solutions is clearly observed at a constant flow rate of 17 ml/s as the tube cross-sectional area decreased due to an increase in compressive transmural pressure. In addition, the viscosity of PAA is drastically decreased due to its high shear-thinning behavior than that of the CMC under the same applied external pressure.

### Characterization of peristaltic flow during the mixing process in a model human stomach

Numerical simulations are performed to investigate the characteristics of peristaltic flow in a model stomach during the mixing and digestion process. The geometrical model for the stomach consists of an axisymmetric tube of varying diameter with a wall at one end, representing the antrum and closed pylorus. The antral contraction waves (ACWs) that produce the peristaltic flow are modeled as traveling waves that deform the boundary and consequently the computational mesh. This geometrical model is implemented into the open source code OpenFOAM. A parametric study is performed in which the fluid viscosity, wave speed, wave width, and maximum relative occlusion are varied. The effect of these parameters on the retropulsive jet induced near the pylorus and the recirculation between pairs of consecutive ACWs is investigated. Both of these flow features contribute to the mixing and digestion process. The retropulsive jet is quantified by its peak velocity and length along the centerline. For each wave geometry, these quantities are found to be independent of the Reynolds number for low Reynolds numbers, while for Reynolds numbers exceeding one, the peak centerline velocity decreases and the jet length increases as the Reynolds number increases. Moreover, the velocity and pressure curves are found to scale with the wave speed at low Reynolds numbers. Between different wave geometries, scaling laws are proposed and tested for the peak centerline velocity and jet length. Particle tracking and vorticity plots show that mixing efficiency increases when the relative occlusion increases, as well as when the viscosity or wave width decreases.

### Impact of airflow on the heat transfer conditions inside an oven cavity, characterized using particle imaging velocimetry

The complex airflow in convection ovens directly influences the heat transferred to the product placed inside, thereby affecting product quality. Characterization of related airflow profiles can provide scientific understanding for improvement of oven designs as well as important parameters for simulation of involved thermal processes. In this study, the particle-imaging velocimetry (PIV) technique was applied to visualize airflow inside a household convection oven with samples placed at three different locations on a baking tray. The oven cavity was modified for optical access, and airflow was measured at room temperature. A 30 mW green laser was used for illuminating tracer particles in a laser sheet that were generated using incense sticks. The flow patterns were captured using a high-speed camera at 1000 fps. The vorticity and turbulent kinetic energy parameters derived from velocity fields reflected adequate mixing of air inside the cavity. The computed heat transfer coefficient distribution from the boundary layer flow fields to the sample surface ranged between 2.0 and 18.3 W m−2 K−1. The results showed separation of the laminar boundary layer from the object surface at angles of 85°–90°. The PIV-algorithms and boundary layer flow derived parameters developed in this study can be used for refined characterization of complex air or gas flows and related heat transfer characteristics in closed cavity convection ovens and the like arrangements.

### Effect of bolus viscosity on carbohydrate digestion and glucose absorption processes: An in vitro study

Digestion is the process of breaking down food into smaller nutrient components which can be easily absorbed in the intestinal tract. The aim of this study was to experimentally investigate the influence of bolus (gastric content) viscosity on digestion and nutrient absorption processes, using an in vitro gastrointestinal model, the TIM-1 system. Two types of simple carbohydrates, namely, glucose and maltodextrin, were used as model foods. The initial bolus viscosity was varied (∼1 mPa·s, ∼15 mPa·s, and ∼100 mPa·s) using different glycerol-water proportions. A fluorescent molecular rotor compound (Fast Green For Coloring Food) was used to monitor viscosity changing patterns of the gastrointestinal content during digestion in the in vitro stomach and small intestinal sections. The digested-nutrient absorption data indicated that the initial bolus viscosity did not significantly affect the glucose absorption process in the small intestine. However, an increase in the initial bolus viscosity from ∼1 mPa·s to ∼15 mPa·s reduced the maltodextrin to glucose conversion by 35%. A further increase in the initial bolus viscosity from ∼15 mPa·s to ∼100 mPa·s did not significantly reduce the maltodextrin to glucose conversion.

### Retention and infiltration of bacteria on a plant leaf driven by surface water evaporation

Evaporation-driven internal flows within a sessile droplet can transport microorganisms close to the leaf surface and facilitate their infiltration into the available openings, such as stomata. Here, using microfabricated surfaces out of polydimethylsiloxane, the sole effects of evaporation of sessile droplets in contamination of plant leaves was studied. These surfaces were patterned with stomata, trichomes, and grooves that are common surface microstructures on plant leaves. Evaporation of sessile droplets, containing bacterial suspensions, on real leaves and fabricated surfaces was studied using confocal microscopy. To provide insight about the effects of leaf hydrophobicity and surface roughness on the bacterial retention and infiltration, variations of contact angle of sessile droplets at these surfaces were measured during evaporation. The results showed that evaporation-driven flow transported bacteria close to the surface of spinach leaves and fabricated surfaces, leading to distinct infiltration into the stomata. Larger size and wider spacing of the micropores, and a more hydrophilic surface, led bacteria to spread more at the droplet base area and infiltrate into more stomata. Evaporation-driven movement of contact line, which can sweep bacteria over the leaf surface, was shown to lead to bacterial infiltration into the stomatal pores. Findings should help improve microbial safety of leafy greens.

### Numerical and experimental investigation of dough kneading in a three-dimensional spiral kneader

This work reports on the first three-dimensional viscoelastic dough kneading simulation performed in a spiral kneader. Unstructured tetrahedral grids were generated using ICEM CFD 17.1. Viscoelastic volume-of-fluid simulations were performed using OpenFOAM v.4.0 in combination with the RheoTool package v.2.0. The White-Metzner model with a Bird-Carreau type of shear-rate dependency of the viscosity and relaxation time was utilized to describe the rheology of the dough matrix. We validated our numerical method by simulating the viscoelastic rod climbing benchmark problem in a cylindrical bowl. The temporal evolution of the dough surface was compared with screenshots obtained with a high-speed video camera during laboratory kneading. We found that the curvature of the free surface matches the experimental data well. With our numerical approach, we were able to predict the formation, extension, and breakup of dough pockets. The dough is convected around the inner stationary rod by the rotation of the outer cylindrical bowl, whereas the spiral arm located in between these two parts produces spiral flow patterns. Vertical mixing is not as good as radial mixing and may be enhanced by utilizing two spiral arms similar to hand kneading. Industrial kneading geometries and processes may be further optimized by performing such types of simulations.

### Contraction of a shear-thinning axisymmetric cavity

We investigate the capillary driven collapse of a small contracting cavity or hole in a shear-thinning fluid. We find that shear-thinning effects accelerate the collapse of the cavity by decreasing the apparent liquid viscosity near the cavity’s moving front. Scaling arguments are used to derive a power-law relationship between the size of the cavity and the rate of collapse. The scaling predictions are then corroborated and fully characterized using high-fidelity simulations. The new findings have implications for natural and technological systems including neck collapse during microbubble pinch-off, the integrity of perforated films and biological membranes, the stability of bubbles and foams in the food industry, and the fabrication of nanopore based biosensors.

### Numerical study on electrohydrodynamic multiple droplet interactions

Author(s): P. S. Casas, M. Garzon, L. J. Gray, and J. A. Sethian

We present a numerical study of inviscid multiple droplet coalescence and break-up under the action of electric forces. Using an embedded potential flow model for the droplet hydrodynamics, coupled with an unbounded exterior electrostatic problem, we are able to perform computations through various ...

[Phys. Rev. E 100, 063111] Published Mon Dec 30, 2019

### Flagellated bacteria swim in circles near a rigid wall

Author(s): Yunyoung Park, Yongsam Kim, and Sookkyung Lim

The rotation of bacterial flagella driven by rotary motors enables the cell to swim through fluid. Bacteria run and reorient by changing the rotational direction of the motor for survival. Fluid environmental conditions also change the course of swimming; for example, cells near a solid boundary dra...

[Phys. Rev. E 100, 063112] Published Mon Dec 30, 2019