Quiescent Medium Research Articles

Wave breaking, dispersive shock wave, and phase shift for the defocusing complex modified KdV equation.

We study the problem of wave breaking for a simple wave propagating to a quiescent medium in the framework of the defocusing complex modified KdV (cmKdV) equation. It is assumed that a cubic root singularity is formed at the wave-breaking point. The dispersive regularization of wave breaking leads to the generation of a dispersive shock wave (DSW). We describe the DSW as a modulated periodic wave in the framework of the Gurevich-Pitaevskii approach based on the Whitham modulation theory. The generalized hodograph method is used to solve the Whitham equations, and the boundaries of the DSW are found. Most importantly, we determine the correct phase shift for the DSW from the generalized phase relationships and the modified Gurevich-Pitaevskii matching conditions, so that a complete description of the DSW is obtained rather than just its envelope. All of our analytical predictions agree well with the numerical simulations.

Thermodynamic analysis of nano-electrospray induced gas jets

Nano-electrospray (nES) produces a plume of charged liquid droplets which have drag interactions with the surrounding gas after they are emitted from a source capillary. The resulting induced gas flow has often been considered unimportant, but we have demonstrated that a gas microjet of significant velocity up to 10s of m/s can be produced. In this work we present a thermodynamic framework that enables analysis of gas jet generation from electrosprays and introduce the important metrics for such analysis, effectiveness (a measure of momentum transfer from the electrosprayed aerosol to gas) and efficiency (a measure of energy conversion from electrical energy generating the electrospray to gas kinetic energy). This analytical framework is applicable to any two-phase flows consisting of discrete conservative-force-driven particles which exchange momentum with an inert, otherwise quiescent fluid medium to yield a co-flowing two-phase jet. We apply this framework to sprays of water from nano-electrospray emitters to demonstrate that increasing the applied electrical potential difference, increasing liquid mass flowrate, and decreasing droplet size all can increase electrospray induced gas jet strength, but only the latter two do so while also increasing the momentum transfer effectiveness and energy conversion efficiency.

Long‐time asymptotics and the radiation condition with time‐periodic boundary conditions for linear evolution equations on the half‐line and experiment

AbstractThe asymptotic Dirichlet‐to‐Neumann (D‐N) map is constructed for a class of scalar, constant coefficient, linear, third‐order, dispersive equations with asymptotically time/periodic Dirichlet boundary data and zero initial data on the half‐line, modeling a wavemaker acting upon an initially quiescent medium. The large time asymptotics for the special cases of the linear Korteweg‐de Vries and linear Benjamin–Bona–Mahony (BBM) equations are obtained. The D‐N map is proven to be unique if and only if the radiation condition that selects the unique wave number branch of the dispersion relation for a sinusoidal, time‐dependent boundary condition holds: (i) for frequencies in a finite interval, the wave number is real and corresponds to positive group velocity, and (ii) for frequencies outside the interval, the wave number is complex with positive imaginary part. For fixed spatial location , the corresponding asymptotic solution is (i) a traveling wave or (ii) a spatially decaying, time‐periodic wave. The linearized BBM asymptotics are found to quantitatively agree with viscous core‐annular fluid experiments.

On the gravitational fall of a non-spherical particle in a quiescent fluid medium

Closed-form analytical solutions have been derived for the gravitational fall of a non-spherical particle in a quiescent fluid. The Boussinesq-Basset-Oseen equation accounting for history force and particle slip effects was applied to derive the particle motion equation, using a sphericity-dependent drag law for transitional flow in the range 0.001<Re≤100000 and valid for sphericities >0.50. The derived closed-form solutions were validated with published experimental data and the accuracy was verified using published approximate analytical solutions and numerical results. The closed-form solutions were found to agree with experiments and produced more accurate results than other published approximate analytical solutions. Also, the effects of sphericity, Basset force and particle slip on the particle motion were investigated and discussed. The present analytical solutions are applicable to zero and non-zero initial velocity, steady and unsteady motion, and the corresponding displacements and accelerations. Additionally, new settling velocity formula valid for non-spherical particles was derived.

Compact and quiescent circumgalactic medium and Ly α haloes around extremely red quasars

ABSTRACT Red quasars may represent a young stage of galaxy evolution that provide important feedback to their host galaxies. We are studying a population of extremely red quasars (ERQs) with exceptionally fast and powerful outflows, at median redshift z = 2.6. We present Keck/Keck Cosmic Web Imager integral field spectra of 11 ERQs, which have median colour i–W3 = 5.9 mag, median 〈 Lbol 〉 ≈ 5 × 1047 erg s−1, Ly α halo luminosity 〈 Lhalo 〉 = 5 × 1043 erg s−1, and maximum linear size &amp;gt;128 kpc. The ERQ haloes are generally similar to blue quasar haloes, following known trends with Lbol in halo properties. ERQs have halo symmetries similar to Type-I blue quasars, suggesting Type-I spatial orientations. ERQ 〈 Lhalo 〉 is ∼2-dex below blue quasars, which is marginal due to scatter, but consistent with obscuration lowering photon escape fractions. ERQ haloes tend to have more compact and circularly symmetric inner regions than blue quasars, with median exponential scale lengths ∼9 kpc, compared with ∼16 kpc for blue quasars. When we include the central regions not available in blue quasar studies (due to point spread function problems), the true median ERQ halo scale length is just ∼6 kpc. ERQ haloes are kinematically quiet, with median velocity dispersion 293 km s−1, consistent with expected virial speeds. Overall, we find no evidence for feedback on circumgalactic scales, and the current episode of quasar activity (perhaps due to long outflow travel times) has not been around long enough to affect the circumgalactic medium. We confirm the narrow Ly α-emission spikes found in ERQ aperture spectra are halo features, and are useful for systemic redshifts and measuring outflow speeds in other features.

Characterisation of an independently controlled coaxial synthetic jet

This paper presents the hot-wire measurements to characterise the flow field of a novel coaxial synthetic jet (CSJ) actuator. The CSJ actuator is formed by positioning two single-acting synthetic jet (SJ) actuators coaxially (0° orientation angle) along with their own flow actuation mechanism (piezo-electric diaphragms). The CSJ is formed by the periodic suction and expulsion of the fluid into a quiescent medium employing the piezo diaphragms through the inner and annular openings (orifices), which have an equal hydraulic diameter (dh) of 3 mm. This novel configuration facilitates independent control of excitation voltage (V), frequency (f) for inner and annular jets, and additionally, various phase differences (∅s) between the inner and annular jets. The resonance frequency of both the inner and annular cavities are obtained separately as 350 Hz, and 320 Hz, respectively. The inner jet is operated at Reynolds number Re=1100 (V=50 V, and f=350 Hz), which remains fixed for all the test cases. The CSJ flow field is analysed for three mass flux ratios (Mrs) as 0.7, 1.0, and 2.0, which are achieved by operating both the diaphragms independently at various excitation voltages for a fixed f=350 Hz, and at various fs for a fixed excitation voltage of 50 V. Moreover, the effect of ∅s (range: 0° to 180° in the step of 45°) by leading the inner or annular jet is examined while the CSJ is operated at these Mrs. It has been observed that the strength and spreading of the CSJ can be enhanced by providing ∅s between the jets, without investing any additional power for flow excitation. It is important to notice that leading the weaker jet enhances its contribution to the creation of the CSJ, which improves the CSJ's strength and spread. The CSJ flow field is compared with that of the inner SJ, and annular SJ, operated individually, to illustrate the superior performance of the CSJ. The paper conveys that the CSJ’s strength and spreading can be manipulated significantly with the independent control facility, which is feasible with this configuration.

Acoustic velocity analogy formulation for sources in quiescent medium

The prediction of near field acoustic velocity is necessary when using equivalent source method and evaluating multi acoustic fields problem. According to the idea of acoustic analogy, this paper induces a vector wave equation of aeroacoustics by rearranging the conservation equations of mass and momentum with a permeable surface. Then, an analytical formulation of the acoustic velocity, called formulation V2A, is derived for sources in a quiescent medium by solving the vector wave equation with the free-space Green’s function. The validity of the formulation is confirmed by numerical results for a stationary monopole, a stationary dipole source, and a rotating monopole source in a quiescent medium. The result indicates that the predication of formulation V2A is nearly identical to the exact solutions no matter in far-field or near-field.

Swimming of Buoyant Bacteria in Quiescent Medium and Shear Flows.

Gravity has an unavoidable effect on all living organisms inhabiting fluidic surroundings. To investigate the spatial distribution of bacteria in quiescent fluids and their rheotactic behavior in shear flows under buoyancy, we adjust the buoyant force to regulate bacterial swimming in a microfluidic channel. It is found that swimming bacteria of Escherichia coli exhibit an obvious vertical separation when exposed to a medium with high density and gradually gather close to the up wall within minutes. The bacterial population presents a net upward number flux, which enhances the trapping of motile bacteria onto the up surface as a result of buoyancy force apart from the hydrodynamic and kinematic interactions in quiescent fluids. When flow is imposed into the channel, the buoyancy effect is however significantly suppressed. Additionally, the drift velocity perpendicular to the buoyancy vector as a result of chirality-induced transverse swimming decreases with buoyancy force. However, this transverse drift capability is recovered after excluding the intrinsic swimming motility in a quiescent medium. Failing to escape from the trapping as a result of buoyant force allows for a facile separation of bacteria along the vertical direction. The findings also offer a controllable way to redisperse and homogenize the bacteria distribution close to walls by imposing a weak shear flow.

Thermal radiation effect on Non-Newtonian Casson fluid through a porous material over a magnetic field with buoyancy

The magnetohydrodynamic (MHD) chemically reactive of Casson non-Newtonian nanofluid flow on a two-dimensional incompressible steady from stretched sheet in a porous quiescent medium with buoyancy effect is investigated numerically. Additional effects included in the originality of the model are the applied magnetic field and solar radiation effect. The Chebyshev collocation method (CCM) was used to solve the ordinary differential equations (ODEs) with MATHEMATICA 11.3 software. The present tables and graphs show the performance of fluid physical quantities, momentum flow, energy distribution, nanoparticle concentration, and velocity for various values of applicable dimensionless numbers. The numerical outcomes demonstrate the effect of different physical parameters of the fluid, and it was observed that the velocity profile increased as the thermal and mass Grashof number increased due to an increase in buoyant force caused by heat transferred from the vertical plate to the fluid but decreased as the Casson parameter increased due to a decrease in its yield stress, porosity, and magnetic parameter. Also Analyses reveal that the thermal profile reduce with an increase in variable thermal conductivity parameter. This study will be of considerable economic value to marine engineers, mechanical engineers, physicists, chemical engineers, and others since its application will help them improve their operations.

Immersed buoyant viscoplastic injections

In this study, the injection of a viscoplastic (yield stress) fluid into a quiescent Newtonian medium is experimentally investigated, using a range of experimental methods, including high-speed camera imaging, laser-induced fluorescence (LIF), and ultrasound Doppler velocimetry (UDV) techniques. The case of our consideration is the continuous downward injection of a Carbopol solution, as a core fluid, through an eccentric inner pipe, placed inside a vertical closed-end pipe filled with a glycerin–water solution. The injected fluid is always heavier than the in-situ fluid and the fluids are miscible. As the injection continues, a filament of the core fluid immersed in the in-situ fluid is formed, for which it has been shown that there exist three distinct flow patterns, namely, the breakup, coiling, and bulging (buckling) regimes. Our focus in this study is to analyse the detailed flow features and sub-regimes at longer times, from an experimental perspective. To generalize our results, they are presented versus the governing dimensionless numbers of the flow, i.e. the buoyancy number, the Bingham number, the viscosity ratio, and the falling height. The breakup regime is analysed in terms of the yielding, necking and pinch-off process, the length of filaments, and their subsequent falling behaviours, the coiling regime in terms of the regular, free and irregular coiling behaviours, and the bulging (buckling) regime in terms of the appearance of a detached falling part and the maximum penetration depth. The results of this work can find applications, in particular, in the plug and abandonment (e.g. cementing processes) of oil and gas wells and 3D printing technologies. • Experimental analysis of immersed buoyant viscoplastic injection in Newtonian fluid. • Observed flow regimes classified into breakup, coiling, and bulging. • Analysis of yielding, necking/pinch-off, and length of filaments for breakup regime. • Coiling subregimes categorized as regular, free, and irregular coiling. • Analysis of maximum penetration depth and subregimes in bulging regime.

The pH dependence of dissolution kinetics of zinc oxide

Zinc oxide (ZnO) powders are used as feed additives for supplementation in diet of animals. Because zinc dissolution rate strongly influences the digestibility of zinc by animals and their stomach has variable pH, the dissolution kinetics of ZnO are studied at the several pH of relevance between 2 and 4. The dissolution of ZnO has been investigated with the help of modeling the dissolution kinetics measured in vitro at various pH. Dissolution is faster in acidic medium. But the acceleration of dissolution at low pH is moderate compared to what would be expected on the basis of the strong pH dependence of ZnO solubility. The concentration of Zn2+ in the quiescent medium at the surface of ZnO particles is much lower than its solubility. It is proposed as a rationale, that hydroxide anions released during dissolution accumulate at the surface of the positively charged ZnO surface, and that the dissolution kinetics is mainly controlled by the diffusion of H+ ions from the bulk solution to the surface.

One-Way Acoustic Guiding Under Transverse Fluid Flow

In a moving acoustic medium, sound waves travel differently with and against the fluid flow. This well-established acoustic effect is backed by the intuition that the fluid velocity bias imparts momentum on the propagating acoustic waves, thus violating reciprocity. Based on this conception, fluid flow that is transverse to the wave direction of propagation will not break reciprocity. In this paper we contrast this common wisdom and theoretically show that the interplay between transverse mean flow and transverse structural gliding asymmetry can yield strong nonreciprocity and even, surprisingly, one-way acoustic waveguiding. To demonstrate that, we analyze a waveguide that comprises a few adjacent acoustic subdiffraction chains, i.e., linear chains of acoustic scatterers with monopolar or dipolar response. The structure is embedded within a medium with mean flow velocity that is transverse to the waveguide axis. We find the symmetry breaking conditions under which nonreciprocity is obtained, and we show how, under transverse mean flow, with Mach numbers as low as 0.02, one-way propagation of the acoustic wave is obtained on a sub-wavelength-thick acoustic waveguide. To demonstrate the phenomenon, we introduce two models. One in which the scatterers are assumed to be pointlike and the flow is homogeneous, and a second, in which we accommodate the issue of possible wakes created by the presence of scatterers inside the flow. The latter setup exhibits no direct interaction of the scatterers with the flow, by placing the waveguide in a quiescent medium adjacent to a flowing medium. Our results push forward the understanding of acoustic nonreciprocity, and may open another venue for the design of nonreciprocal acoustic wave devices for various applications.

Infrared Spectroscopic Survey of the Quiescent Medium of Nearby Clouds. II. Ice Formation and Grain Growth in Perseus and Serpens

The properties of dust change during the transition from diffuse to dense clouds as a result of ice formation and dust coagulation, but much is still unclear about this transformation. We present 2–20 μm spectra of 49 field stars behind the Perseus and Serpens Molecular Clouds and establish relationships between the near-infrared continuum extinction (A K) and the depths of the 9.7 μm silicate (τ 9.7) and 3.0 μm H2O ice (τ 3.0) absorption bands. The τ 9.7/A K ratio varies from large, diffuse interstellar medium-like values (∼0.55), to much lower ratios (∼0.26). Above extinctions of A K ∼ 1.2 (A V ∼ 10; Perseus, Lupus, dense cores) and ∼2.0 (A V ∼ 17; Serpens), the τ 9.7/A K ratio is lowest. The τ 9.7/A K reduction from diffuse to dense clouds is consistent with a moderate degree of grain growth (sizes up to ∼0.5 μm), increasing the near-infrared color excess (and thus A K), but not affecting the ice and silicate band profiles. This grain growth process seems to be related to the ice column densities and dense core formation thresholds, highlighting the importance of density. After correction for Serpens foreground extinction, the H2O ice formation threshold is in the range of A K = 0.31–0.40 (A V = 2.6–3.4) for all clouds, and thus grain growth takes place after the ices are formed. Finally, abundant CH3OH ice (∼21% relative to H2O) is reported for 2MASSJ18285266+0028242 (Serpens), a factor of >4 larger than for the other targets.

The dominant underlying parameters controlling the dispersion of falling particle curtains

A new analytical model of a free-falling curtain of heavier-than-fluid particles from a wedge-shaped hopper in a quiescent medium is presented and used to determine the key underlying–non-dimensional parameters that control its dispersion. The model calculates the particle velocity and the volumetric flow rate of the induced air into the particle stream, using an Eulerian approach based on the momentum transfer between the two phases. It employs a new drag model to account for the sphericity of the particles over a wide range of Reynolds numbers to achieve a root mean square error of less than 10% in the predicted drag coefficient relative to available data over a wide range of sphericities (ψ = 0.023 − 1), even including granular particles. The solid-phase is modelled as a stream of particles, with the dynamics of the stream approximated by a stream coefficient determined from the published experimental data. The effects of particle size, mass flow rate, sphericity, and particle density on the particle velocity, entrained air, curtain thickness, and solid fraction are incorporated into the model. The model is used to provide new method of characterising the evolution of falling particle curtains onto a single regime map, which collapses all previous data. The velocity in near-field is controlled by the flow in the hopper. It then transitions to a similarity regime in which the mean velocity of particle stream normalised by the terminal velocity of single particle scales with the axial distance from the nozzle exit normalised by the product of the particle diameter and Froude number. Further downstream again the particles asymptote toward the settling velocity of the individual particles, which is greater when particles are decelerated from above than when accelerated from below. Other insights, such as the role of non-sphericity, are also reported.

Effect of interfacial kinetics on the settling of a drop in a viscous medium

Multiphase emulsions, such as drops in a continuous medium, tend to have surfactant-like impurities present at the interfaces, either naturally or introduced artificially for stability, which may influence the flow field and, hence, alter the motion of the drops through a host of different mechanisms. Here, we carry out a robust analysis to characterize multiple aspects of such interfacial phenomena by studying the settling of a drop in a quiescent viscous medium. The surface active agents are assumed to be bulk-insoluble and non-ideal, while the interface itself is assumed to have its own rheology, described by the Boussinesq–Scriven model. The diffusive fluxes of the surfactants are expressed in a thermodynamically consistent manner as proportional to the chemical potential gradient, which results in concentration dependent diffusivity. We subsequently derive semi-analytical solutions for approximately spherical drops without any other restrictions on the transport processes. Our results reveal that stresses originating from interfacial rheology tend to decrease the settling velocity and at the same time make the surfactant concentration uniform across the surface. Remarkably, this settling velocity is revealed to be independent of the choice of the free-energy isotherms and the extent of packing of the surfactants when a variable diffusivity is correctly accounted for. These insights will be helpful in better understanding of the underlying dynamics of surfactant-laden drops, having potential applications in microfluidic devices, food and pharmaceutical industries, and separation processes.

Dynamics of an oil-coated bubble rising in a quiescent water medium

Bubbles encapsulated by an organic bulk phase are widely present in the ocean and many industrial processes. We present experiments on a rising oil-coated compound bubble in quiescent water. By immobilizing the compound bubble surface and increasing the compound bubble effective density, the oil coating causes a smaller bubble shape deformation, changing the wake dynamics and forces acting on the bubble, and thereby its drag coefficient and path oscillation. The compound bubble zigzag oscillation is observed to decay significantly with time above a critical oil volume fraction. These results may provide guidance for simulations and applications of bubbly flows with compound interfaces.

On the compressible biglobal stability of the mean flow motion in porous channels

This work relies on a compressible biglobal stability approach to describe the wave dynamics in a planar rocket chamber modeled as a porous channel. At first, the effectiveness of the compressible formulation is demonstrated by reproducing, in the absence of a mean flow, the Helmholtz frequencies and mode shapes. Next, the unsteady vorticity fluctuations, which intensify near the walls, are shown to be consistent with those associated with parietal vortex shedding. In this context, the penetration depth of vorticoacoustic waves is found to be strongly dependent on the penetration number. The latter gauges the cubic power of the injection speed to the product of kinematic viscosity, chamber half-height, and frequency squared. As for the strictly hydrodynamic modes, they seem to develop at the porous walls and grow in the core region, where the mean flow velocity is most appreciable. The ensuing modal analysis enables us to predict both longitudinal and transverse modes for several test cases, thus illustrating the tendency of hydrodynamic modes to intensify at higher injection speeds and longer chambers. Furthermore, by repeating the analysis with an active mean flow, one finds that successive increases in the injection speed gradually reduce the predicted frequencies relative to the eigenmodes obtained in a quiescent medium. Finally, recognizing that the spectral analysis is capable of recovering both longitudinal and transverse modes induced by acoustic and hydrodynamic disturbances, their coupled interactions, which often lead to specifically amplified frequencies in static tests, are robustly captured, namely, without resorting to any particular wave decomposition.

Approximate analytical solution of time-fractional non-linear heat equation via fractional power series method

A time-fractional heat equation arising in a quiescent medium is established, and its approximate analytical solution is obtained by the fractional power series method. The results show that the method performs extremely well in terms of efficiency and simplicity.

The dynamics of bouncing, partially coalescing, liquid metal droplets in a viscous medium

Planar partial coalescence is a phenomenon in which a droplet at a free surface or interface between two fluids coalesces into the plane surface producing a smaller droplet rather than coalescing completely. This smaller, ‘daughter’ droplet will be driven towards the interface by gravity and capillary forces resulting in a cascade effect of progressively small daughter droplets until the Ohnesorge Number approaches $\sim$ 1 and the cascade terminates with a full coalescence event. This paper utilizes a room temperature liquid metal alloy composed of gallium, indium and tin to study partial coalescence in a viscous quiescent medium and observed bouncing of the coalescing droplets on the interface. We observed the event using high speed videography measuring effects such as the droplet to daughter droplet ratio, droplet velocities, droplet bounce heights and coefficients of restitution for the bouncing event. An existing model (Honey &amp; Kavehpour, Phys. Rev. E, vol. 73, 2006) from our group was used, validated and expanded upon to include buoyancy effects to estimate the initial velocity of the droplet and we developed two new models for the droplet travel and maximum bounce height. The first utilizes the Stokes model for drag to moderate success while the second utilizes a model from Beard &amp; Pruppacher (J. Atmos. Sci., vol. 26, 1969, pp. 1066–1072) and a fourth-order Runge–Kutta numerical integration scheme to predict the droplet velocity and position as functions of time. Additionally the coefficient of restitution was determined from the model using a shooting method technique in tandem with measured data to find a coefficient of restitution value of $A = 0.27 \pm 0.06$ . This ‘bouncing drop’ phenomenon continues in a quiescent viscous fluid to the sub-micron scale and was facilitated by the material properties of the liquid metal including the high density, moderate viscosity and particularly high interfacial tension.

Dynamics of a single bubble rising in a quiescent medium

In the present work, an experimental analysis was performed to characterise the flow field around a single bubble of different diameters ∼ 2.77–3.53 mm) rising in a quiescent medium aiming to determine the effect of bubble size on kinetic energy distribution. The velocity field was measured using a non-intrusive particle image velocimetry (PIV) technique and kinetic energy spectrum was determined in both transverse and longitudinal directions applying a Fast Fourier Transformation (FFT). Both small- and large-scale motions of the flow field were identified and separated using a discreate wavelet transformation (DWT) method. It was found that the energy spectrum of the large-scale motions depended on the bubble size while the small-scale energy spectrum was nearly independent of it. The slopes of the energy spectrum were found to be close to -5/3 and -3 for the large- and small-scale regimes, respectively and the transition of slope was observed to occur at the wavenumber corresponding to the bubble diameter. Using the measured velocity field data, a turbulence kinetic energy (TKE) budget analysis was performed involving five components namely kinetic energy production, turbulent transport, pressure diffusion, viscous diffusion, and energy dissipation. Overall, it was observed that in the vicinity of bubble surface, turbulence production term was not entirely balanced by the dissipation term; and turbulent transport and pressure diffusion term also had significant contributions.