Motionless Liquid Research Articles

Modeling heat‐mass transport for MHD bio‐convection Carreau nanofluid with Joule heating containing both gyrotactic microbes and nanoparticles diffusion

AbstractThe study of a bio‐convection is a natural progression that happens as microbes transport unsystematically in single‐celled or colony‐like environments; as they live ubiquitously, individuals, as in rodents, and plant forms. They're so much denser than liquid, owing to which, microbes develop a basis of bio‐convection. Gyrotactic microbes are individuals that dip up‐stream in contradiction of gravity in motionless liquid, producing the higher portion of the deferment to be thicker than the lesser part. Bioconvection's significance can be realized in a diversity of bio‐microsystems, for instance, bio‐tech allied to mass transport, biofuels, enzyme biosensors and fraternization. Together with nanofluids, a mixture of bioconvective is working to progress the structure's thermal enactment which has uses in diverse scientific structures. Recent study has related the progress of extrusion features, radiative heat progression and biofuel fabrication to the use of nanoparticles. The essential plans of the modern scrutinization are to examine the magneto bioconvection flow of nonlinear radiative Carreau fluid persuades by the nanofluid and Joule heating. Additionally, Convective conditions of heat, mass and motile microorganism with heat sink/source and chemical reaction have been explored. By means of similarity alteration to alter the nonlinear partial differential equations into nonlinear Ordinary differential equations (ODE). The solutions of subjected equations have been attained by exploiting the bvp4c algorithm. Homotopic algorithm has been also executed for comparison of bvp4c results and former studies. The impacts of relatable factors on diverse fields are sketched in graphic form. The study explores temperature field enhancement for thermo Biot and Brownian motion factors. Furthermore, the fluid concentration exaggerates for mass Biot and chemical reaction factor; however, declines for Brownian motion factor. The motile density field decays with the rising values for Peclet number and intensifies for motile density Biot factor. The comparison tables of current work and previous work also have been presented for the authentication of work with two different techniques.

Strong compression of bubbles in water, acetone and benzol

Strong compression of the medium in cavitation bubbles in water, acetone and benzol realizing in the final stage of their collapse in the initially motionless liquid at a temperature of 293 K is considered. At the beginning of the collapse, the radius of the bubbles is 500 μm, the vapor in the bubbles is in its saturation state at the temperature of the surrounding liquid. The pressure of water and benzol is varied in the range 1 ≤ p0 ≤ 100 bar to determine its values at which the degree of compression of the medium inside the cavitation bubbles in these liquids is close to that achieved inside the cavitation bubble in acetone at the pressure p0 = 15 bar. It is shown that in the case of the bubble in benzol such a degree of the vapor compression can be achieved at p0 = 4 bar, whereas in the case of the bubble in water, even p0 = 100 bar is not enough.

Oscillatory Marangoni flows with inertia

When the surface of a liquid has a non-uniform distribution of a surfactant that lowers surface tension, the resulting variation in surface tension drives a flow that spreads the surfactant towards a uniform distribution. We study the spreading dynamics of an insoluble and non-diffusing surfactant on an initially motionless liquid. We derive solutions for the evolution over time of sinusoidal variations in surfactant concentration with a small initial amplitude relative to the average concentration. In this limit, the coupled flow and surfactant transport equations are linear. In contrast to exponential decay when the inertia of the flow is negligible, the solution for unsteady Stokes flow exhibits oscillations when inertia is sufficient to spread the surfactant beyond a uniform distribution. This oscillatory behaviour exhibits two properties that distinguish it from that of a simple harmonic oscillator: the amplitude changes sign at most three times, and the decay at late times follows a power law with an exponent of $-3/2$. As the surface oscillates, the structure of the subsurface flow alternates between one and two rows of counter-rotating vortices, starting with one row and ending with two during the late-time monotonic decay. We also examine numerically the evolution of the surfactant distribution when the system is nonlinear due to a large initial amplitude.

Molecular turbulent evaporation in a gravitational field

An analysis of the convective mechanism of the evaporation of a motionless liquid layer into a closed space has been carried out. It has been shown that the intensity of evaporation is comparable with the intensity of momentum transport in the laminar-turbulent region of flows in smooth pipes.

Integration of a new shape-dependent particle–fluid drag coefficient law in the multiphase Eulerian–Lagrangian code MFIX-DEM

A new shape-dependent fluid–particle drag law has been added into the open source fluid dynamic software MFIX-DEM (MFIX-Discrete Element Method), which is the Eulerian–Lagrangian version of the classic MFIX Eulerian–Eulerian multiphase flow model. The drag law had been obtained by previous settling experiments of volcanic pumices in a motionless Newtonian liquid (water or alcohol). Pumices are characterized by a highly irregular shape, which is much different from a sphere and drastically influences fluid drag. The new drag law defines the particle–fluid drag coefficient as a function of both the fluid regime and particle characteristics, of which the shape factor is a compact descriptor that quantifies how the particle shape differs from a simple sphere. As a validation of the integration of the new drag law in the simulation software MFIX-DEM, the code has been used to replicate the experiment results. The comparison with simulations performed with other formulas demonstrates that, by means of the new drag law, a significant improvement in the capability of the MFIX-DEM code to predict the terminal velocities of irregularly shaped particles is obtained. Thanks to this implementation, MFIX-DEM should be used, from now on, for simulating fluid–particle flows in which the particles are significantly different from simple spheres, as is usually the case of environmental flows like explosive eruptions or ash and pollutant dispersal. Based on the results of this research, in the future an improved version of MFIX-DEM will be also presented, with a drag law useful also in the case of mixtures to be treated with a Eulerian–Eulerian multiphase model.

On the Marangoni Instability in Gas Absorption

The non-steady-state process of a gas absorption by initially motionless liquid is investigated. Nonlinear analysis of the thermo-capillary instability showed that the transition of the process to unstable convective regime is determined by two sharply different characteristic times. First one is the time of neutral perturbations, when the fluctuations of the concentration of absorbable substance, temperature and the liquid velocity stop decrease and begin to grow together, but their intensity is too small to influence on the absorption rate. The second one is the time much greater than the first, when the perturbations reach sufficient values, and the absorption process turns to the convective regime. The results obtained explain the well-known experimental data on delaying of the transition of the absorption process to the unstable convective regime.

Measurements of gas/oil free surface deformation caused by parallel gas flow

Flow-induced dynamic free-surface deformations are experimentally studied in a confined liquid volume of 5cSt silicone oil (Prandtl number Pr = 68). The geometry of the problem is a liquid column concentrically surrounded by an annular gas channel. A gas stream entering the duct from the top or bottom entrains the motionless liquid. The dynamic deformation of the gas–liquid interface is caused by a steady axisymmetric shear-driven flow. The experiments are performed in normal gravity conditions and the static deformation of a liquid bridge interface is unavoidable. The magnitude and shape of the dynamic surface deformation are analyzed using optical measurements with a comprehensive treatment of the images. The deviation of the free surface shape from the corresponding equilibrium profile is determined with an uncertainty of about 0.1 μm. The order of magnitude of the interface deformation is proportional to the capillary number, which is defined as the ratio of the viscous force per unit area to the capillary pressure. The study is performed for a large range of volumes and aspect ratios as well as for different gas velocities. As a general trend, the dynamic deformation grows with the gas velocity, which plays the role of a driving force, but a linear dependence is not observed for all volume ratios, despite the small Reynolds numbers, 280 < Reg < 560. The dynamic deformation displays a strong dependence on the liquid volume ratio and the direction of the gas stream parallel to the interface. When the gas flow is directed against gravity, the largest interface deformations are observed at the smallest volumes among the analyzed ones. In contrast, when the gas stream is aligned with gravity, then the deformations decrease with a decrease in the volume ratio, at a certain value attaining zero (vanishing) and then changing sign.

Formation and evolution of bubbly screens in confined oscillating bubbly liquids

We consider the dynamics of dilute monodisperse bubbly liquid confined by two plane solid walls and subject to small-amplitude high-frequency oscillations normal to the walls. The initial state corresponds to the uniform distribution of bubbles and motionless liquid. The period of external driving is assumed much smaller than typical relaxation times for a single bubble but larger than the period of volume eigenoscillations. The time-averaged description accounting for the two-way coupling between the liquid and the bubbles is applied. We show that the model predicts accumulation of bubbles in thin sheets parallel to the walls. These singular structures, which are formally characterized by infinitely thin width and infinitely high concentration, are referred to as bubbly screens. The formation of a bubbly screen is described analytically in terms of a self-similar solution, which is in agreement with numerical simulations. We study the evolution of bubbly screens and detect a one-dimensional stationary state, which is shown to be unconditionally unstable.

Suppression of heterogeneous bubble nucleation by upstream subcooled liquid flow

The threshold levels for quasi-steady-state bubble nucleation on a smooth platinum surface located in a microchannel, both with and without liquid flow, are explored. The measured threshold for motionless liquid compares well with the theoretical value as calculated from the classical kinetics of nucleation. The measured threshold for the case of flow in the microchannel exceeds the measured value for motionless liquid and even exceeds the theoretical value. The observed phenomena suggest that in the absence of impurities, classical theory can accurately predict the heterogeneous nucleation. In addition, subcooled fluids were found to suppress bubble nucleation.

Plunging of a liquid jet into a motionless liquid

Plunging of a liquid jet into a motionless liquid

Thermal influence of boundaries on the onset of Rayleigh-Bénard convection

The Bubnov-Galerkin method was applied to the problem of onset of convection in a horizontally infinite liquid layer set between two blocks with different thermal conductivities and thicknesses. The critical Rayleigh number ( Ra c) and wavenumber ( k c ) were determined for a range of conductivities and thicknesses. Computations, based on the finite element method, for the steady conductive regime (motionless liquid) suggest that lateral walls, with different thermal admittances appropriate to a finite vessel, have no appreciable effect on Ra c and k c when the aspect ratio is larger than two. Values calculated from the theoretical model are in reasonable agreement with experimental results.

On the evolution of double-diffusive intrusions into a stably stratified liquid: a study of the layer merging process

The nonlinear evolution of double-diffusive instabilities into a laterally heated stably stratified motionless liquid is studied through direct numerical simulation in a two-dimensional set-up. In this paper, we consider liquids which are initially stratified through a constant salt gradient. The stages of evolution of the intrusions and their spatial scales correspond well with those observed in laboratory experiments. A central process in the evolution is that of layer merging. A particular case of layer merging is analysed in detail and a new physical description of this process is proposed, to which we refer as ‘layer sandwiching’.

Instability of the equilibrium of a liquid below its vapour between horizontal heated plates

We study the stability of a motionless liquid below its vapour between heated horizontal plates. The temperature of the bottom plate is held below the vaporization temperature and the top plate is hotter than the vaporization temperature. A water film is on the cold plate and a vapour film on the hot plate. We find a basic solution depending only on the variable y normal to the plates, with steady distributions of temperature, a null velocity and no phase change. The linear stability of this basic state is studied in the frame of incompressible fluid dynamics, without convection, but allowing for phase change. An ambiguity in the choice of the conditions to be required of the temperature at the phase-change boundary is identified and discussed. It is shown that the basic state of equilibrium is overstable under conditions of large temperature gradient, when the other parameters have suitable values. An analysis of the energy of the most dangerous disturbance shows that the source of the instability is associated with change of phase.

Turbulent dispersion of particles in self-generated homogeneous turbulence

Turbulent dispersion of particles in their self-generated homogeneous turbulent field was studied both experimentally and theoretically. Measurements involved nearly monodisperse spherical glass particles (nominal diameters of 0.5, 1.0 and 2.0 mm) falling with uniform particle number fluxes in a nearly stagnant water bath. Particle Reynolds numbers based on terminal velocities were 38, 156, and 545 for the three particle sizes. The flows were dilute with particle volume fractions less than 0.01%. Measurements included particle motion calibrations, using motion-picture shadowgraphs; and streamwise and cross-stream mean and fluctuating particle velocities, using a phase-discriminating laser velocimeter. Liquid-phase properties were known from earlier work. Particle properties were predicted based on random-walk calculations using statistical time-series methods to simulate liquid velocities along the particle path.Calibrations showed that particle drag properties were within 14% of estimates based on the standard drag correlation for spheres, however, the particles (particularly the 1.0 and 2.0 mm diameter particles) exhibited self-induced lateral motion even in motionless liquid due to eddy-shedding and irregularities of shape. Particle velocity fluctuations were primarily a function of the rate of dissipation of kinetic energy in the liquid since this variable controls liquid velocity fluctuations. Streamwise particle velocity fluctuations were much larger than cross-stream particle velocity fluctuations (2–5:1) largely due to varying terminal velocities caused by particle size variations. Cross-stream particle and liquid velocity fluctuations were comparable owing to the combined effects of turbulent dispersion and self-induced motion. Predicted mean and fluctuating particle velocities were in reasonably good agreement with the measurements after accounting for effects of particle size variations and self-induced motion. However, the theory must be extended to treat self-induced motion and to account for observations that this motion was affected by the turbulent environment.

Marangoni instability in a liquid layer confined between two concentric spherical surfaces under zero-gravity conditions

A liquid layer containing a single solute is bounded on the outside by a rigid spherical surface and on the inside by a concentric gas/liquid interface. The solute evaporates from the liquid to the gas phase and, if the surface tension depends on the solute concentration, surface-tension driven convective flows may arise (Marangoni instability). Assuming zero-gravity conditions and using a normal-mode approach, we study the linear stability of the time-dependent, spherically-symmetric concentration profiles in a motionless liquid. Numerical results are presented for Marangoni numbers and perturbation wave numbers in the case of neutral stability. It turns out that the system's stability properties are strongly dependent on the curvature of the interface and on the mass-transfer Biot number.

The coupling of Marangoni and capillary instabilities in an annular thread of liquid

A motionless liquid bridge with annular cross section is bounded on the inside by a heated rod and on the outside by a deformable interface. This bridge is subjected to both capillary and classical Marangoni instabilities. In this paper, the linear stability of this annular thread of liquid, under zero gravity, is studied. The coupling of both instabilities gives rise to unstable traveling waves. Furthermore, it is shown that the Marangoni instability cannot stabilize capillary breakup.

Calculation of the hydrodynamic reactions on a solid airfoil oscillating in a motionless liquid

Calculation of the hydrodynamic reactions on a solid airfoil oscillating in a motionless liquid

A note on the singularities in the theory of water waves with an inertial surface

AbstractThis note is concerned with the derivation of velocity potentials describing the generation of infinitesimal gravity waves in a motionless liquid with an inertial surface composed of uniformly distributed floating particles, due to fundamental line and point sources with time-dependent strengths submerged in a liquid of finite constant depth.

On the generation of water waves at an inertial surface

AbstractIn this paper we develop the Laplace-transform method to solve initial-value problems for the velocity potential describing the generation of infinitesimal capillary-gravity waves in a motionless liquid with an inertial surface composed of uniformly distributed floating particles. The two principal problems considered are the forced motions due to a submerged wave source and an immersed vertical plane wave-maker, which begin to operate in a time-dependent manner at a given instant. The transformed potentials are calculated using techniques similar to those which are effective in traditional time-harmonic problems with a free surface. The steady-state development in the time-harmonic example taken demonstrates the existence of outgoing progressive waves under any inertial surface, in contrast to the case of no surface tension when such waves cannot propagate under an inertial surface that is too heavy. The solution is also noted of the Cauchy-Poisson problem for the free motion flowing an intial elevation of the inertial surface, which is obtained by the same method.

Stability of a liquid layer with bubbling

The article discusses a new type of instability of a horizontal layer of a motionless liquid, due to the motion of bubbles of gas or of particles of a suspension through the layer. It is shown that, when a certain critical mass flow rate of the gas or the suspension is attained, due to the essential inhomogeneity of the velocity of the gas bubbles, the layer becomes unstable and convective flow develops in a Benard cell. With the motion of bubbles in the field of gravity, the criterion of instability is found to be independent of the size of the bubbles and the kinematic viscosity of the liquid.