Nonhomogeneous Fluids Research Articles

On the steady viscous flow of a nonhomogeneous asymmetric fluid

We consider a boundary value problem for the system of equations describing the stationary motion of a viscous nonhomogeneous asymmetric fluid in a bounded planar domain having a C 2 boundary. We use a stream-function formulation after the manner of Frolov (Math Notes 53(5–6):650–656, 1993) in which the fluid density depends on the stream-function by means of another function determined by the boundary conditions. This allows for dropping some of the equations, most notably the continuity equation. We show existence to the resulting system using Galerkin method.

Dynamic Characterization of Non-Homogeneous Magnetorheological Fluids Based Multi-Layer Beam

The vibration properties of multi-layer beam structure comprising axially non-homogeneous magneto-rheological (MR) fluids layer are investigated. The governing equations of a non-homogeneous MR fluids multi-layered beam are formulated using finite element method and Ritz formulation. The validity of the proposed finite element formulations is demonstrated by comparing the results with those obtained from the Ritz formulation. The properties of different configurations of a non-homogeneous MR-fluid beam are evaluated to investigate the influences of the location of the different MR-fluids for various boundary conditions. The properties in terms of natural frequencies and loss factors corresponding to various modes are evaluated under different magnetic field intensities. The effect of location of the fluid treatment on deflection mode shapes is also investigated. The results suggest that the natural frequencies and loss factors of the non-homogeneous MR fluid beams are strongly influenced not only by the intensity of the applied magnetic field, but also by the location of the MR fluids. It is also concluded that the application of non-homogeneous MR fluids could also alter the deflection pattern of the beam, particularly the location of the peak deflection.

Interference of lee waves over mountain ranges

Abstract. Internal waves in the atmosphere and ocean are generated frequently from the interaction of mean flow with bottom obstacles such as mountains and submarine ridges. Analysis of these environmental phenomena involves theoretical models of non-homogeneous fluid affected by the gravity. In this paper, a semi-analytical model of stratified flow over the mountain range is considered under the assumption of small amplitude of the topography. Attention is focused on stationary wave patterns forced above the rough terrain. Adapted to account for such terrain, model equations involves exact topographic condition settled on the uneven ground surface. Wave solutions corresponding to sinusoidal topography with a finite number of peaks are calculated and examined.

Transparent heater for study of the boiling crisis near the vapor–liquid critical point

New design for a pressurized optical cell dedicated to study the boiling crisis in non-homogeneous critical fluids in microgravity conditions is presented. The main characteristic concerns in situ integration of a heating device as a form of transparent resistive thin layer appropriate for light transmission observation of the liquid film boiling, by monitoring the thermal power produced by this heater. High-resolution and high-speed optical diagnostics complement in situ temperature measurements. Illustrations of the high-level performances are provided by the preliminary results obtained during the Earth's tests of the CNES-DECLIC facility, using two (vertical and horizontal) configurations of the heating device with respect to the gravity field acceleration.

Classical solutions to Navier–Stokes equations for nonhomogeneous incompressible fluids with non-negative densities

We study the Navier–Stokes equations for nonhomogeneous incompressible fluids in a bounded domain Ω of R 3 . We first prove the existence and uniqueness of local classical solutions to the initial boundary value problem of linear Stokes equations and then we obtain the existence and uniqueness of local classical solutions to the Navier–Stokes equations with vacuum under the assumption that the data satisfies a natural compatibility condition.

On the solvability of the Navier-Stokes equations for a nonhomogeneous non-Newtonian fluid

On the solvability of the Navier-Stokes equations for a nonhomogeneous non-Newtonian fluid

Analysis of an iterative method for variable density incompressible fluids

We derive error bounds for an iterative method used by Okamoto to prove the existence of strong solutions for the equations of nonhomogeneous incompressible fluids.

Stability of the plane shear flow of dilute polymeric solutions

Three variants of Oldroyd-B model are analyzed for stability of the base profile in plane Couette flow of dilute polymeric fluid at moderate Reynolds number. The stability to two-dimensional disturbances is analyzed for the linearized problem as well as the weakly nonlinear flow. We begin with the classical Oldroyd-B model with emphasis on the disturbances with axial wavenumber α∼Re1/2, where Re is the Reynolds number based on maximum velocity and channel width. For linearly stable flow, the finite amplitude stability is analyzed using the equilibrium flow method, wherein the nonlinear flow is assumed to be at the transition point. For the classical Oldroyd-B fluid, the threshold kinetic energy for the equilibrium wall mode disturbances is found to be higher for the viscoelastic fluid than for the Newtonian fluid. In the second variant, the Oldroyd-B model with additional artificial diffusivity is studied. In this model, the diffusion modes, not present in the classical Oldroyd-B model, are introduced. For large wavenumber disturbances, the diffusion modes become the slowest decaying modes in comparison to the wall modes. The threshold energy for the diffusive Oldroyd-B model is smaller than that for the Newtonian fluid. The third variant of the Oldroyd-B model accounts for the nonhomogeneous polymer concentration coupled with the polymeric stress field. While the base profile is linearly stable for the first two models, the nonhomogeneous Oldroyd-B fluid exhibits an instability in the linear analysis. The “concentration mode” becomes unstable when the fluid Weissenberg number exceeds a certain transition value. This mode of instability, driven by the stress-induced fluctuations in polymer number density, renders the uniform polymer concentration profile unstable leading to the well-known phenomenon of flow-induced demixing.

Pullback attractor for non-homogeneous micropolar fluid flows in non-smooth domains

In this paper, which concerns two-dimensional non-autonomous micropolar fluid flows in a Lipschitz bounded domain with non-homogeneous boundary conditions, the existence of a pullback attractor in H is shown under the following assumptions: the external forces f ( t ) ∈ L loc 2 ( R , V ′ ) satisfying ∫ − ∞ t e σ s | f ( s ) | V ′ 2 < ∞ for some σ > 0 characterized later; and the non-homogeneous boundary condition φ ( x ) ∈ L ∞ ( ∂ Ω ) .

Nonlocal density correlations as a signature of Hawking radiation from acoustic black holes

We have used the analogy between gravitational systems and nonhomogeneous fluid flows to calculate the density-density correlation function of an atomic Bose-Einstein condensate in the presence of an acoustic black hole. The emission of correlated pairs of phonons by Hawking-like process results into a peculiar long-range density correlation. Quantitative estimations of the effect are provided for realistic experimental configurations.

On quasi-stationary models of mixtures of compressible fluids

We consider mixtures of compressible viscous fluids consisting of two miscible species. In contrast to the theory of non-homogeneous incompressible fluids where one has only one velocity field, here we have two densities and two velocity fields assigned to each species of the fluid. We obtain global classical solutions for quasi-stationary Stokes-like system with interaction term.

Error Bounds for Semi-Galerkin Approximations of Nonhomogeneous Incompressible Fluids

We consider the spectral semi-Galerkin method applied to the nonhomogeneous Navier-Stokes equations. Under certain conditions it is known that the approximate solutions constructed through this method converge to a global strong solution of these equations. Here, we derive an optimal uniform in time error estimate in the H 1 norm for the velocity. We also derive an error estimate for the density in some spaces L r

Efficient Numerical Solution of the Density Profile Equation in Hydrodynamics

We discuss the numerical treatment of a nonlinear second order boundary value problem in ordinary differential equations posed on an unbounded domain which represents the density profile equation for the description of the formation of microscopical bubbles in a non-homogeneous fluid. For an efficient numerical solution the problem is transformed to a finite interval and polynomial collocation is applied to the resulting boundary value problem with essential singularity. We demonstrate that this problem is well-posed and the involved collocation methods show their classical convergence order. Moreover, we investigate what problem statement yields favorable conditioning of the associated collocation equations. Thus, collocation methods provide a sound basis for the implementation of a standard code equipped with an a posteriori error estimate and an adaptive mesh selection procedure. We present a code based on these algorithmic components that we are currently developing especially for the numerical solution of singular boundary value problems of arbitrary, mixed order, which also admits to solve problems in an implicit formulation. Finally, we compare our approach to a solution method proposed in the literature and conclude that collocation is an easy to use, reliable and highly accurate way to solve problems of the present type.

Uniform attractors of non-homogeneous micropolar fluid flows in non-smooth domains

Two-dimensional non-autonomous micropolar fluid flows in a Lipschitz bounded domain with non-homogeneous boundary conditions is investigated. For a normal external function, which is not necessarily translation compact, in , the existence of a D(A1/4) uniform attractor abstracting bounded sets of L2 is shown. This attractor coincides with that derived by assuming the external function to be normal with respect to the weak topology of .

Statistical field theory for a multicomponent fluid: The collective variables approach

Using the collective variables (CV) method the basic relations of statistical field theory of a multicomponent non-homogeneous fluids are reconsidered. The corresponding CV action depends on two sets of scalar fields - fields $\rho_{\alpha}$ connected to the local density fluctuations of the $\alpha$th species of particles and fields $\omega_{\alpha}$ conjugated to $\rho_{\alpha}$. The explicit expressions for the CV field correlations and their relation to the density correlation functions are found. The perturbation theory is formulated and a mean field level (MF) of the theory is considered in detail.

Nonhomogeneous incompressible Bingham viscoplastic as a limit of nonlinear fluids

The equations for the nonhomogeneous incompressible Bingham fluid are considered and existence of a weak solution is proved for a two-dimensional boundary-value problem with periodic boundary conditions. The rheology of such a fluid is defined by an yield stress τ ∗ and a discontinuous stress–strain law. A fluid volume stiffens if its local stresses do not exceed τ ∗ , and a fluid behaves like a non-linear fluid otherwise. The flow equations are formulated in the stress–velocity–density–pressure setting. Our approach is different from that of Duvaut–Lions developed for the classical Bingham viscoplastic. We do not apply the variational inequality but make use an approximation of the generalized Bingham fluid by a non-Newtonian fluid with a continuous constitutive law.

Reduced models for modal analysis of fluid–structure systems taking into account compressibility and gravity effects

It is proposed to investigate and discuss, from theoretical point of view, various reduced order variational formulations for modal analysis of linear vibrations of bounded fluid–structure systems with free surface, taking into account possible gravity/compressibility interactions, in a non-homogeneous fluid situation. Those formulations are based on substructural synthesis techniques and various modal reduction schemes are then obtained. In a previous paper, various original formulations have been exhibited associated to numerical validation. The present paper starts from those formulations in order to construct theoretically various reduced order models.

Confocal micro-PIV measurements of three-dimensional profiles of cell suspension flow in a square microchannel

A detailed measurement of the blood flow velocity profile in microchannels in vitro is fundamental to better understand the biomechanics of microcirculation. Therefore it is very important to determine the influence of suspended blood cells on the flow behaviour with high accuracy and spatial resolution. We measured the flow of blood cells suspended in a physiological fluid within a square microchannel using a confocal particle image velocimetry (PIV) system and compared it to pure water. This emerging technology combines a conventional PIV system with a spinning confocal microscope and has the ability to obtain high-resolution images and three-dimensional (3D) optical section velocity measurements. The good agreement obtained between the measured and estimated results suggests that macroscale flow theory can be used to predict the flow behaviour of a homogeneous fluid within a 100 µm square microchannel. Our results also demonstrated the potential of the confocal system for generating 3D profiles and consequently obtaining detailed information on microscale effects in microchannels using both homogeneous and non-homogeneous fluids, such as a suspension of blood cells. Furthermore, the results obtained from our confocal micro-PIV system show the ability of this system to measure velocities up to 0.52 mm s−1 in a blood cell suspension fluid.

Ultrasonic Field Modeling in Multilayered Fluid Structures Using the Distributed Point Source Method Technique

In the field of nondestructive evaluation (NDE), the newly developed distributed point source method (DPSM) is gradually gaining popularity. DPSM is a semi-analytical technique used to calculate the ultrasonic field (pressure and velocity fields) generated by ultrasonic transducers. This technique is extended in this paper to model the ultrasonic field generated in multilayered nonhomogeneous fluid systems when the ultrasonic transducers are placed on both sides of the layered fluid structure. Two different cases have been analyzed. In the first case, three layers of nonhomogeneous fluids constitute the problem geometry; the higher density fluid is sandwiched between two identical fluid half-spaces. In the second case, four layers of nonhomogeneous fluids have been considered with the fluid density monotonically increasing from the bottom to the top layer. In both cases, analyses have been carried out for two different frequencies of excitation with various orientations of the transducers. As expected, the results show that the ultrasonic field is very sensitive to the fluid properties, the orientation of the fluid layers, and the frequency of excitation. The interaction effect between the transducers is also visible in the computed results. In the pictorial view of the resulting ultrasonic field, the interface between two fluid layers can easily be seen.

Existence results for the flow of a nonhomogeneous visco-elastic fluid

In this paper, we consider a two-phase problem consisting of viscous incompressible fluid and visco-elastic particles. We pose the full system of equations modelling the motion of the fluid/solid system. The unique solvability is established locally and globally, in time with so-called smallness restrictions. Further, existence of a weak solution is treated.