Nonhomogeneous Fluids Research Articles

Global well-posedness and exponential decay for 3D nonhomogeneous magneto-micropolar fluid equations with vacuum

<p style='text-indent:20px;'>We consider an initial boundary value problem of three-dimensional (3D) nonhomogeneous magneto-micropolar fluid equations in a bounded simply connected smooth domain with homogeneous Dirichlet boundary conditions for the velocity and micro-rotational velocity and Navier-slip boundary condition for the magnetic field. We prove the global existence and exponential decay of strong solutions provided that some smallness condition holds true. Note that although the system degenerates near vacuum, there is no need to require compatibility conditions for the initial data via time weighted techniques.</p>

Global strong solution to the nonhomogeneous micropolar fluid equations with large initial data and vacuum

<p style='text-indent:20px;'>We study the Cauchy problem of nonhomogeneous micropolar fluid equations with zero density at infinity in the whole plane <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}^2 $\end{document}</tex-math></inline-formula>. We derive the global existence and uniqueness of strong solutions if the initial density decays not too slowly at infinity. Note that the initial data can be arbitrarily large and the initial density can contain vacuum states and even have compact support. Our method relies upon the delicate weighted energy estimates and the structural characteristics of the system under consideration.</p>

Global well-posedness and decay estimates to the 3D Cauchy problem of nonhomogeneous magneto-micropolar fluid equations with vacuum

We investigate a model of nonhomogeneous magneto-micropolar fluids in the whole three-dimensional space R3. Under the assumption that the initial energy is suitably small, we prove the global existence and decay estimates of strong solutions. Moreover, there is no need to impose some compatibility condition on the initial data via time weighted techniques although the system under consideration degenerates near vacuum. Our analysis is based on delicate energy estimates and the structural characteristics of the model.

Equivalence between Wolf and Yukawa non-homogeneous fluids in a gravitational field

A density functional description for a charged fluid immersed in a gravitational field is presented, using a local density approximation. The screened pair electrostatic interaction between particles is described with the Wolf potential model, and a thermodynamic perturbation theory is used to obtain the homogeneous free energy required by the local density approximation. Density profiles behaviour is explored for the Wolf fluid as a function of the potential range, temperature and bulk density. An approximate equivalence based on kinetic theory is applied to relate the range parameters of Wolf and Yukawa potentials. Through a detailed comparison among the local density profiles of both fluid descriptions, a precise correspondence relationship between Yukawa and Wolf non-homogeneous fluids can be established.

Weak–strong uniqueness for a class of generalized dissipative weak solutions for non-homogeneous, non-Newtonian and incompressible fluids

We consider a system of PDEs describing a non-homogeneous, non-Newtonian and incompressible fluid in a space-periodic domain. We define the generalized dissipative weak solutions as well as give a proof of its existence, when the boundary data is provided. The main result of this work is the weak–strong uniqueness of the defined solutions.

Computational analysis of nonhomogeneous fluid flow in a two-cylinder-driven rectangular cavity

This paper involves a two-dimensional computational study of flow evolution patterns and the temperature distribution at evolved states of a fluid under compressible conditions contained within a driven rectangular cavity with two symmetrically placed circular cylinders, where one cylinder is heated and the other cooled. Conditions developed by varying the positions of the cylinders within the cavity, by varying the initial conditions of temperature distributions of the fluid as well as temperatures at which the cylinders are held to heat or cool the flow and by varying the orientation of the direction of rotation of the cylinders with respect to each other – either opposing or identical – are studied. The analyses are conducted by observing the temperature distributions over the streamline patterns, the velocity profiles over a line dividing the cavity length in half and the temperature distribution over a line dividing the cavity height in half. Best mixing conditions have been found to be for cavities with cylinders placed close to each other and rotating in identical directions.

Global Strong Solution and Exponential Decay of 3D Nonhomogeneous Asymmetric Fluid Equations with Vacuum

Global Strong Solution and Exponential Decay of 3D Nonhomogeneous Asymmetric Fluid Equations with Vacuum

Global existence and exponential decay of strong solutions for 2D nonhomogeneous micropolar fluids with density-dependent viscosity

We study an initial boundary value problem of two-dimensional nonhomogeneous micropolar fluid equations with density-dependent viscosity and non-negative density. Applying the Desjardins interpolation inequality and delicate energy estimates, we show the global existence of a unique strong solution under the condition that ‖∇μ(ρ0)‖Lq is suitably small. Moreover, we prove that the velocity and the micro-rotational velocity converge exponentially to zero in H2 as time goes to infinity.

Frequency and Amplitude Modulations of a Moving Structure in Unsteady Non-Homogeneous Density Fluid Flow

A fluid-structure interaction’s effects on the dynamics of a hydrofoil immersed in a fluid flow of non-homogeneous density is presented and analyzed. A linearized model is applied to solve the fluid-structure coupled problem. Fluid density variations along the hydrofoil upper surface, based on the sinusoidal cavity oscillations, are used. It is shown that for the steady cavity case, the value of cavity length Lp does not affect the amplitude of the hydrofoil displacements. However, the natural frequency of the structure increases according to Lp. In the unsteady cavity case, the variations of the added mass and added damping (induced by the fluid density rate of change) generate frequency and amplitude modulations in the hydrofoil dynamics. To analyse this phenomena, the empirical mode decomposition, a well established data-driven method to handle such modulations, is used.

Strong solutions to the Cauchy problem of two-dimensional nonhomogeneous micropolar fluid equations with nonnegative density

Strong solutions to the Cauchy problem of two-dimensional nonhomogeneous micropolar fluid equations with nonnegative density

On the Convergence Rate of Spectral Approximations for the Equations of Nonhomogeneous Incompressible Fluids

In this paper, we are concerned about the convergence rates of spectral semi-Galerkin methods to solve the equations describing the motion of a nonhomogeneous viscous incompressible fluid. This approach allows the study of density dependent viscosity.

Contactless Pneumoelectric Fluid Viscosity Measurement Device

We review a variety of contactless techniques for fluid viscosity measurement. We discuss contactless aero-hydrodynamic techniques capable of providing high-accuracy viscosity measurements for non-homogeneous and non-transparent fluids over the range 2–100 Pa·s. We describe a very promising approach in need of additional work–a contactless aero-hydrodynamic technique that involves using a pulsed gas jet to distort the surface of the fluid being measured and determining the viscosity based on the time required to reach a specified deformation level after the gas jet comes on. We have developed a contactless aero-hydrodynamic device with a laser triangulation detector to measure the range to the surface of the liquid; this viscosity measurement device supports full automation, while providing a significant increase in measurement accuracy. We studied four possible options for implementation of the device, and selected the best option to improve the measurement accuracy and reduce the sensitivity of the device to external effects. We describe the design and operating principle for the device, and describe how device design parameters affect systematic and random measurement error. The relative measurement error in fluid viscosity was 2% or less over the entire range from 2 to 100 Pa·s. This contactless aero-hydrodynamic device will be useful for measurement of viscous fluids in a wide variety of industrial fields.

Flow and heat transfer over a thin needle immersed in a porous medium filled with an Al2O3-water nanofluids using Buongiorno’s two-phase model

In this study, we analyze the flow and heat transfer in a two-phase non-homogeneous Buongiorno fluid model over a thin needle immersed in a porous medium filled with an -water nanofluid. The model takes into account particle Brownian movement and thermophoresis that significantly influence the thermal conductivity and other properties of the nanofluid leading to an increase in the rate of heat transportation. The study seeks to investigate the importance of Buongiorno’s two-phase model on the flow and thermal behaviour of -water nanofluid. For this model, we investigate how changes in certain system parameters, such as the matrix porosity affect the flow, skin friction, the heat and mass transfer coefficients. The spectral quasilinearization method is used to solve the transport equations. The results show that an improvement in matrix porosity reduces the skin friction, the heat and mass transfer rates.

Regularity and uniqueness of Kelvin-Voigt models for nonhomogeneous and incompressible fluids

Generalized Kelvin-Voigt equations governing nonhomogeneous and incompressible fluids are considered in this work. In this work, we establish the existence of weak solutions to the considered model. Sufficient conditions ensuring more regular solutions and its uniqueness are also considered.

Effect of Micropolar Fluid Properties on the Blood Flow in a Human Carotid Model

Blood is a non-homogeneous fluid that flows inside the human artery system and provides the cells with nutrients. In this study the auto rotation effect of blood’s microstructure on its flow inside a human carotid model is studied by using a micropolar fluid model. The study aims to investigate the flow differences that occur due to its microstructure as compared to a Newtonian fluid. We focus on the vortex viscosity effect, i.e., the ratio of microrotation viscosity to the total one, because this is the only parameter that affects directly the fluid flow. Simulations in a range of vortex viscosities, are carried out in a 3D human carotid model that is computationally reconstructed. All of the simulations are conducted at the diastolic Reynolds number that occurs in the human carotid. Results indicate that micropolarity affects blood velocity in the range of parameters studied by 4%. As micropolarity is increased, higher velocities in the center of vessels and lower near the boundaries are found as compared to a Newtonian fluid consideration. This is an indication that the increase of the fluid’s micropolarity leads to an increase of the boundary layer thickness. More importantly, an increase in vortex viscosity and the resulting increase in microrotation result in decreased shear stress in the carotid’s walls; this finding can be significant in regards to the onset and the development of atherosclerosis. Finally, the flow distribution at the carotid seems to heavily be affected by the geometry and the micropolarity of the fluid.

Global Existence and Exponential Decay of Strong Solutions of Nonhomogeneous Magneto-Micropolar Fluid Equations with Large Initial Data and Vacuum

The present paper concerns an initial boundary value problem of two-dimensional nonhomogeneous magneto-micropolar fluid equations with nonnegative density. We establish the global existence and exponential decay rates of strong solutions. In particular, the initial data can be arbitrarily large. The key idea is to use a lemma of Desjardins (Arch Rational Mech Anal 137:135–158, 1997).

Influence of the Marangoni Effect on the Emergence of Fluid Rotation in a Thermogravitational Boundary Layer

Steady axisymmetric regimes of the fluid flow in a thermogravitational boundary layer near the free surface with a nonuniform temperature distribution on this boundary are calculated for equations of fluid motion in the Oberbeck-Boussinesq approximation, where the viscosity and thermal diffusivity are small. With due allowance for the thermocapillary effect, it is demonstrated that nonhomogeneous fluid flow regimes with rotation can arise in the boundary layer owing to a bifurcation in the case of local cooling of the free surface, whereas rotation outside this layer is absent.

Transport Properties in Nanochannels: Ionic Size-, Permittivity-, and Viscosity-Related Effects

The transport properties in nanochannels are examined using a modified electrokinetic model (MEM) that takes into account the finite ion size by modeling the hydrated ions as charged dielectric spheres so that the electrolyte solution becomes a nonhomogeneous fluid characterized by permittivity and viscosity values that are both functions of the local ionic concentrations. We show that the simultaneous consideration of ionic size, permittivity, and viscosity effects always improve on the predictions of the standard electrokinetic model for point-like ions (SEM), with corrections that are significant in the nanofluidic system’s parameter range. The results reported herein are expected to provide a deeper understanding of the ion transport and fluid flow in nanofluidic devices.

Rayleigh–Taylor instability for nonhomogeneous incompressible fluids with Navier‐slip boundary conditions

This paper is concerned with the Rayleigh–Taylor instability for the nonhomogeneous incompressible Navier–Stokes equations with Navier‐slip boundary conditions around a steady state in an infinite slab, where the Navier‐slip coefficients do not have defined sign and the slab is horizontally periodic. Motivated by Jiang et al. (Sci. China Math., 2013), we extend the result from Dirichlet boundary condition to Navier‐slip boundary conditions. Our results indicate the factor that “heavier density with increasing height” still plays a key role in the instability under Navier‐slip boundary conditions.

The Plane Exterior Boundary-Value Problem for Nonhomogeneous Fluids

It is proved that the Stokes problem for nonhomogeneous viscous fluids in an exterior Lipschitz two-dimensional domain has a solution if and only if the data satisfy a suitable compatibility condition. Moreover, it is showed that it is unique in large uniqueness classes.