ROTARY OSCILLATION OF A RIGID SPHERE IN A COUPLE STRESS FLUID

In this paper, the rotary oscillation of a rigid sphere in an incompressible couple stress fluid is studied. The classical no slip boundary conditions are imposed on spherical boundary. Moreover, it is assumed that the couple stresses on the boundary of the sphere vanish. In the present study, the motion is generated by a sudden rotary oscillation of the rigid sphere about an axe passing through its center with a time-dependent angular velocity. Stokasian assumption is taken into consideration so that the non-linear terms are neglected in the equation of motion. The torque experienced by the couple stress fluid on the spherical body is obtained using an integral formula. Exact solutions are obtained and results are illustrated through graphs.

On the Perturbation of the Three-Dimensional Stokes Flow of Micropolar Fluids by a Constant Uniform Magnetic Field in a Circular Cylinder

Modern engineering technology involves the micropolar magnetohydrodynamic flow of magnetic fluids. Here, we consider a colloidal suspension of non-conductive ferromagnetic material, which consists of small spherical particles that behave as rigid magnetic dipoles, in a carrier liquid of approximately zero conductivity and low-Reynolds number properties. The interaction of a 3D constant uniform magnetic field with the three-dimensional steady creeping motion (Stokes flow) of a viscous incompressible micropolar fluid in a circular cylinder is investigated, where the magnetization of the ferrofluid has been taken into account and the magnetic Stokes partial differential equations have been presented. Our goal is to apply the proper boundary conditions, so as to obtain the flow fields in a closed analytical form via the potential representation theory, and to study several characteristics of the flow. In view of this aim, we make use of an improved new complete and unique differential representation of magnetic Stokes flow, valid for non-axisymmetric geometries, which provides the velocity and total pressure fields in terms of easy-to-find potentials. We use these results to simulate the creeping flow of a magnetic fluid inside a circular duct and to obtain the flow fields associated with this kind of flow

UNSTEADY ROTATIONAL MOTION OF A MICROPOLAR FLUID INSIDE A RIGHT CIRCULAR CYLINDER USING STATE SPACE APPROACH

In this work, the unsteady rotational motion of an incompressible micropolar fluid inside a right circular cylinder is investigated. The classical no-slip and no-spin boundary conditions are proposed. The problem is solved analytically using the state space approach together with Laplace transform technique. The inverse Laplace transform is carried out numerically using a numerical technique based on Fourier series expansion. Numerical results for the flow field functions are represented graphically for different values of the time and micropolarity parameters

Rheological effects of micropolar slime on the gliding motility of bacteria with slip boundary condition

The gliding organisms are phylogenetically diverse with their hundreds of types, different shapes and several mechanism of motility. Gliding bacteria are rod-shaped bacteria without any flagella on their surface. They exhibit a creeping type of self-powered motion when nearly in contact with a solid surface. These bacteria leave an adhesive trail of slime and propel themselves by producing undulating waves in their body, which is one possible mode of motility for gliding bacteria. In the present study an undulating surface model is considered to discuss this type of bacterial locomotion. The classical Navier-Stokes equations are incapable of explaining the slime rheology at the microscopic level. Micropolar fluid dynamics however provides a solid framework for mimicking bacterial physical phenomena at both micro and nano-scales, and therefore in the present study, the constitutive equations of micropolar fluid are implemented to characterize the rheology of the slime. The flow equations are formulated under long wavelength and low Reynolds number assumptions. Exact expressions for stream function and pressure gradient are obtained. The speed of the gliding bacteria is numerically calculated by using a modified Newton-Raphson method. In addition, when the glider is fixed, the effects of micropolar slime parameters on the velocity, micro-rotation (angular velocity) of spherical slime particles, pressure rise per wavelength, pumping and trapping phenomena are also shown graphically and discussed in detail. The study is relevant to emerging biofuel cell technologies and also bacterial biophysics

Turbulent Micropolar SPH Fluids with Foam

In this paper we introduce a novel micropolar material model for the simulation of turbulent inviscid fluids. The governing equations are solved by using the concept of Smoothed Particle Hydrodynamics (SPH). SPH fluid simulations suffer from numerical diffusion which leads to a lower vorticity, a loss in turbulent details and finally in less realistic results. To solve this problem we propose a micropolar fluid model. The micropolar fluid model is a generalization of the classical Navier-Stokes equations, which are typically used in computer graphics to simulate fluids. In contrast to the classical Navier-Stokes model, micropolar fluids have a microstructure and therefore consider the rotational motion of fluid particles. In addition to the linear velocity field these fluids have a field of microrotation which represents existing vortices and provides a source for new ones. Our novel micropolar model can generate realistic turbulences, is linear and angular momentum conserving, can be easily integrated in existing SPH simulation methods and its computational overhead is negligible. Another important visual feature of turbulent liquids is foam. Therefore, we present a post-processing method which considers microrotation in the foam generation. It works completely automatic and requires only one user-defined parameter to control the amount of foam

Structural, Magnetic, Dielectric, Electrical, Optical and Thermal Properties of Nanocrystalline Materials: Synthesis, Characterization and Application

This book is a collection of the research articles and review article, published in special issue "Structural, Magnetic, Dielectric, Electrical, Optical and Thermal Properties of Nanocrystalline Materials: Synthesis, Characterization and Application"

Linear and non-linear analyses of convection in a micropolar fluid occupying a porous medium

Linear and weakly non-linear analyses of convection in a micropolar fluid occupying a high-porosity medium are performed. The Brinkman-Eringen momentum equation is considered. The linear and non-linear analyses are, respectively, based on the normal mode technique and truncated representation of Fourier series. The linear theory for a two-phase system reiterates that the preferred mode of convection is stationary as in the case of a single-phase system. An autonomous system of differential equations representing cellular convection arising in the study is considered to analyse the critical points. The Nusselt number is obtained as a function of micropolar and porous medium parameters. © 2002 Elsevier Science Ltd. All rights reserved

Numerical solutions for axisymmetric non-Newtonian stagnation enrobing flow, heat and mass transfer with application to cylindrical pipe coating dynamics

Heat and mass transfer in variable thermal conductivity micropolar axisymmetric stagnation enrobing flow on a cylinder is studied. Numerical solutions are obtained with an optimized variational finite element procedure and also a finite difference method. Graphical variations of velocity, angular velocity, temperature and concentration are presented for the effects of Reynolds number, viscosity ratio, curvature parameter, Prandtl number and Schmidt number. Excellent agreement is obtained for both finite element method (FEM) and finite difference method (FDM) computations. Further validation is achieved with a Chebyshev spectral collocation method (SCM). Skin friction is elevated with greater Reynolds number whereas it is suppressed with increasing micropolar parameter. Heat transfer rate decreases with an increase in the thermal conductivity parameter. Temperature and thermal boundary layer thickness is reduced with increasing thermal conductivity parameter and Reynolds number. Greater Reynolds number accelerates the micro-rotation values. Higher Schmidt number reduces the mass transfer function (species concentration) values. The mathematical model is relevant to polymeric manufacturing coating (enrobing) flows