Peristaltic transport of bi-viscosity fluids through a curved tube : a mathematical model for intestinal flow

The human intestinal tract is a long curved tube constituting the final section of the digestive system in which nutrients and water are mostly absorbed. Motivated by the dynamics of chyme in the intestine, a mathematical model is developed to simulate the associated transport phenomena via peristaltic transport. Rheology of chyme is modelled using the Nakamura-Sawada bi-viscosity non-Newtonian formulation. The intestinal tract is considered as a curved tube geometric model. Low Reynolds number (creeping hydrodynamics) and long wavelength approximations are taken into consideration.Analytical solutions of the moving boundary value problem are derived for velocity field,pressure gradient and pressure rise. Streamline flow visualization is achieved with Mathematica symbolic software. Peristaltic pumping phenomenon and trapping of the bolus are also examined. The influence of curvature parameter, apparent viscosity coefficient (rheological parameter) and volumetric flow rate on flow characteristics is described. Validation of analytical solutions is achieved with a MAPLE17 numerical quadrature algorithm. The work is relevant to improving understanding of gastric hydrodynamics and provides a benchmark for further computational fluid dynamics (CFD) simulations

Mathematical modelling of pressure-driven micropolar biological flow due to metachronal wave propulsion of beating cilia

In this paper, we present an analytical study of pressure-driven flow of micropolar non-Newtonian physiological fluids through a channel comprising two parallel oscillating walls. The cilia are arranged at equal intervals and protrude normally from both walls of the infinitely long channel. A metachronal wave is generated due to natural beating of cilia and the direction of wave propagation is parallel to the direction of fluid flow. Appropriate expressions are presented for deformation via longitudinal and transverse velocity components induced by the ciliary beating phenomenon with cilia assumed to follow elliptic trajectories. The conservation equations for mass, longitudinal and transverse (linear) momentum and angular momentum are reduced in accordance with the long wavelength and creeping Stokesian flow approximations and then normalized with appropriate transformations. The resulting non-linear moving boundary value problem is solved analytically for constant micro-inertia density, subject to physically realistic boundary conditions. Closed-form expressions are derived for axial velocity, angular velocity, volumetric flow rate and pressure rise. The transport phenomena are shown to be dictated by several non-Newtonian parameters, including micropolar material parameter and Eringen coupling parameter, and also several geometric parameters, viz eccentricity parameter, wave number and cilia length. The influence of these parameters on streamline profiles (with a view to addressing trapping features via bolus formation and evolution), pressure gradient and other characteristics are evaluated graphically. Both axial and angular velocities are observed to be substantially modified with both micropolar rheological parameters and furthermore are significantly altered with increasing volumetric flow rate. Free pumping is also examined. An inverse relationship between pressure rise and flow rate is computed which is similar to that observed in Newtonian fluids. The study is relevant to hemodynamics in narrow capillaries and also bio-inspired micro-fluidic devices

Mathematical model for ciliary-induced transport in MHD flow of Cu-H2O nanoßuids with magnetic induction

Motivated by novel developments in surface-modified, nanoscale, magnetohydrodynamic (MHD) biomedical devices, we study theoretically the ciliary induced transport by metachronal wave propagation in hydromagnetic flow of copper-water nanofluids through a parallel plate channel. Under the physiological constraints, creeping flow is taken into consideration i.e. inertial forces are small compared with viscous forces. The metachronal wavelength is also considered as very large for cilia induced MHD flow. Magnetic Reynolds number is sufficiently large to invoke magnetic induction effects. The physical problem is linearized and exact solutions are developed for the resulting boundary value problem. Closed-form expressions are presented for the stream function, pressure rise, induced magnetic field function and temperature. Mathematica symbolic software is used to compute and illustrate numerical results. The influence of physical parameters on velocity profile, pressure gradient and trapping of bolus are discussed with the aid of graphs. The present computations are applicable to simulations of flow control of in nano-magneto-biomimetic technologies

Magneto-nanofluid flow with heat transfer past a stretching surface for the new heat flux model using numerical approach

Sheet processing of magnetic nanomaterials is emerging as a new branch of smart materials manufacturing. The efficient production of such materials combines many physical phenomena including magnetohydrodynamics (MHD), nanoscale, thermal and mass diffusion effects. To improve understanding of complex inter-disciplinary transport phenomena in such systems, mathematical models provide a robust approach. Motivated by this, herein we develop a mathematical model for steady, laminar, magnetohydrodynamic, incompressible nanofluid flow, heat and mass transfer from a stretching sheet. A uniform constant strength magnetic field is applied transverse to the plane of the stretching flow. The Buonjiornio nanofluid model is employed to represent thermophoretic and Brownian motion effects. A non-Fourier (Cattaneo-Christov) model is deployed to simulate thermal conduction effects of which the Fourier model is a special case when thermal relaxation effects are neglected. The governing conservation equations are rendered dimensionless with suitable scaling transformations. The emerging nonlinear boundary value problem is solved with a fourth order Runge-Kutta algorithm and also shooting quadrature. Validation is achieved with earlier non-magnetic and forced convection flow studies. The influence of key thermophysical parameters e.g. Hartmann magnetic number, thermal Grashof number, thermal relaxation time parameter, Schmidt number, thermophoresis parameter, Prandtl number and Brownian motion number on velocity, skin friction, temperature, Nusselt number, Sherwood number and nano-particle concentration distributions is investigated. A strong elevation in temperature accompanies an increase in Brownian motion parameter whereas increasing magnetic parameter is found to reduce heat transfer rate at the wall (Nusselt number). Nano-particle volume fraction is observed to be strongly suppressed with greater thermal Grashof number, Schmidt number and thermophoresis parameter whereas it is elevated significantly with greater Brownian motion parameter. Higher temperatures are achieved with greater thermal relaxation time values i.e. the non-Fourier model predicts greater values for temperature than the classical Fourier model

On the design of experiments for the study of relativistic nonlinear optics in the limit of single-cycle pulse duration and single-wavelength spot size

We propose a set of experiments with the aim of studying for the first time relativistic nonlinear optics in the fundamental limits of single-cycle pulse duration and single-wavelength spot size. The laser system that makes this work possible is now operating at the Center for Ultrafast Optical Science at the University of Michigan. Its high repetition rate (1 kHz) will make it possible to perform a detailed investigation of relativistic effects in this novel regime. This study has the potential to make the field of relativistic optics accessible to a wider community and to open the door for real-world applications of relativistic optics, such as electron/ion acceleration and neutron and positron production.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45803/1/11452_2005_Article_253.pd