Two-Fluid Model of Biofilm Disinfection

We consider a dynamic model of biofilm disinfection in two dimensions. The biofilm is treated as a viscous fluid immersed in a fluid of less viscosity. The bulk fluid moves due to an imposed external parabolic flow. The motion of the fluid is coupled to the biofilm inducing motion of the biofilm. Both the biofilm and the bulk fluid are dominated by viscous forces, hence the Reynolds number is negligible and the appropriate equations are Stokes equations. The governing partial differential equations are recast as boundary integral equations using a version of the Lorenz reciprocal relationship. This allows for robust treatment of the simplified fluid/biofilm motion. The transport of nutrients and antimicrobials, which depends directly on the velocities of the fluid and biofilm, is also included. Disinfection of the bacteria is considered under the assumption that the biofilm growth is overwhelmed by disinfection. Supported by NSF award DMS-0612467.     

Mixed Convection Boundary Layer Flow over a Moving Vertical Flat Plate in an External Fluid Flow with Viscous Dissipation Effect

The steady boundary layer flow of a viscous and incompressible fluid over a moving vertical flat plate in an external moving fluid with viscous dissipation is theoretically investigated. Using appropriate similarity variables, the governing system of partial differential equations is transformed into a system of ordinary (similarity) differential equations, which is then solved numerically using a Maple software. Results for the skin friction or shear stress coefficient, local Nusselt number, velocity and temperature profiles are presented for different values of the governing parameters. It is found that the set of the similarity equations has unique solutions, dual solutions or no solutions, depending on the values of the mixed convection parameter, the velocity ratio parameter and the Eckert number. The Eckert number significantly affects the surface shear stress as well as the heat transfer rate at the surface.     

Effects of Porosity and Mixed Convection on MHD Two Phase Fluid Flow in an Inclined Channel

The present study deals with the flow and heat transfer analysis of two immiscible fluids in an inclined channel embedded in a porous medium. The channel is divided in two phases such that a third grade fluid occupies the phase I and a viscous fluid occupies the phase II. Both viscous and third grade fluids are electrically conducting. A constant magnetic field is imposed perpendicular to the channel walls. The mathematical model is developed by using Darcy''s and modified Darcy''s laws for viscous and third grade fluids respectively. The transformed ordinary differential equations are solved numerically using a shooting method. The obtained results are presented graphically and influence of emerging parameters is discussed in detail.     

Propulsion Modeling and Analysis of a Biomimetic Swimmer

<正> We have studied a biomimetic swimmer based on the motion of bacteria such as Escherichia coli (E. coli) theoretically andexperimentally. The swimmer has an ellipsoidal cell body propelled by a helical filament. The performance of this swimmer wasestimated by modeling the dynamics of a swimmer in viscous fluid. We applied the Resistive Force Theory (RFT) on this modelto calculate the linear swimming speed and the efficiency of the model. A parametric study on linear velocity and efficiency tooptimize the design of this swimmer was demonstrated. In order to validate the theoretical results, a biomimetic swimmer wasfabricated and an experiment setup was prepared to measure the swimming speed and thrust force in silicone oil. The experimentalresults agree well with the theoretical values predicted by RFT. In addition, we studied the flow patterns surrounding thefilament with a finite element simulation with different Reynolds number (Re) to understand the mechanism of propulsion. Thesimulation results provide information on the nature of flow patterns generated by swimming filament. Furthermore, the thrustforces from the simulation were compared with the thrust forces from theory. The simulation results are in good agreement withthe theoretical results.     

Radiative Hydromagnetic Flow of Jeffrey Nanofluid by an Exponentially Stretching Sheet

Two-dimensional hydromagnetic flow of an incompressible Jeffrey nanofluid over an exponentially stretching surface is examined in the present article. Heat and mass transfer analysis is performed in the presence of thermal radiation, viscous dissipation, and Brownian motion and thermophoresis effects. Mathematical modelling of considered flow problem is developed under boundary layer and Rosseland’s approximations. The governing nonlinear partial differential equations are converted into ordinary differential equations via transformations. Solution expressions of velocity, temperature and concentration are presented in the series forms. Impacts of physical parameters on the dimensionless temperature and concentration are shown and discussed. Skin-friction coefficients are analyzed numerically. A comparison in a limiting sense is provided to validate the present series solutions.     

Numerical simulations of undulatory swimming at moderate Reynolds number

We perform numerical simulations of the swimming of a three-linkage articulated system in a moderately viscous regime. The computational methodology focuses on the creation, diffusion and transport of vorticity from the surface of the bodies into the fluid. The simulations are dynamically coupled, in that the motion of the three-linkage swimmer is computed simultaneously with the dynamics of the fluid. The novel coupling scheme presented in this work is the first to exploit the relationship between vorticity creation and body dynamics. The locomotion of the system, when subject to undulatory inputs of the hinges, is computed at Reynolds numbers of 200 and 1000. It is found that the forward swimming speed increases with the Reynolds number, and that in both cases the swimming is slower than in an inviscid medium. The vortex shedding is examined, and found to exhibit behavior consistent with experimental flow visualizations of fish.     

Effect of Joule Heating and Thermal Radiation in Flow of Third Grade Fluid over Radiative Surface

This article addresses the boundary layer flow and heat transfer in third grade fluid over an unsteady permeable stretching sheet. The transverse magnetic and electric fields in the momentum equations are considered. Thermal boundary layer equation includes both viscous and Ohmic dissipations. The related nonlinear partial differential system is reduced first into ordinary differential system and then solved for the series solutions. The dependence of velocity and temperature profiles on the various parameters are shown and discussed by sketching graphs. Expressions of skin friction coefficient and local Nusselt number are calculated and analyzed. Numerical values of skin friction coefficient and Nusselt number are tabulated and examined. It is observed that both velocity and temperature increases in presence of electric field. Further the temperature is increased due to the radiation parameter. Thermal boundary layer thickness increases by increasing Eckert number.     

Viscous flow through slowly expanding or contracting porous walls with low seepage Reynolds number: a model for transport of biological fluids through vessels

In this article, the problem of laminar, isothermal, incompressible and viscous flow in a rectangular domain bounded by two moving porous walls, which enable the fluid to enter or exit during successive expansions or contractions, is investigated. The governing non-linear equations and their associated boundary conditions are transformed into a highly non-linear ordinary differential equation. The series solution of the problem is obtained by utilising the homotopy perturbation method. Graphical results are presented to investigate the influence of the non-dimensional wall dilation rate and seepage Reynolds number (Re) on the velocity, normal pressure distribution and wall shear stress. Since the transport of biological fluids through contracting or expanding vessels is characterised by low seepage Res, the current study focuses on the viscous flow driven by small wall contractions and expansions of two weakly permeable walls.     

Effects of Geometric Parameters on Swimming of Micro Organisms with Single Helical Flagellum in Circular Channels

We present a computational fluid dynamics (CFD) model for the swimming of micro organisms with a single helical flagellum in circular channels. The CFD model is developed to obtain numerical solutions of Stokes equations in three dimensions, validated with experiments reported in literature, and used to analyze the effects of geometric parameters, such as the helical radius, wavelength, radii of the channel and the tail and the tail length on forward and lateral swimming velocities, rotation rates, and the efficiency of the swimmer. Optimal shapes for the speed and the power efficiency are reported. Effects of Brownian motion and electrostatic interactions are excluded to emphasize the role of hydrodynamic forces on lateral velocities and rotations on the trajectory of swimmers. For thin flagella, as the channel radius decreases, forward velocity and the power efficiency of the swimmer decreases as well; however, for thick flagella, there is an optimal radius of the channel that maximizes the velocity and the efficiency depending on other geometric parameters. Lateral motion of the swimmer is suppressed as the channel is constricted below a critical radius, for which the magnitude of the lateral velocity reaches a maximum. Results contribute significantly to the understanding of the swimming of bacteria in micro channels and capillary tubes.     

Effects of Geometric Parameters on Swimming of Micro Organisms with Single Helical Flagellum in Circular Channels

We present a computational fluid dynamics (CFD) model for the swimming of micro organisms with a single helical flagellum in circular channels. The CFD model is developed to obtain numerical solutions of Stokes equations in three dimensions, validated with experiments reported in literature, and used to analyze the effects of geometric parameters, such as the helical radius, wavelength, radii of the channel and the tail and the tail length on forward and lateral swimming velocities, rotation rates, and the efficiency of the swimmer. Optimal shapes for the speed and the power efficiency are reported. Effects of Brownian motion and electrostatic interactions are excluded to emphasize the role of hydrodynamic forces on lateral velocities and rotations on the trajectory of swimmers. For thin flagella, as the channel radius decreases, forward velocity and the power efficiency of the swimmer decreases as well; however, for thick flagella, there is an optimal radius of the channel that maximizes the velocity and the efficiency depending on other geometric parameters. Lateral motion of the swimmer is suppressed as the channel is constricted below a critical radius, for which the magnitude of the lateral velocity reaches a maximum. Results contribute significantly to the understanding of the swimming of bacteria in micro channels and capillary tubes.     

Heat Transfer Analysis for Stationary Boundary Layer Slip Flow of a Power-Law Fluid in a Darcy Porous Medium with Plate Suction/Injection

In this paper, we investigate the slip effects on the boundary layer flow and heat transfer characteristics of a power-law fluid past a porous flat plate embedded in the Darcy type porous medium. The nonlinear coupled system of partial differential equations governing the flow and heat transfer of a power-law fluid is transformed into a system of nonlinear coupled ordinary differential equations by applying a suitable similarity transformation. The resulting system of ordinary differential equations is solved numerically using Matlab bvp4c solver. Numerical results are presented in the form of graphs and the effects of the power-law index, velocity and thermal slip parameters, permeability parameter, suction/injection parameter on the velocity and temperature profiles are examined.     

Three-Dimensional Flow of an Oldroyd-B Nanofluid towards Stretching Surface with Heat Generation/Absorption

This article addresses the steady three-dimensional flow of an Oldroyd-B nanofluid over a bidirectional stretching surface with heat generation/absorption effects. Suitable similarity transformations are employed to reduce the governing partial differential equations into coupled nonlinear ordinary differential equations. These nonlinear ordinary differential equations are then solved analytically by using the homotpy analysis method (HAM). Graphically results are presented and discussed for various parameters, namely, Deborah numbers and , heat generation/absorption parameter Prandtl parameter , Brownian motion parameters, thermophoresis parameter and Lewis number . We have seen that the increasing values of the Brownian motion parameter and thermophoresis parameter leads to an increase in the temperature field and thermal boundary layer thickness while the opposite behavior is observed for concentration field and concentration boundary layer thickness. To see the validity of the present work, the numerical results are compared with the analytical solutions obtained by Homotopy analysis method and noted an excellent agreement for the limiting cases.     

Rayleigh-Taylor instability in quantum magnetized viscous plasma

Quantum effects on Rayleigh-Taylor instability of stratified viscous plasmas layer under the influence of vertical magnetic field are investigated. By linearly solving the viscous QMHD equations into normal mode, a forth-order ordinary differential equation is obtained to describe the velocity perturbation. Then the growth rate is derived for the case where a plasma with exponential density distribution is confined between two rigid planes. The results show that, the presence of vertical magnetic field beside the quantum effect will bring about more stability on the growth rate of unstable configuration for viscous plasma, which is greater than that of inviscous plasma.     

Viscous flow through slowly expanding or contracting porous walls with low seepage Reynolds number: a model for transport of biological fluids through vessels

In this article, the problem of laminar, isothermal, incompressible and viscous flow in a rectangular domain bounded by two moving porous walls, which enable the fluid to enter or exit during successive expansions or contractions, is investigated. The governing non-linear equations and their associated boundary conditions are transformed into a highly non-linear ordinary differential equation. The series solution of the problem is obtained by utilising the homotopy perturbation method. Graphical results are presented to investigate the influence of the non-dimensional wall dilation rate and seepage Reynolds number (Re) on the velocity, normal pressure distribution and wall shear stress. Since the transport of biological fluids through contracting or expanding vessels is characterised by low seepage Res, the current study focuses on the viscous flow driven by small wall contractions and expansions of two weakly permeable walls.     

Modelling inert gas exchange in tissue and mixed-venous blood return to the lungs

Inert gas exchange in tissue has been almost exclusively modelled by using an ordinary differential equation. The mathematical model that is used to derive this ordinary differential equation assumes that the partial pressure of an inert gas (which is proportional to the content of that gas) is a function only of time. This mathematical model does not allow for spatial variations in inert gas partial pressure. This model is also dependent only on the ratio of blood flow to tissue volume, and so does not take account of the shape of the body compartment or of the density of the capillaries that supply blood to this tissue. The partial pressure of a given inert gas in mixed-venous blood flowing back to the lungs is calculated from this ordinary differential equation. In this study, we write down the partial differential equations that allow for spatial as well as temporal variations in inert gas partial pressure in tissue. We then solve these partial differential equations and compare them to the solution of the ordinary differential equations described above. It is found that the solution of the ordinary differential equation is very different from the solution of the partial differential equation, and so the ordinary differential equation should not be used if an accurate calculation of inert gas transport to tissue is required. Further, the solution of the PDE is dependent on the shape of the body compartment and on the density of the capillaries that supply blood to this tissue. As a result, techniques that are based on the ordinary differential equation to calculate the mixed-venous blood partial pressure may be in error.     

Flow and Heat Transfer to Sisko Nanofluid over a Nonlinear Stretching Sheet

The two-dimensional boundary layer flow and heat transfer to Sisko nanofluid over a non-linearly stretching sheet is scrutinized in the concerned study. Our nanofluid model incorporates the influences of the thermophoresis and Brownian motion. The convective boundary conditions are taken into account. Implementation of suitable transformations agreeing with the boundary conditions result in reduction of the governing equations of motion, energy and concentration into non-linear ordinary differential equations. These coupled non-linear ordinary differential equations are solved analytically by using the homotopy analysis method (HAM) and numerically by the shooting technique. The effects of the thermophoresis and Brownian motion parameters on the temperature and concentration fields are analyzed and graphically presented. The secured results make it clear that the temperature distribution is an increasing function of the thermophoresis and Brownian motion parameters and concentration distribution increases with the thermophoresis parameter but decreases with the Brownian motion parameter. To see the validity of the present work, we made a comparison with the numerical results as well as previously published work with an outstanding compatibility.     

Multiscale modelling as a tool to prescribe realistic boundary conditions for the study of surgical procedures

This work was motivated by the problems of analysing detailed 3D models of vascular districts with complex anatomy. It suggests an approach to prescribing realistic boundary conditions to use in order to obtain information on local as well as global haemodynamics. A method was developed which simultaneously solves Navier-Stokes equations for local information and a non-linear system of ordinary differential equations for global information. This is based on the principle that an anatomically detailed 3D model of a cardiovascular district can be achieved by using the finite element method. In turn the finite element method requires a specific boundary condition set. The approach outlined in this work is to include the system of ordinary differential equations in the boundary condition set. Such a multiscale approach was first applied to two controls: (i) a 3D model of a straight tube in a simple hydraulic network and (ii) a 3D model of a straight coronary vessel in a lumped-parameter model of the cardiovascular system. The results obtained are very close to the solutions available for the pipe geometry. This paper also presents preliminary results from the application of the methodology to a particular haemodynamic problem: namely the fluid dynamics of a systemic-to-pulmonary shunt in paediatric cardiac surgery.     

Epithelial Fluid Transport: Protruding Macromolecules and Space Charges Can Bring about Electro-Osmotic Coupling at the Tight Junctions

The purpose of the present work is to investigate whether the idea of epithelial fluid transport based on electro-osmotic coupling at the level of the leaky tight junction (TJ) can be further supported by a plausible theoretical model. We develop a model for fluid transport across epithelial layers based on electro-osmotic coupling at leaky tight junctions (TJ) possessing protruding macromolecules and fixed electrical charges. The model embodies systems of electro-hydrodynamic equations for the intercellular pathway, namely the Brinkman and the Poisson-Boltzmann differential equations applied to the TJ. We obtain analytical solutions for a system of these two equations, and are able to derive expressions for the fluid velocity profile and the electrostatic potential. We illustrate the model by employing geometrical parameters and experimental data from the corneal endothelium, for which we have previously reported evidence for a central role for electro-osmosis in translayer fluid transport. Our results suggest that electro-osmotic coupling at the TJ can account for fluid transport by the corneal endothelium. We conclude that electro-osmotic coupling at the tight junctions could represent one of the basic mechanisms driving fluid transport across some leaky epithelia, a process that remains unexplained.     

Heat and Mass Transfer in Unsteady Rotating Fluid Flow with Binary Chemical Reaction and Activation Energy

In this study, the Spectral Relaxation Method (SRM) is used to solve the coupled highly nonlinear system of partial differential equations due to an unsteady flow over a stretching surface in an incompressible rotating viscous fluid in presence of binary chemical reaction and Arrhenius activation energy. The velocity, temperature and concentration distributions as well as the skin-friction, heat and mass transfer coefficients have been obtained and discussed for various physical parametric values. The numerical results obtained by (SRM) are then presented graphically and discussed to highlight the physical implications of the simulations.