Transient magneto-peristaltic flow of couple stress biofluids: A magneto-hydro-dynamical study on digestive transport phenomena

Magnetic fields are increasingly being utilized in endoscopy and gastric transport control. In this regard, the present study investigates the influence of a transverse magnetic field in the transient peristaltic rheological transport. An electrically-conducting couple stress non-Newtonian model is employed to accurately simulate physiological fluids in peristaltic flow through a sinusoidally contracting channel of finite length. This model is designed for computing the intra-bolus oesophageal and intestinal pressures during the movement of food bolus in the digestive system under magneto-hydro-dynamic effects. Long wavelength and low Reynolds number approximations have been employed to reduce the governing equations from nonlinear to linear form, this being a valid approach for creeping flows which characterizes physiological dynamics. Analytical approximate solutions for axial velocity, transverse velocity, pressure gradient, local wall shear stress and volumetric flow rate are obtained for the non-dimensional conservation equations subject to appropriate boundary conditions. The effects of couple stress parameter and transverse magnetic field on the velocity profile, pressure distribution, local wall shear stress and the averaged flow rate are discussed with the aid of computational results. The comparative study of non-integral and integral number of waves propagating along the finite length channel is also presented. Magnetic field and non-Newtonian properties are found to strongly influence peristaltic transport.     

Numerical simulation of peristaltic flow of a biorheological fluid with shear-dependent viscosity in a curved channel

Peristaltic motion of a non-Newtonian Carreau fluid is analyzed in a curved channel under the long wavelength and low Reynolds number assumptions, as a simulation of digestive transport. The flow regime is shown to be governed by a dimensionless fourth-order, nonlinear, ordinary differential equation subject to no-slip wall boundary conditions. A well-tested finite difference method based on an iterative scheme is employed for the solution of the boundary value problem. The important phenomena of pumping and trapping associated with the peristaltic motion are investigated for various values of rheological parameters of Carreau fluid and curvature of the channel. An increase in Weissenberg number is found to generate a small eddy in the vicinity of the lower wall of the channel, which is enhanced with further increase in Weissenberg number. For shear-thinning bio-fluids (power-law rheological index, n < 1) greater Weissenberg number displaces the maximum velocity toward the upper wall. For shear-thickening bio-fluids, the velocity amplitude is enhanced markedly with increasing Weissenberg number.     

Steady-state axisymmetric configurations of a weakly ionized plasma in the field of a rotating magnetized spherical body

Self-consistent steady-state axisymmetric configurations of a plasma envelope with a uniform anisotropic conductivity around a rotating magnetized spherical body are considered. A set of electrodynamic and magnetohydrodynamic equations is analyzed under the assumption that the mass velocity of a moving weakly ionized plasma has only the azimuthal component. The equations describing the profile of the angular frequency of the rotating plasma envelope, the magnetic field, the conduction currents, and the plasma density distribution are solved in the limit of a strong anisotropy of the conductivity of a weakly ionized gas. The applicability of the results obtained to a qualitative interpretation of the phenomena occurring in the plasmaspheres of magnetized planets is discussed.     

Mathematical modelling of ciliary propulsion of an electrically-conducting Johnson-Segalman physiological fluid in a channel with slip

Bionic systems frequently feature electromagnetic pumping and offer significant advantages over conventional designs via intelligent bio-inspired properties. Complex wall features observed in nature also provide efficient mechanisms which can be utilized in biomimetic designs. The characteristics of biological fluids are frequently non-Newtonian in nature. In many natural systems super-hydrophobic slip is witnessed. Motivated by these phenomena, in this paper, we discussed a mathematical model for the cilia-generated propulsion of an electrically-conducting viscoelastic physiological fluid in a ciliated channel under the action of magnetic field. The rheological behavior of the fluid is simulated with the Johnson-Segalman constitutive model which allows internal wall slip. The regular or coordinated movement of the ciliated edges (which line the internal walls of the channel) is represented by a metachronal wave motion in the horizontal direction which generates a two-dimensional velocity profile. This mechanism is imposed by a periodic boundary condition which generates propulsion in the channel flow. Under the classical lubrication approximation, the boundary value problem is non-dimensionalized and solved analytically with a perturbation technique. The influence of the geometric, rheological (slip and Weissenberg number) and magnetic parameters on velocity, pressure gradient and the pressure rise (evaluated via the stream function in symbolic software) are presented graphically and interpreted at length.     

Comparison of substance supply in static and perfusion cultures based on mass transport phenomena

Mass transport phenomena in cell culture can be formulated by using classical reaction-diffusion equations; however, in practice, it is difficult to solve these equations analytically. Here, we used computer simulation to solve these equations, and compared the time-dependent concentration profile of substances in conventional static culture with that in perfusion culture. The simulated glucose consumption in static culture agreed with that of actual culture conditions used in a general cell culture experiment. The simulation of perfusion culture revealed that the geometry of the chamber and its operating parameters are critical to obtaining a sufficient supply of substances. We also found that the previously reported perfusion chambers are well designed and operate under adequate conditions. Our kinetic model of time-dependent concentration profiles for general substances based on mass transport phenomena could, therefore, be used for the optimal design of a microfluidic perfusion culture chip.     

Time Dependent MHD Nano-Second Grade Fluid Flow Induced by Permeable Vertical Sheet with Mixed Convection and Thermal Radiation

The aim of present paper is to study the series solution of time dependent MHD second grade incompressible nanofluid towards a stretching sheet. The effects of mixed convection and thermal radiation are also taken into account. Because of nanofluid model, effects Brownian motion and thermophoresis are encountered. The resulting nonlinear momentum, heat and concentration equations are simplified using appropriate transformations. Series solutions have been obtained for velocity, temperature and nanoparticle fraction profiles using Homotopy Analysis Method (HAM). Convergence of the acquired solution is discussed critically. Behavior of velocity, temperature and concentration profiles on the prominent parameters is depicted and argued graphically. It is observed that temperature and concentration profiles show similar behavior for thermophoresis parameter Νt but opposite tendency is noted in case of Brownian motion parameter Νb. It is further analyzed that suction parameter S and Hartman number Μ depict decreasing behavior on velocity profile.     

Peristaltic transport in a channel with a porous peripheral layer: model of a flow in gastrointestinal tract

Peristaltic transport in a two dimensional channel, filled with a porous medium in the peripheral region and a Newtonian fluid in the core region, is studied under the assumptions of long wavelength and low Reynolds number. The fluid flow is investigated in the waveframe of reference moving with the velocity of the peristaltic wave. Brinkman extended Darcy equation is utilized to model the flow in the porous layer. The interface is determined as a part of the solution using the conservation of mass in both the porous and fluid regions independently. A shear-stress jump boundary condition is used at the interface. The physical quantities of importance in peristaltic transport like pumping, trapping, reflux and axial velocity are discussed for various parameters of interest governing the flow like Darcy number, porosity, permeability, effective viscosity etc. It is observed that the peristalsis works as a pump against greater pressure in two-layered model with a porous medium compared with a viscous fluid in the peripheral layer. Increasing Darcy number Da decreases the pumping and increasing shear stress jump constant beta results in increasing the pumping. The limits on the time averaged flux Q for trapping in the core layer are obtained. The discussion on pumping, trapping and reflux may be helpful in understanding some of the fluid dynamic aspects of the transport of chyme in gastrointestinal tract.     

Thermal and Concentration Stratifications Effects in Radiative Flow of Jeffrey Fluid over a Stretching Sheet

In this article we investigate the heat and mass transfer analysis in mixed convective radiative flow of Jeffrey fluid over a moving surface. The effects of thermal and concentration stratifications are also taken into consideration. Rosseland''s approximations are utilized for thermal radiation. The nonlinear boundary layer partial differential equations are converted into nonlinear ordinary differential equations via suitable dimensionless variables. The solutions of nonlinear ordinary differential equations are developed by homotopic procedure. Convergence of homotopic solutions is examined graphically and numerically. Graphical results of dimensionless velocity, temperature and concentration are presented and discussed in detail. Values of the skin-friction coefficient, the local Nusselt and the local Sherwood numbers are analyzed numerically. Temperature and concentration profiles are decreased when the values of thermal and concentration stratifications parameters increase. Larger values of radiation parameter lead to the higher temperature and thicker thermal boundary layer thickness.     

Impact of Cattaneo-Christov Heat Flux in Jeffrey Fluid Flow with Homogeneous-Heterogeneous Reactions

Two-dimensional stretched flow of Jeffrey fluid in view of Cattaneo-Christov heat flux is addressed. Effects of homogeneous-heterogeneous reactions are also considered. Suitable transformations are used to form ordinary differential equations. Convergent series solutions are computed. Impact of significant parameters on the velocity, temperature, concentration and skin friction coefficient is addressed. Analysis of thermal relaxation is made. The obtained results show that ratio of relaxation to retardation times and Deborah number have inverse relation for velocity profile. Temperature distribution has decreasing behavior for Prandtl number and thermal relaxation time. Also concentration decreases for larger values of strength of homogeneous reaction parameter while it increases for strength of heterogeneous reaction parameter.     

Engineered bone culture in a perfusion bioreactor: a 2D computational study of stationary mass and momentum transport

Successful bone cell culture in large implants still is a challenge to biologists and requires a strict control of the physicochemical and mechanical environments. This study analyses from the transport phenomena viewpoint the limiting factors of a perfusion bioreactor for bone cell culture within fibrous and porous large implants (2.5 cm in length, a few cubic centimetres in volume, 250 μm in fibre diameter with approximately 60% porosity).

A two-dimensional mathematical model, based upon stationary mass and momentum transport in these implants is proposed and numerically solved. Cell oxygen consumption, in accordance theoretically with the Michaelis–Menten law, generates non linearity in the boundary conditions of the convection diffusion equation. Numerical solutions are obtained with a commercial code (Femlab® 3.1; Comsol AB, Stockholm, Sweden). Moreover, based on the simplification of transport equations, a simple formula is given for estimating the length of the oxygen penetration within the implant.

Results show that within a few hours of culture process and for a perfusion velocity of the order of 10^? 4 m s^? 1, the local oxygen concentration is everywhere sufficiently high to ensure a suitable cell metabolism. But shear stresses induced by the fluid flow with such a perfusion velocity are found to be locally too large (higher than 10^? 3 Pa). Suitable shear stresses are obtained by decreasing the velocity at the inlet to around 2 × 10^? 5 m s^? 1. But consequently hypoxic regions (low oxygen concentrations) appear at the downstream part of the implant.

Thus, it is suggested here that in the determination of the perfusion flow rate within a large implant, a compromise between oxygen supply and shear stress effects must be found in order to obtain a successful cell culture.     

Peristaltic motion of Phan–Thien–Tanner fluid in the presence of slip condition

This investigation considers the peristaltic flow of a Phan–Thien–Tanner fluid in the presence of slip condition and induced magnetic field. By use of the long wavelength and low Reynolds number approximations, closed form series solutions for stream function, pressure gradient, magnetic force function, axial induced magnetic field, and current density were obtained. The pressure gradient and frictional forces per wavelength were computed by numerical integration. The velocity slip condition in terms of shear stress is taken into account. Graphical results show the comparison between no-slip and viscous fluid cases. Pumping and trapping phenomena are discussed.     

Peristaltic biofluids flow through vertical porous human vessels using third-grade non-Newtonian fluids model

In this paper, the heat and flow characteristic of third-grade non-Newtonian biofluids flow through a vertical porous human vessel due to peristaltic wall motion are studied. The third-grade model can describe shear thinning (or shear thickening) and normal stress differences, which is acceptable for biofluids modeling. In order to solve the governing equations, the assumption of long-wavelength approximation is utilized. This hypothesis emphasizes that the wavelength of the peristaltic wall motion is large in comparison with the radius of the human vessel, which is widely acceptable in biological investigations. The analytical perturbation method is employed to solve the governing equations. Consequently, analytical expressions for the velocity profile, shear stress, temperature field, and biofluid flow rate are obtained. In addition, the effects of the governing parameters such as the third-grade non-Newtonian parameter, Grashof Number, Eckert number, and porosity, on the results are examined.     

MHD Mixed Convective Peristaltic Motion of Nanofluid with Joule Heating and Thermophoresis Effects

The primary objective of present investigation is to introduce the novel aspect of thermophoresis in the mixed convective peristaltic transport of viscous nanofluid. Viscous dissipation and Joule heating are also taken into account. Problem is modeled using the lubrication approach. Resulting system of equations is solved numerically. Effects of sundry parameters on the velocity, temperature, concentration of nanoparticles and heat and mass transfer rates at the wall are studied through graphs. It is noted that the concentration of nanoparticles near the boundaries is enhanced for larger thermophoresis parameter. However reverse situation is observed for an increase in the value of Brownian motion parameter. Further, the mass transfer rate at the wall significantly decreases when Brownian motion parameter is assigned higher values.     

Hydromagnetic Flow and Heat Transfer over a Porous Oscillating Stretching Surface in a Viscoelastic Fluid with Porous Medium

An analysis is carried out to study the heat transfer in unsteady two-dimensional boundary layer flow of a magnetohydrodynamics (MHD) second grade fluid over a porous oscillating stretching surface embedded in porous medium. The flow is induced due to infinite elastic sheet which is stretched periodically. With the help of dimensionless variables, the governing flow equations are reduced to a system of non-linear partial differential equations. This system has been solved numerically using the finite difference scheme, in which a coordinate transformation is used to transform the semi-infinite physical space to a bounded computational domain. The influence of the involved parameters on the flow, the temperature distribution, the skin-friction coefficient and the local Nusselt number is shown and discussed in detail. The study reveals that an oscillatory sheet embedded in a fluid-saturated porous medium generates oscillatory motion in the fluid. The amplitude and phase of oscillations depends on the rheology of the fluid as well as on the other parameters coming through imposed boundary conditions, inclusion of body force term and permeability of the porous medium. It is found that amplitude of flow velocity increases with increasing viscoelastic and mass suction/injection parameters. However, it decreases with increasing the strength of the applied magnetic field. Moreover, the temperature of fluid is a decreasing function of viscoelastic parameter, mass suction/injection parameter and Prandtl number.     

Kinetics of C-photosynthate translocation in morning glory vines

The movement of ¹⁴C-photosynthate in morning glory (Ipomea nil Roth, cu. Scarlet O'Hara) vines 2 to 5 meters long was followed by labeling a lone mature leaf with ¹⁴CO₂ and monitoring the arrival rate of tracer at expanding sink leaves on branches along the stem. To a first approximation, the kinetic behavior of the translocation profiles resembled that which would be expected from movement at a single velocity (“plug flow”) without tracer loss from the translocation stream. There was no consistent indication of a velocity gradient along the vine length. The profile moved along the vine as a distinct asymmetrical peak which changes shape only slowly. The spatial distribution of tracer along the vine reasonably matched that predicted on the basis of the arrival kinetics at a sink, assuming plug flow with no tracer loss. These observations are in marked contrast to the kinetic behavior of any mechanism describable by diffusion equations.

However, a progressive change in profile shape (a symmetrical widening) was observed, indicating a range of translocation velocities. A minimum of at least two factors must have contributed to the observed velocity gradient: the exchange of ¹⁴C between sieve elements and companion cells (demonstrated by microautoradiography) and the range of velocities in the several hundred sieve tubes which carried the translocation stream. Possible effects of these two factors on profile spreading were investigated by means of numerical models. The models are necessarily incomplete, due principally to uncertainties about the exchange rate between sieve elements and companion cells and the degree of functional connectivity between sieve tubes of different conductivities. However, most of the observed profile spreading may be reasonably attributed to the combined effects of those two factors.

The mass average velocity of translocation (calculated from the mean times of ¹⁴C arrival at successive sink leaves) was about 75% of the maximum velocity (calculated from the times of initial detection at the same sink leaves), which was usually between 0.6 and 1 cm min⁻¹. Owing to tracer exchange between sieve elements and companion cells, the mass average velocity of tracer in the sieve tubes was probably closer to 86% of the maximum velocity, a figure which agreed with a predicted velocity distribution based on calculated sieve tube conductivities and the size distribution of functional sieve tubes.

     

MHD Free Convective Boundary Layer Flow of a Nanofluid past a Flat Vertical Plate with Newtonian Heating Boundary Condition

Steady two dimensional MHD laminar free convective boundary layer flows of an electrically conducting Newtonian nanofluid over a solid stationary vertical plate in a quiescent fluid taking into account the Newtonian heating boundary condition is investigated numerically. A magnetic field can be used to control the motion of an electrically conducting fluid in micro/nano scale systems used for transportation of fluid. The transport equations along with the boundary conditions are first converted into dimensionless form and then using linear group of transformations, the similarity governing equations are developed. The transformed equations are solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order method with shooting technique. The effects of different controlling parameters, namely, Lewis number, Prandtl number, buoyancy ratio, thermophoresis, Brownian motion, magnetic field and Newtonian heating on the flow and heat transfer are investigated. The numerical results for the dimensionless axial velocity, temperature and nanoparticle volume fraction as well as the reduced Nusselt and Sherwood number have been presented graphically and discussed. It is found that the rate of heat and mass transfer increase as Newtonian heating parameter increases. The dimensionless velocity and temperature distributions increase with the increase of Newtonian heating parameter. The results of the reduced heat transfer rate is compared for convective heating boundary condition and found an excellent agreement.     

A model of pulsatile flow in a uniform deformable vessel.

Simulations of blood flow in natural and artificial conduits usually require large computers for numerical solution of the Navier-Stokes equations. Often, physical insight into the fluid dynamics is lost when the solution is purely numerical. An alternative to solving the most general form of the Navier-Stokes equations is described here, wherein a functional form of the solution is assumed in order to simplify the required computations. The assumed forms for the axial pressure gradient and velocity profile are chosen such that conservation of mass is satisfied for fully established pulsatile flow in a straight, deformable vessel. The resulting equations are cast in finite-difference form and solved explicitly. Results for the limiting cases of rigid wall and zero applied pressure are found to be in good agreement with analytical solutions. Comparison with the experimental results of Klanchar et al. [Circ. Res. 66, 1624-1635 (1990]) also shows good agreement. Application of the model to realistic physiological parameter values provides insight as to the influence of the pulsatile nature of the flow field on wall shear development in the presence of a moving wall boundary. Specifically, the model illustrates the dependence of flow rate and shear rate on the amplitude of the vessel wall motion and the phase difference between the applied pressure difference and the oscillations of the vessel radius. The present model can serve as a useful tool for experimentalists interested in quantifying the magnitude and character of velocity profiles and shearing forces in natural and artificial biologic conduits.     

Mass transfer to fluids flowing through rotating nonaligned straight tubes

Relatively inefficient heat/mass transfer is characteristic of tubular devices if the Reynolds number is low. One method of improving the heat/mass transfer efficiency of such devices is by inducing transverse laminar secondary circulations that are superimposed on the primary flow field; the resulting transverse velocity components lead to fluid mixing and hence augmented mass transfer in the tube lumen. The present work is a theoretical and experimental investigation of the enhanced transport in rotating, nonaligned, straight tubes, a method of transport enhancement that utilizes Coriolis acceleration to create transverse fluid mixing. This technique couples the transport advantages of coiled tubes with the design advantages of straight tubes. The overall mass balance equation is numerically solved for transfer into fluids flowing steadily through rotating nonaligned straight tubes. This solution, for small Coriolis disturbances, incorporates a third order perturbation solution for the primary and secondary flow fields. For sufficiently small Coriolis disturbances the bulk concentration increase is found to be uniquely determined by the value of a single similarity parameter. As the Coriolis disturbance is increased, however, two additional parameters are required to accurately characterize the mass transfer. In general, increasing the Coriolis accelerations results in an increase in mass transfer. There are solution regimens, however, in which increasing this acceleration can lead to a decrease in mass transfer efficiency. This interesting phenomena, which has important design implications, appears to result from velocity-weighting effects on the exiting sample. Experiments, involving the measurement of oxygen transferred into water and blood, produced data that agree with the theoretical predictions.     

Determination of the plasma velocity in an imploding wire array from magnetic field measurements by a gradient probe

A method for measuring the gradient of the magnetic field in the plasma of an imploding wire array is described. Results from measurements of the magnitude and gradient of the magnetic field in a tungsten wire array on the Angara-5-1 facility at currents of ∼3 MA are presented. A novel method for calculating the velocity of the current-carrying plasma in the framework of MHD equations from data on the magnitude and gradient of the magnetic field at a certain point inside the array is proposed. It is demonstrated that a gradient magnetic probe can be used to investigate the plasma current sheath in plasma focus facilities.     

On the pressure response of Eurydice sp. (Isopoda)

Eurydice responds to increased pressure within the 67 to 790 mb range by an upward swimming, the duration of the response being dependent on the magnitude of the pressure change. Release of pressure is followed by downward swimming or passive sinking.

The responses are orientated primarily to gravity, but with a subsidiary photic influence, and brief pulses of 1–2 sec duration are less effective in eliciting a response.

Adaptation to sustained high pressure appears to involve a shift in the stimulus/response curve with no evident loss of sensitivity.

The pattern of swimming behaviour observed following sinusoidal pressure cycles suggests that, over the range of cycles studied, the parameter most effective in inducing the response is change of pressure, or perhaps pressure itself, rather than the velocity component of the stimulus.

Pressure perception is not affected by surface active substances, nor by changes in sea water concentration, suggesting that the process of transduction does not involve compression of a hydrogen gas film on the body surface.