Peristaltic flow of a couple stress fluid in an asymmetric channel

This paper presents an analysis of the peristaltic flow of a couple stress fluid in an asymmetric channel. The asymmetric nature of the flow is introduced through the peristaltic waves of different amplitudes and phases on the channel walls. Mathematical modelling corresponding to a two-dimensional flow has been carried out. The flow analysis is presented under long wavelength and low Reynolds number approximations. Closed form solutions for the axial velocity, stream function and the axial pressure gradient are given. Numerical computations have been carried out for the pressure rise per wavelength, friction forces and trapping. It is noted that there is a decrease in the pressure when the couple stress fluid parameter increases. The variation of the couple stress fluid parameter with the size of the trapped bolus is also similar to that of pressure. Furthermore, the friction force on the lower channel wall is greater than that on the upper channel wall.     

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.     

Transient relative motion of two cells in a channel flow

The hydrodynamic interaction of a red blood cell and a white blood cell in microvessels is studied, by use of a two-dimensional numerical model. The red blood cell, modeled as a small rigid circular cylinder, and the white blood cell, modeled as a larger rigid circular cylinder, are immersed in an incompressible Newtonian fluid in a two-dimensional channel. It is assumed that no external force or moment acts on the model cells, and the effect of inertia forces on the motion of the fluid and the cells is neglected. The velocity field of the suspending fluid and the instantaneous velocities of the two model cells are computed by the finite element method. Using the translational velocities of the model cells obtained, the trajectories of their relative motion are determined, for various initial positions. It is shown that the cells may or may not pass each other or separate, depending on the initial positions. The present results compare well to the experimental results.     

TRPV4 channel is involved in the coupling of fluid viscosity changes to epithelial ciliary activity

Autoregulation of the ciliary beat frequency (CBF) has been proposed as the mechanism used by epithelial ciliated cells to maintain the CBF and prevent the collapse of mucociliary transport under conditions of varying mucus viscosity. Despite the relevance of this regulatory response to the pathophysiology of airways and reproductive tract, the underlying cellular and molecular aspects remain unknown. Hamster oviductal ciliated cells express the transient receptor potential vanilloid 4 (TRPV4) channel, which is activated by increased viscous load involving a phospholipase A(2)-dependent pathway. TRPV4-transfected HeLa cells also increased their cationic currents in response to high viscous load. This mechanical activation is prevented in native ciliated cells loaded with a TRPV4 antibody. Application of the TRPV4 synthetic ligand 4alpha-phorbol 12,13-didecanoate increased cationic currents, intracellular Ca(2+), and the CBF in the absence of a viscous load. Therefore, TRPV4 emerges as a candidate to participate in the coupling of fluid viscosity changes to the generation of the Ca(2+) signal required for the autoregulation of CBF.     

A mathematical note on the fahraeuslindqvist effect in power law fluid

An axisymmetric flow of a power law fluid through circular tubes under constant pressure gradient with the flow parameters varying radially is analyzed theoretically. The main finding is that for the Fahraeus-Lindqvist (F-L) effect to occur, it is necessary to have at least one of the parametersK (consistency) andn (index) as a discontinuous function ofr in the absence of wall slip; and with slip condition the parameters could be continuous functions ofr under specific conditions. In both the cases the existence of more than one discontinuity cannot be ruled out. The results obtained are consistent with experimental findings of blood flow through narrow tubes.     

Cilia-assisted flow of viscoelastic fluid in a divergent channel under porosity effects

Biomechanics and Modeling in Mechanobiology - Cilia-driven laminar flow of an incompressible viscoelastic fluid in a divergent channel has been conducted numerically using the BVP4C technique. The...     

The active and passive ciliary motion in the embryo node: A computational fluid dynamics model

The breaking of left–right symmetry in the mammalian embryo is believed to occur in a transient embryonic structure, the node, when cilia create a leftward flow of liquid. The two-cilia hypothesis proposes that the node contains two kinds of primary cilia: motile cilia that rotate autonomously to generate the leftward fluid flow and passive cilia that act as mechano-sensors, responding to flow. While studies support this hypothesis, the mechanism by which the sensory cilia respond to the fluid flow is still unclear. In this paper, we present a computational model of two cilia, one active and one passive. By employing computational fluid dynamics, deformable mesh computational techniques and fluid–structure interaction analysis, and solving the three-dimensional unsteady transport equations, we study the flow pattern produced by the movement of the active cilium and the response of the passive cilium to this flow. Our results reveal that clockwise rotation of the active cilium can generate a counter-clockwise elliptical rotation and overall lateral displacement for its neighboring passive one, of measurable magnitude and consistent pattern. This supports the plausibility of the two-cilia hypothesis and helps quantify the motion pattern for the passive cilium induced by this regional flow.     

Effect of couple stresses on the unsteady convective diffusion in fluid flow through a channel

A generalized dispersion model is used to obtain exact solution for unsteady convective diffusion in the presence of couple stresses. The effect of the couple stress parameter 'a' on the most dominant dispersion coefficient is clearly depicted. The dimensionless mean concentration distribution is obtained as a function of dimensionless axial distance, time and 'a'. The results for 'pure convection' are also reported. It is shown that the effect of couple stress is predominant only for small values of 'a' and when a----infinity the flow characteristics tend to their equivalents in Newtonian theory. The results of Taylor's dispersion model are recovered as a particular case in the limit tau----infinity.     

Upward flow of pleural liquid near lobar margins due to cardiogenic motion.

In anesthetized, paralyzed, supine rabbits (3-4 kg) during apnea, we injected fluorescent dye or fluorescent microspheres (2 or 6 microns diam) into the dependent pleural space and observed the arrival and movement of the dye or microspheres at superior regions. Injection was through a rib capsule located in the dependent right chest. The dye or microspheres were observed through a pleural window overlying a lobar margin. The vertical distance between the capsule and window was 3-4 cm. The movement of the dye or microspheres was recorded via a fluorescence videomicroscope, and the signals were analyzed for dye transit time and microsphere velocity. The transit time of the dye to traverse the height of the pleural space was calculated from the light intensity vs. time curve. Transit time during apnea averaged 6.0 +/- 3.4 (SD) min (n = 4). Transit time measured after the onset of mechanical ventilation was < 1 min. The direction and speed of a microsphere moving in the relatively thick pleural space adjacent to the lobar margin depended on its distance from the lobar margin. Microspheres moved upward in the pleural space that was in proximity to the lobar margin but downward at farther distances from the lobar margin. Pleural liquid recirculation occurs via the pleural space adjacent to lobar margins.     

A model of localised Rac1 activation in endothelial cells due to fluid flow

Endothelial cells respond to fluid flow by elongating in the direction of flow. Cytoskeletal changes and activation of signalling molecules have been extensively studied in this response, including: activation of receptors by mechano-transduction, actin filament alignment in the direction of flow, changes to cell-substratum adhesions, actin-driven lamellipodium extension, and localised activation of Rho GTPases. To study this process we model the force over a single cell and couple this to a model of the Rho GTPases, Rac and Rho, via a Kelvin-body model of mechano-transduction. It is demonstrated that a mechano-transducer can respond to the normal component of the force is likely to be a necessary component of the signalling network in order to establish polarity. Furthermore, the rate-limiting step of Rac1 activation is predicted to be conversion of Rac-GDP to Rac-GTP, rather than activation of upstream components. Modelling illustrates that the aligned endothelial cell morphology could attenuate the signalling network.     

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.     

Splitting the ciliary axoneme: implications for a "switch-point" model of dynein arm activity in ciliary motion

In the presence of specific inhibitors of beat. 20 microM VO4(3-) or pCa 4, mussel gill lateral (L) cilia can be arrested in two positions--"hands down" or "hands up"--at opposite ends of the stroke cycle. Cilia move to these positions by doublet microtubule sliding. Axonemes of arrested cilia, still tethered to the cell, are intact after demembranation and protease treatment. When reactivated by 4 mM ATP with inhibitors present, about 40% split apart. Splits are not random but occur preferentially between different specific doublets in the two opposite arrest positions. Several different related patterns of splitting are observed; for every pattern in "hands down" axonemes, there is a corresponding complementary split pattern in "hands up" axonemes. In some split patterns two doublets remain firmly attached to the central pair; these also differ depending on axonemal position. Although some of the patterns seen may be artifactual or difficult to explain, the complementary splitting patterns are predictable with simple assumptions by a "switch point" hypothesis of ciliary activity where, during each recovery stroke, doublets 6-8 have active dynein arms, while during each effective stroke, arms on doublets 1-4 become active, and arms 6-8 are turned off. Because of a difference between the patterns seen and the predictions, the status of the arms on doublet 9 is unresolved. The patterns also suggest that a spoke-central sheath attachment cycle may correlate with switching of arm activity during the generation of an asymmetric beat.     

An experimental and computational analysis of primary cilia deflection under fluid flow

In this study we have developed a novel model of the deflection of primary cilia experiencing fluid flow accounting for phenomena not previously considered. Specifically, we developed a large rotation formulation that accounts for rotation at the base of the cilium, the initial shape of the cilium and fluid drag at high deflection angles. We utilised this model to analyse full 3D data-sets of primary cilia deflecting under fluid flow acquired with high-speed confocal microscopy. We found a wide variety of previously unreported bending shapes and behaviours. We also analysed post-flow relaxation patterns. Results from our combined experimental and theoretical approach suggest that the average flexural rigidity of primary cilia might be higher than previously reported (Schwartz et al. 1997, Am J Physiol. 272(1 Pt 2):F132–F138). In addition our findings indicate that the mechanics of primary cilia are richly varied and mechanisms may exist to alter their mechanical behaviour.     

The flow of power law fluids in elastic networks and porous media

The flow of power law fluids, which include shear thinning and shear thickening as well as Newtonian as a special case, in networks of interconnected elastic tubes is investigated using a residual-based pore scale network modeling method with the employment of newly derived formulae. Two relations describing the mechanical interaction between the local pressure and local cross-sectional area in distensible tubes of elastic nature are considered in the derivation of these formulae. The model can be used to describe shear dependent flows of mainly viscous nature. The behavior of the proposed model is vindicated by several tests in a number of special and limiting cases where the results can be verified quantitatively or qualitatively. The model, which is the first of its kind, incorporates more than one major nonlinearity corresponding to the fluid rheology and conduit mechanical properties, that is non-Newtonian effects and tube distensibility. The formulation, implementation, and performance indicate that the model enjoys certain advantages over the existing models such as being exact within the restricting assumptions on which the model is based, easy implementation, low computational costs, reliability, and smooth convergence. The proposed model can, therefore, be used as an alternative to the existing Newtonian distensible models; moreover, it stretches the capabilities of the existing modeling approaches to reach non-Newtonian rheologies.     

Poroelastic analysis of interstitial fluid flow in a single lamellar trabecula subjected to cyclic loading

Trabecula, an anatomical unit of the cancellous bone, is a porous material that consists of a lamellar bone matrix and interstitial fluid in a lacuno-canalicular porosity. The flow of interstitial fluid caused by deformation of the bone matrix is believed to initiate a mechanical response in osteocytes for bone remodeling. In order to clarify the effect of the lamellar structure of the bone matrix—i.e., variations in material properties—on the fluid flow stimuli to osteocytes embedded in trabeculae, we investigated the mechanical behavior of an individual trabecula subjected to cyclic loading based on poroelasticity. We focused on variations in the trabecular permeability and developed an analytical solution containing both transient and steady-state responses for interstitial fluid pressure in a single trabecular model represented by a multilayered two-dimensional poroelastic slab. Based on the obtained solution, we calculated the pressure and seepage velocity of the interstitial fluid in lacuno-canalicular porosity, within the single trabecula, under various permeability distributions. Poroelastic analysis showed that a heterogeneous distribution of permeability produces remarkable variations in the fluid pressure and seepage velocity in the cross section of the individual trabecula, and suggests that fluid flow stimuli to osteocytes are mostly governed by the value of permeability in the neighborhood of the trabecular surfaces if there is no difference in the average permeability in a single trabecula.     

A role for p38 MAPK in the regulation of ciliary motion in a eukaryote

Background  

Motile cilia are essential to the survival and reproduction of many eukaryotes; they are responsible for powering swimming of protists and small multicellular organisms and drive fluids across respiratory and reproductive surfaces in mammals. Although tremendous progress has been made to comprehend the biochemical basis of these complex evolutionarily-conserved organelles, few protein kinases have been reported to co-ordinate ciliary beat. Here we present evidence for p38 mitogen-activated protein kinase (p38 MAPK) playing a role in the ciliary beat of a multicellular eukaryote, the free-living miracidium stage of the platyhelminth parasite Schistosoma mansoni.