Analysis of flow in a cone-and-plate apparatus with respect to spatial and temporal effects on endothelial cells

Endothelial cells, covering the inner surface of vessels and the heart, are permanently exposed to fluid flow, which affects the endothelial structure and the function. The response of endothelial cells to fluid shear stress is frequently investigated in cone-plate systems. For this type of device, we performed an analytical and numerical analysis of the steady, laminar, three-dimensional flow of a Newtonian fluid at low Reynolds numbers. Unsteady oscillating and pulsating flow was studied numerically by taking the geometry of a corresponding experimental setup into account. Our investigation provides detailed information with regard to shear-stress distribution at the plate as well as secondary flow. We show that: (i) there is a region on the plate where shear stress is almost constant and an analytical approach can be applied with high accuracy; (ii) detailed information about the flow in a real cone-plate device can only be obtained by numerical simulations; (iii) the pulsating flow is quasi-stationary; and (iv) there is a time lag on the order of 10(-3) s between cone rotation and shear stress generated on the plate.     

Cytoplasmic motion induced by cytoskeleton stretching and its effect on cell mechanics

Cytoplasmic motion assumed as a steady state laminar flow induced by cytoskeleton stretching in a cell is determined and its effect on the mechanical behavior of the cell under externally applied forces is demonstrated. Non-Newtonian fluid is assumed for the multiphase cytoplasmic fluid and the analytical velocity field around the macromolecular chain is obtained by solving the reduced nonlinear momentum equation using homotopy technique. The entropy generation by the fluid internal friction is calculated and incorporated into the entropic elasticity based 8-chain constitutive relations. Numerical examples showed strengthening behavior of cells in response to externally applied mechanical stimuli. The spatial distribution of the stresses within a cell under externally applied fluid flow forces were also studied.     

Microcontinuum model for pulsatile blood flow through a stenosed tube

The effects of polar nature of blood and pulsatility on flow through a stenosed tube have been analysed by assuming blood as a micropolar fluid. Linearized solutions of basic equations are obtained through consecutive applications of finite Hankel and Laplace transforms. The analytical expressions for axial and particle angular velocities, wall shear stress, resistance to flow and apparent viscosity have been obtained. The axial velocity profiles for Newtonian and micropolar fluids have been compared. The interesting observation of this analysis is velocity, in certain parts of cycle, for micropolar fluid is higher than Newtonain fluid. Variation of apparent viscosity eta a with tube radius shows both inverse Fahraeus-Lindqvist and Fahraeus-Lindqvist effects. Finally, the resistance to flow and wall shear stress for normal and diseased blood have been computed and compared.     

Casson fluid model for pulsatile flow of blood under periodic body acceleration

Pulsatile flow of a Casson fluid under the influence of a periodic body acceleration has been studied in this paper. An implicit finite difference numerical procedure has been used to analyze the flow. Applicability of this method has been checked by comparing the obtained results with the analytical solution for Newtonian flow and explicit scheme solution. The agreement between the implicit and explicit scheme solutions and the analytical solution is good (error less than 1%). Flow variables have been computed at three locations in cardiovascular system (wide (femoral) and narrow (arteriole and coronary) tubes). Effects of yield stress, tube radius and pressure gradient combined, body acceleration amplitude and frequency etc., on flow have been studied. The following observations have been made: (i) Initial transient time It changes with yield stress in narrow tubes are insignificant, whereas in wide tubes It decreases with yield stress; (ii) The axial velocity and fluid acceleration variations with yield stress are uniform (changes only quantitatively, profiles shape remain same) in narrow tubes, whereas in wide tubes these variations are non-uniform (profiles change qualitatively as well as quantitatively); (iii) Yield stress effects on wall shear amplitude are insignificant in narrow tubes (congruent to 0.3% in arteriole and congruent to 6% in femoral); and (iv) For Newtonian fluid, mean flow rate does not change with body acceleration amplitude a0 and frequency fb but it increases (decreases) with a0(fb) for Casson fluid.     

Oscillatory flow of blood in a stenosed artery

In order to understand the abnormal flow conditions of blood in a locally constricted blood vessel, the analytical results are obtained for the oscillatory flow of blood which behaves as a Newtonian fluid. It is here assumed that the surface roughness is cosine-shaped and the maximum height of the roughness is very small compared with the radius of the unconstricted tube. Numerical solutions are presented for the instantaneous flow rate, resistive impedance, wall shear stress and phase lag.     

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 Hybrid Analytical/Numerical Model for the Characterization of Preferential Flow Path with Non-Darcy Flow

Due to the long-term fluid-solid interactions in waterflooding, the tremendous variation of oil reservoir formation parameters will lead to the widespread evolution of preferential flow paths, thereby preventing the further enhancement of recovery efficiency because of unstable fingering and premature breakthrough. To improve oil recovery, the characterization of preferential flow paths is essential and imperative. In efforts that have been previously documented, fluid flow characteristics within preferential paths are assumed to obey Darcy''s equation. However, the occurrence of non-Darcy flow behavior has been increasingly suggested. To examine this conjecture, the Forchheimer number with the inertial coefficient estimated from different empirical formulas is applied as the criterion. Considering a 10% non-Darcy effect, the fluid flow in a preferential path may do experience non-Darcy behavior. With the objective of characterizing the preferential path with non-Darcy flow, a hybrid analytical/numerical model has been developed to investigate the pressure transient response, which dynamically couples a numerical model describing the non-Darcy effect of a preferential flow path with an analytical reservoir model. The characteristics of the pressure transient behavior and the sensitivities of corresponding parameters have also been discussed. In addition, an interpretation approach for pressure transient testing is also proposed, in which the Gravitational Search Algorithm is employed as a non-linear regression technology to match measured pressure with this hybrid model. Examples of applications from different oilfields are also presented to illustrate this method. This cost-effective approach provides more accurate characterization of a preferential flow path with non-Darcy flow, which will lay a solid foundation for the design and operation of conformance control treatments, as well as several other Enhanced Oil Recovery projects.     

Effect of tumor shape and size on drug delivery to solid tumors

ABSTRACT: Tumor shape and size effect on drug delivery to solid tumors are studied, based on the application of the governing equations for fluid flow, i.e., the conservation laws for mass and momentum, to physiological systems containing solid tumors. The discretized form of the governing equations, with appropriate boundary conditions, is developed for predefined tumor geometries. The governing equations are solved using a numerical method, the element-based finite volume method. Interstitial fluid pressure and velocity are used to show the details of drug delivery in a solid tumor, under an assumption that drug particles flow with the interstitial fluid. Drug delivery problems have been most extensively researched in spherical tumors, which have been the simplest to examine with the analytical methods. With our numerical method, however, more complex shapes of the tumor can be studied. The numerical model of fluid flow in solid tumors previously introduced by our group is further developed to incorporate and investigate non-spherical tumors such as prolate and oblate ones. Also the effects of the surface area per unit volume of the tissue, vascular and interstitial hydraulic conductivity on drug delivery are investigated.     

Fluid mechanics in the perivascular space

Perivascular space (PVS) within the brain is an important pathway for interstitial fluid (ISF) and solute transport. Fluid flowing in the PVS can affect these transport processes and has significant impacts on physiology. In this paper, we carry out a theoretical analysis to investigate the fluid mechanics in the PVS. With certain assumptions and approximations, we are able to find an analytical solution to the problem. We discuss the physical meanings of the solution and particularly examine the consequences of the induced fluid flow in the context of convection-enhanced delivery (CED). We conclude that peristaltic motions of the blood vessel walls can facilitate fluid and solute transport in the PVS.     

Effects of periodic accelerations on blood flow in arteries

This paper discusses the flow of blood in large artries under the influence of linear periodic acceleration. The governing equations and boundary conditions are established and analytical solutions for the velocity, fluid acceleration, bulk flow and shear stress are obtained. The results for these physical quantitites are computed for the case of an artery the size of a normal human aorta. It is found that the flow field variables are directly proportional to the external accelerating force. The behaviour of the velocity profile along the radial distance at different stages of times at fixed applied acceleration is also shown.     

Fluid flow and convective transport of solutes within the intervertebral disc

Previous experimental and analytical studies of solute transport in the intervertebral disc have demonstrated that for small molecules diffusive transport alone fulfils the nutritional needs of disc cells. It has been often suggested that fluid flow into and within the disc may enhance the transport of larger molecules. The goal of the study was to predict the influence of load-induced interstitial fluid flow on mass transport in the intervertebral disc.An iterative procedure was used to predict the convective transport of physiologically relevant molecules within the disc. An axisymmetric, poroelastic finite-element structural model of the disc was developed. The diurnal loading was divided into discrete time steps. At each time step, the fluid flow within the disc due to compression or swelling was calculated. A sequentially coupled diffusion/convection model was then employed to calculate solute transport, with a constant concentration of solute being provided at the vascularised endplates and outer annulus. Loading was simulated for a complete diurnal cycle, and the relative convective and diffusive transport was compared for solutes with molecular weights ranging from 400 Da to 40 kDa.Consistent with previous studies, fluid flow did not enhance the transport of low-weight solutes. During swelling, interstitial fluid flow increased the unidirectional penetration of large solutes by approximately 100%. Due to the bi-directional temporal nature of disc loading, however, the net effect of convective transport over a full diurnal cycle was more limited (30% increase). Further study is required to determine the significance of large solutes and the timing of their delivery for disc physiology.     

Linear and nonlinear analyses of pulsatile blood flow in a cylindrical tube

A non-Newtonian shear-thinning constitutive relation is proposed to study pulsatile flow of whole blood in a cylindrical tube. The constitutive relation, which satisfies the principle of material frame indifference, is derived from viscometric data obtained from whole blood over a range of hematocrits. Assuming axisymmetric flow in a rigid cylindrical tube of constant diameter, a second-order, nonlinear partial differential equation governing the axial velocity component is obtained. Imposing a periodic pressure gradient, the governing equation was solved numerically using finite difference methods over a range of Stokes values and hematocrits. For a forcing frequency of 1 Hz, results are presented over tube diameters ranging between 0.1 and 2 cm and over hematocrits ranging between 10 and 80%. For a given hematocrit, velocity profiles predicted for the non-Newtonian model under sinusoidal forcing reveal attenuated volume flow rate and enhanced vorticity transport over the tube cross-section relative to a Newtonian fluid having a viscosity corresponding to the high shear-rate limit. For moderate to high Stokes numbers, consistent with flow in large arteries, our results revealed a viscosity distribution that was nearly time invariant. An analytic solution was obtained for a fluid having arbitrarily prescribed radially varying, temporally invariant viscosity and density distributions under arbitrary periodic pressure forcing. Close agreement was observed between our numerical and analytical results when the imposed viscosity distribution was chosen to approximate the time-averaged viscosity distribution predicted by the shear-thinning non-Newtonian model. For St > or approximately= 100, the disparity between our results and those of a Newtonian fluid of constant viscosity grows with a decreasing ratio of the DC to AC components of the pressure-gradient amplitude below 50%. In particular, for any purely oscillatory pressure-gradient (vanishing DC component), the Womersley solution is a particularly poor predictor of the amplitude and phase of wall shear rate for over half of the flow cycle. Under such circumstances, the analytical models presented here provide a simple and accurate means of estimating instantaneous wall shear rate, knowing only the pressure gradient and hematocrit.     

Analysis of the flow field induced by the sessile peritrichous ciliate Opercularia asymmetrica

The feeding mechanism of the sessile protozoon Opercularia asymmetrica (Oligohymenophorea, Peritrichia) relies on the cilia beat generating a flow field that convectively transports suspended particles and dissolved substances to the oral cavity of the organism. By use of optical micro-flow measurement and theoretical methods the flow environment of two neighbouring peritrichous ciliate cells is studied. Both, yeast cells (Saccharomyces cerevisiae) and artificial flow tracers are used for the visualisation of the flow field. Artificial tracers are rejected by the protozoa and deviate from the fluid path lines, while yeast cells follow the flow almost perfectly. This is shown through a dimensional analysis of the involved hydrodynamic forces on the tracers. The measured flow field exhibits maximum velocities of 25 microm/s at around 20 microm distance ahead of an individual ciliate. The flow field extends 200 microm from the location of the ciliate. A nicking motion of the protozoon is observed and found not to obey any periodic law. Multiples of protozoa exhibit most commonly an alternating cilia beat regime generating a non-stationary flow field. It can be shown through theoretical methods that fluid exchange is enhanced in this alternating regime compared to a flow field generated by a single ciliate. Fluid exchange depends on the distance of the ciliates from each other and on the alteration frequency of the cilia beat. The comparison of an analytical Stokes' flow solution with the observed fluid flow serves to determine the force required to maintain the flow field against viscous dissipation. The force magnitude is in the order of magnitude of 10-100 pN.     

Influence of fluid-flow direction on effective permeability of the vertebral end plate: an analytical model

Convective transports in the vertebral end plate (VEP) play a significant role in the homeostasis of the spine. A few studies hypothesised that the hydraulic resistance or effective permeability of the VEP could be dependant upon fluid-flow direction. Results were influenced by species, region of interest within the end plate and pathology. Some results were contradictory. We propose an analytical model based on steady-state Newtonian flows in capillary media to develop a phenomenological analysis of convective transport through the VEP. This dependence was established using a biquadratic analytical function involving porosities of subchondral bone, capillary bed and cartilage end plate. Discussion of results provided a theoretical justification for variable and/or contradictory experimental results concerning the amount of energy lost by fluid during its course through the end plate. Tissue porosities and, especially, those relative to the capillary bed could strongly influence the dependence of fluid energy loss on flow direction and could potentially modify tissue homeostasis related to the day and night cycle.     

Plug flow cytometry extends analytical capabilities in cell adhesion and receptor pharmacology

BACKGROUND: Plug flow cytometry is a recently developed system for the automated delivery of multiple small boluses or "plugs" of cells or particles to the flow cytometer for analysis. Important system features are that sample plugs are of precisely defined volume and that the sample vessel need not be pressurized. We describe how these features enable direct cell concentration determinations and novel ways to integrate flow cytometers with other analytical instruments. METHODS: Adhesion assays employed human polymorphonuclear neutrophils (PMNs) loaded with Fura Red and Chinese hamster ovary (CHO) cells cotransfected with genes for green fluorescent protein (GFP) and human P-selectin. U937 cells expressing the human 7-transmembrane formyl peptide receptor were loaded with the fluorescent probe indo-1 for intracellular ionized calcium determinations. A computer-controlled syringe or peristaltic pump loaded the sample into a sample loop of the plug flow coupler, a reciprocating eight-port valve. When the valve position was switched, the plug of sample in the sample loop was transported to the flow cytometer by a pressure-driven fluid line. RESULTS: In stirred mixtures of PMNs and CHO cells, we used plug flow cytometry to directly quantify changes in concentrations of nonadherent singlet PMNs. This approach enabled accurate quantification of adherent PMNs in multicell aggregates. We constructed a novel plug flow interface between the flow cytometer and a cone-plate viscometer to enable real-time flow cytometric analysis of cell-cell adhesion under conditions of uniform shear. The High Throughput Pharmacology System (HTPS) is an instrument used for automated programming of complex pharmacological cell treatment protocols. It was interfaced via the plug flow coupling device to enable rapid (< 5 min) flow cytometric characterization of the intracellular calcium dose-response profile of U937 cells to formyl peptide. CONCLUSIONS: By facilitating the coupling of flow cytometers to other fluidics-based analytical instruments, plug flow cytometry has extended analytical capabilities in cell adhesion and pharmacological characterization of receptor-ligand interactions.     

Optimal Homotopy Asymptotic Method for Flow and Heat Transfer of a Viscoelastic Fluid in an Axisymmetric Channel with a Porous Wall

In this article, an approximate analytical solution of flow and heat transfer for a viscoelastic fluid in an axisymmetric channel with porous wall is presented. The solution is obtained through the use of a powerful method known as Optimal Homotopy Asymptotic Method (OHAM). We obtained the approximate analytical solution for dimensionless velocity and temperature for various parameters. The influence and effect of different parameters on dimensionless velocity, temperature, friction factor, and rate of heat transfer are presented graphically. We also compared our solution with those obtained by other methods and it is found that OHAM solution is better than the other methods considered. This shows that OHAM is reliable for use to solve strongly nonlinear problems in heat transfer phenomena.     

Ultrasonic particle-concentration for sheathless focusing of particles for analysis in a flow cytometer.

BACKGROUND: The development of inexpensive small flow cytometers is recognized as an important goal for many applications ranging from medical uses in developing countries for disease diagnosis to use as an analytical platform in support of homeland defense. Although hydrodynamic focusing is highly effective at particle positioning, the use of sheath fluid increases assay cost and reduces instrument utility for field and autonomous remote operations. METHODS: This work presents the creation of a novel flow cell that uses ultrasonic acoustic energy to focus small particles to the center of a flowing stream for analysis by flow cytometry. Experiments using this flow cell are described wherein its efficacy is evaluated under flow cytometric conditions with fluorescent microspheres. RESULTS: Preliminary laboratory experiments demonstrate acoustic focusing of flowing 10-microm latex particles into a tight sample stream that is approximately 40 microm in diameter. Prototype flow cytometer measurements using an acoustic-focusing flow chamber demonstrated focusing of a microsphere sample to a central stream approximately 40 microm in diameter, yielding a definite fluorescence peak for the microspheres as compared with a broad distribution for unfocused microspheres. CONCLUSIONS: The flow cell developed here uses acoustic focusing, which inherently concentrates the sample particles to the center of the sample stream. This method could eliminate the need for sheath fluid, and will enable increased interrogation times for enhanced sensitivity, while maintaining high particle-analysis rates. The concentration effect will also enable the analysis of extremely dilute samples on the order of several particles per liter, at analysis rates of a few particles per second. Such features offer the possibility of a truly versatile low-cost portable flow cytometer for field applications.     

Heat Transfer Analysis of MHD Thin Film Flow of an Unsteady Second Grade Fluid Past a Vertical Oscillating Belt

This article aims to study the thin film layer flowing on a vertical oscillating belt. The flow is considered to satisfy the constitutive equation of unsteady second grade fluid. The governing equation for velocity and temperature fields with subjected initial and boundary conditions are solved by two analytical techniques namely Adomian Decomposition Method (ADM) and Optimal Homotopy Asymptotic Method (OHAM). The comparisons of ADM and OHAM solutions for velocity and temperature fields are shown numerically and graphically for both the lift and drainage problems. It is found that both these solutions are identical. In order to understand the physical behavior of the embedded parameters such as Stock number, frequency parameter, magnetic parameter, Brinkman number and Prandtl number, the analytical results are plotted graphically and discussed.     

A biomechanical approach to Ediacaran hypotheses: how to weed the Garden of Ediacara

Flume experiments and analytical approaches are undertaken to determine the stability of flat-lying Ediacaran organisms in fluid flow. Organisms such as Dickinsonia would not have been viable if reconstructed as free-living worms or syncytia. Models of flat-lying Ediacarans occupying a range of densities well beyond those of suggested modern analogs were dislodged by fluid flow taken as typical of Ediacaran paleoenvironments. Analytical tests suggest that parameters such as thickness of the organism and its coefficient of friction have little effect over the range of flows being considered here. These results lead to four non-exclusive interpretations of fossils of flat-lying Ediacarans: (1) The organisms have been transported from a quieter environment (in which case their pristine preservation is similarly puzzling); (2) they had a density approaching that of a flatfish; (3) they were secured to the substrate in some manner; (4) they lived partially or wholly beneath the substrate surface.