Abstract: Solutal dispersion phenomena are associated with the nanoparticle-based drug delivery in the cardiovascular system to cure cardiovascular disorder. In the present problem, we explored the solutal transport for an unsteady blood flow through a microvessel with wall absorption. The rheology of blood is characterized by a two-fluid model similar to three-layer flow, namely, the core region, the intermediate region, and the peripheral region. The nature of the blood is considered as Casson fluid near the axis of the microvessel and Newtonian fluid close to the wall of the microvessel (at the intermediate and peripheral region). The peripheral region and the wall of the microvessel are permeable, and the permeability of the microvessel wall is defined by the Darcy–Brinkman model. The permeability of the inner surface of the microvessel is subjected to a slip condition at the surface. The stress-jump condition acts at the interface of the intermediate and peripheral region. The impact of the absorption parameter, velocity slip, yield stress, stress jump constant, nanoparticle volume fraction, and permeability on the velocity, exchange coefficient, convection coefficient, dispersion coefficient, and mean concentration is shown. It observed that the mean concentration boosts by the yield stress, nanoparticle volume fraction, and absorption parameters. The stress jump constant and permeability boost the convection coefficient, while the dispersion coefficient is restricted by the yield stress and absorption parameter.

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Topics: Microvessel (52%), Newtonian fluid (51%)

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5 results found

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On dispersion of solute in a hydromagnetic flow between two parallel plates with boundary absorption

Subham Dhar^{1}, Nanda Poddar^{1}, Kajal Kumar Mondal^{1}, Bijoy S. Mazumder^{2} +1 more•Institutions (3)

Abstract: It is well known that the widely applied Taylor diffusion model predicts the longitudinal distribution of tracers. Some recent studies indicate that the transverse concentration distribution is highly significant for large dispersion times. The present study describes an analytical approach to explore the two-dimensional concentration dispersion of a solute in the hydromagnetic laminar flow between two parallel plates with boundary absorption. The analytical expressions for the transverse concentration distribution and the mean concentration distribution of the tracers up to second-order approximation are derived using Mei's homogenization technique. The effects of the Peclet number and Hartmann number on the Taylor dispersivity are shown. It is also observed how the transverse and longitudinal mean concentration distributions are influenced by the magnetic effect, dispersion times, and boundary absorption. It is remarkable to note that the boundary absorption creates a large non-uniformity on the transverse concentration in a hydromagnetic flow between two parallel plates.

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Topics: Laminar flow (55%), Hartmann number (53%), Dispersion (optics) (52%) ... read more

1 Citations

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Abstract: A mathematical study on solute dispersion has been carried out in a stenotic tube having an absorptive wall—a study relevant to arterial pharmacokinetics. The rheology of blood is represented by Casson model and the solute is introduced at a point that is uniformly distributed over the cross section. The two-dimensional fluid flow is considered in this study. The governing equations of motion for the flow of Casson fluid, for the transport of solute in the lumen as well as in the tissue along with appropriate initial and boundary conditions, are numerically solved by leveraging the Marker and Cell method and the immersed boundary method in staggered grids formulation. Following the introduction of solute, we provide a comprehensive investigation of the influence of the wall absorption parameter (κ), yield stress (τy), and the severity of the stenosis (ξ) on the three transport coefficients, namely, the fraction of solute remaining in the fluid phase, the apparent convection velocity, and the dispersion coefficient. Simulated results predict the diminishing magnitudes of the transport coefficients with the increase in the values of yield stress and absorption parameter. Moreover, the transport coefficients and the axial mean concentration get significantly perturbed by the severity of the stenosis. Obtained results presented graphically concur with existing steady-state results in the literature. The present study would certainly be of some use in the case of targeted drug delivery and in treatment related to microvascular disease.

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Topics: Fluid dynamics (52%), Immersed boundary method (52%)

1 Citations

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Abstract: This contribution is to add to the timely celebration of Professor R. B. Bird's outstanding career and accomplishments. Following introductory remarks on material/fluid types, the paper reviews the concept of yield stress. Although yield stress has been studied for several decades, it is still very much a topic of current interest. This paper covers phenomenological yield stress models as well as experimental techniques to measure yield stress. It also discusses, in particular, problems associated with very low yield stress measurements that occur with bio-fluids such as blood.

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Abstract: Taylor's approach on the dispersion phenomenon is generalized for solute transport in a two-phase laminar flow of immiscible fluids in a slit. The reduced-order models for solute transport are derived using Reynolds decomposition and averaging techniques from which the exact analytical expressions for all elements of the dispersion tensor and the matrix of coefficients of the advection term are derived. It is shown that the dispersion tensor is generally not symmetric, and the asymmetry originates from the presence of an interface between the two fluids. We also discussed conditions at which the solute transport in a two-phase laminar flow in a slit lead to dispersion barrier, osmotic dispersion, and reverse dispersion. The results provide a thorough insight into modeling solute transport across an interface/film in two-phase stratified flows and find applications in the design and optimization of microfluidic devices where two fluids flow in laminar contact.

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Topics: Laminar flow (60%), Dispersion (optics) (56%), Stratified flows (54%) ... read more

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Abstract: The present study considers the mathematical modelling of unsteady non-Newtonian hydro-magnetic nanohemodynamics through a rigid cylindrical artery featuring two different stenoses (composite and irregular).
The Ostwald-De Waele power-law fluid model is adopted to simulate the non-Newtonian characteristics of
blood. Inspired by drug delivery applications for cardiovascular treatments, blood is considered doped with
a homogenous suspension of biocompatible nanoparticles. The arterial vessel exhibits the permeability
effect (lateral influx/efflux), and an external magnetic field is also applied in the radial direction to the flow.
A combination of the Buongiorno and Tiwari-Das nanoscale models is adopted. The strongly nonlinear
nature of the governing equations requires a robust numerical method, and therefore the finite difference
technique is deployed to solve the resulting equations. Validation of solutions for the pure blood case
(absence of nanoparticles) is included. Comprehensive solutions are presented for shear-thickening (n=1.5)
and shear-thinning (n=0.5) blood flow for the effects of crucial nanoscale thermophysical, solutal
parameters, and hydrodynamic parameters. Comparison of profiles (velocity, temperature, wall shear stress,
and flow rate) is also made for composite and irregular stenosis. Colour visualization of streamline plots is
included for pure blood and nano mediated blood both with and without applied magnetic field. The
inclusion of nanoparticles (Cu/blood) within blood increases the axial velocity of blood. By applying
external magnetic field in the radial direction, axial velocity is significantly damped whereas much less
dramatic alterations are computed in blood temperature and concentration profiles. The simulations are
relevant to the diffusion of nano-drugs in magnetic targeted treatment of stenosed arterial diseases.

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Topics: Blood flow (54%), Permeability (electromagnetism) (51%)

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46 results found

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Abstract: When a soluble substance is introduced into a fluid flowing slowly through a small-bore tube it spreads out under the combined action of molecular diffusion and the variation of velocity over the cross-section. It is shown analytically that the distribution of concentration produced in this way is centred on a point which moves with the mean speed of flow and is symmetrical about it in spite of the asymmetry of the flow. The dispersion along the tube is governed by a virtual coefficient of diffusivity which can be calculated from observed distributions of concentration. Since the analysis relates the longitudinal diffusivity to the coefficient of molecular diffusion, observations of concentration along a tube provide a new method for measuring diffusion coefficients. The coefficient so obtained was found, with potassium permanganate, to agree with that measured in other ways. The results may be useful to physiologists who may wish to know how a soluble salt is dispersed in blood streams.

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Topics: Taylor dispersion (58%), Molecular diffusion (58%), Diffusion (business) (55%) ... read more

4,286 Citations

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Abstract: Sir Geoffrey Taylor has recently discussed the dispersion of a solute under the simultaneous action of molecular diffusion and variation of the velocity of the solvent. A new basis for his analysis is presented here which removes the restrictions imposed on some of the parameters at the expense of describing the distribution of solute in terms of its moments in the direction of flow. It is shown that the rate of growth of the variance is proportional to the sum of the molecular diffusion coefficient, D, and the Taylor diffusion coefficient $\kappa $a$^{2}$U$^{2}$/D, where U is the mean velocity and a is a dimension characteristic of the cross-section of the tube. An expression for $\kappa $ is given in the most general case, and it is shown that a finite distribution of solute tends to become normally distributed.

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Topics: Taylor dispersion (58%), Molecular diffusion (54%), Diffusion (business) (53%)

2,228 Citations

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Axel R. Pries^{1}, Timothy W. Secomb^{1}, T Gessner^{1}, Markus Sperandio^{1} +2 more•Institutions (1)

Abstract: Resistance to blood flow through peripheral vascular beds strongly influences cardiovascular function and transport to tissue. For a given vascular architecture, flow resistance is determined by the rheological behavior of blood flowing through microvessels. A new approach for calculating the contribution of blood rheology to microvascular flow resistance is presented. Morphology (diameter and length), flow velocity, hematocrit, and topological position were determined for all vessel segments (up to 913) of terminal microcirculatory networks in the rat mesentery by intravital microscopy. Flow velocity and hematocrit were also predicted from mathematical flow simulations, in which the assumed dependence of flow resistance on diameter, hematocrit, and shear rate was optimized to minimize the deviation between measured and predicted values. For microvessels with diameters below approximately 40 microns, the resulting flow resistances are markedly higher and show a stronger dependence on hematocrit than previously estimated from measurements of blood flow in narrow glass tubes. For example, flow resistance in 10-microns microvessels at normal hematocrit is found to exceed that of a corresponding glass tube by a factor of approximately 4. In separate experiments, flow resistance of microvascular networks was estimated from direct measurements of total pressure drop and volume flow, at systemic hematocrits intentionally varied from 0.08 to 0.68. The results agree closely with predictions based on the above-optimized resistance but not with predictions based on glass-tube data. The unexpectedly high flow resistance in small microvessels may be related to interactions between blood components and the inner vessel surface that do not occur in smooth-walled tubes.

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Topics: Fåhræus effect (66%), Fåhræus–Lindqvist effect (62%), Blood viscosity (58%) ... read more

550 Citations

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Abstract: The problem of non-Newtonian and nonlinear blood flow through a stenosed artery is solved numerically where the non-Newtonian rheology of the flowing blood is characterised by the generalised Power-law model. An improved shape of the time-variant stenosis present in the tapered arterial lumen is given mathematically in order to update resemblance to the in vivo situation. The vascular wall deformability is taken to be elastic (moving wall), however a comparison has been made with nonlinear visco-elastic wall motion. Finite difference scheme has been used to solve the unsteady nonlinear Navier–Stokes equations in cylindrical coordinates system governing flow assuming axial symmetry under laminar flow condition so that the problem effectively becomes two-dimensional. The present analytical treatment bears the potential to calculate the rate of flow, the resistive impedance and the wall shear stress with minor significance of computational complexity by exploiting the appropriate physically realistic prescribed conditions. The model is also employed to study the effects of the taper angle, wall deformation, severity of the stenosis within its fixed length, steeper stenosis of the same severity, nonlinearity and non-Newtonian rheology of the flowing blood on the flow field. An extensive quantitative analysis is performed through numerical computations of the desired quantities having physiological relevance through their graphical representations so as to validate the applicability of the present model.

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Topics: Laminar flow (55%), Flow (mathematics) (51%)

251 Citations

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Abstract: THE viscometry of human blood has been represented by a number of empirical equations. Their usefulness has been limited to relatively narrow ranges of shear rate. Among the equations suggested, Casson's equation has been used for calculating the shear strength of blood and for describing its viscometry at shear rates below 5 sec−1 (refs. 1 and 4) (equation 1): where τ is shear stress, γ is shear rate, K is Casson viscosity, C is shear strength of suspension.

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Topics: Shear rate (65%), Rheometer (64%), Shear stress (60%) ... read more

199 Citations