Magnetic Drug Targeting in the Permeable Blood Vessel—The Effect of Blood Rheology

2010 ◽  
Vol 1 (2) ◽  
Author(s):  
S. Shaw ◽  
P. V. S. N. Murthy
Keyword(s):  
Newtonian Fluid ◽  
Volume Fraction ◽  
Fluid Model ◽  
Fluid Velocity ◽  
Blood Rheology ◽  
Present Problem ◽  
Magnetic Drug Targeting ◽  
Magnetic Targeting ◽  
Tumor Microvasculature ◽  
Embedded Nanoparticles

The present investigation deals with finding the trajectories of the drug dosed magnetic carrier particle in a microvessel, which is subjected to the external magnetic field. We consider the physical model that was given in the work of Furlani and Furlani (2007, “A Model for Predicting Magnetic Targeting of Multifunctional Particles in the Microvasculature,” J. Magn. Magn. Mater., 312, pp. 187–193), but deviating by taking the non-Newtonian fluid model for the blood in the permeable microvessel. Both the Herschel–Bulkley fluid and Casson models are considered to analyze the present problem. The expression for the fluid velocity in the permeable microvessel is obtained using the analogy given by Decuzzi et al. (2006, “The Effective Dispersion of Nanovectors Within the Tumor Microvasculature,” Ann. Biomed. Eng., 34, pp. 633–641) first. Then the expression for the fluidic force for the carrier particle traversing in the non-Newtonian fluid is obtained. Several factors that influence the magnetic targeting of the carrier particles in the microvasculature, such as the permeability of the inner wall, size of the carrier particle, the volume fraction of embedded nanoparticles, and the diameter of the microvessel are considered in the present problem. The trajectories of the carrier particles are found in both invasive and noninvasive targeting systems. A comparison is made between the trajectories in these cases in both the Casson and Herschel–Bulkley fluid models. The present results for the permeable microvessel are compared with the impermeable inner wall trajectories given by Shaw et al. (2010, “Effect of Non-Newtonian Characteristics of Blood on Magnetic Targeting in the Impermeable Micro Vessel,” J. Magn. Magn. Mater., 322, pp. 1037–1043). Also, a prediction of the capture of therapeutic magnetic nanoparticle in the human permeable microvasculature is made for different radii and volume fractions in both the invasive and noninvasive cases.

scholarly journals Hydrodynamics Interactions of Metachronal Waves on Particulate-Liquid Motion through a Ciliated Annulus: Application of Bio-Engineering in Blood Clotting and Endoscopy

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 532 ◽  
Author(s):  
Muhammad Mubashir Bhatti ◽  
Asmaa F. Elelamy ◽  
Sadiq M. Sait ◽  
Rahmat Ellahi
Keyword(s):  
Newtonian Fluid ◽  
Volume Fraction ◽  
Fluid Model ◽  
Flow Behavior ◽  
Blood Clot ◽  
Fluid Velocity ◽  
Particle Volume Fraction ◽  
Particle Volume ◽  
Entire Cross Section ◽  
Bio Engineering

This study deals with the mass transport phenomena on the particle-fluid motion through an annulus. The non-Newtonian fluid propagates through a ciliated annulus in the presence of two phenomenon, namely (i) endoscopy, and (ii) blood clot. The outer tube is ciliated. To examine the flow behavior we consider the bi-viscosity fluid model. The mathematical modeling has been formulated for small Reynolds number to examine the inertia free flow. The purpose of this assumption is that wavelength-to-diameter is maximal, and the pressure could be considerably uniform throughout the entire cross-section. The resulting equations are analytically solved, and exact solutions are given for particle- and fluid-phase profiles. Computational software Mathematica has been used to evaluate both the closed-form and numerical results. The graphical behavior across each parameter has been discussed in detail and presented with graphs. The trapping mechanism is also shown across each parameter. It is noticed clearly that particle volume fraction and the blood clot reveal converse behavior on fluid velocity; however, the velocity of the fluid reduced significantly when the fluid behaves as a Newtonian fluid. Schmidt and Soret numbers enhance the concentration mechanism. Furthermore, more pressure is required to pass the fluid when the blood clot appears.

The Effect of Shape Factor on the Magnetic Targeting in the Permeable Microvessel With Two-Phase Casson Fluid Model

2011 ◽  
Vol 2 (4) ◽  
Author(s):  
Sachin Shaw ◽  
P. V. S. N. Murthy
Keyword(s):  
Magnetic Field ◽  
Volume Fraction ◽  
Fluid Model ◽  
Casson Fluid ◽  
Magnetic Drug Targeting ◽  
Magnetic Targeting ◽  
Two Phase ◽  
Coupled Equations ◽  
Casson Fluid Model ◽  
Phase Fluid

The present investigation deals with magnetic drug targeting in a microvessel of radius 5 μm using two-phase fluid model. The microvessel is divided into the endothelial glycocalyx layer wherein the blood obeys Newtonian character and a core region wherein the blood obeys the non-Newtonian Casson fluid character. The carrier particles, bound with nanoparticles and drug molecules, are injected into the vascular system upstream from the malignant tissue and are captured at the tumor site using a local applied magnetic field near the tumor position. Brinkman model is used to characterize the permeable nature of the inner wall of the microvessel. The expressions for the fluidic force for the carrier particle traversing in the two-phase fluid in the microvessel and the magnetic force due to the external magnetic field are obtained. Several factors that influence the magnetic targeting of the carrier particles in the microvasculature, such as the size and shape of the carrier particle, the volume fraction of embedded magnetic nanoparticles, and the distance of separation of the magnet from the axis of the microvessel, are considered in the present problem. The system of coupled equations is solved to obtain the trajectories of the carrier particle in the noninvasive case.

Mathematical Model on Magnetic Drug Targeting in a Permeable Microvessel

2013 ◽  
Author(s):  
S. Shaw ◽  
P. Sibanda ◽  
P. V. S. N. Murthy
Keyword(s):  
Magnetic Field ◽  
Mathematical Model ◽  
Magnetic Nanoparticles ◽  
Volume Fraction ◽  
Therapeutic Agents ◽  
Core Material ◽  
Magnetic Drug Targeting ◽  
Magnetic Targeting ◽  
Malignant Tissue

A mathematical model is presented for predicting magnetic targeting of multifunctional carrier particles that deliver therapeutic agents to malignant tissue in vivo. These particles consist of a nonmagnetic core material that contains embedded magnetic nanoparticles and therapeutic agents such as photodynamic sensitizers. For in vivo therapy, the particles are injected into the micro vascular system upstream from malignant tissue, and captured at the tumor using an applied magnetic field. In this paper, a mathematical model is developed for predicting noninvasive magnetic targeting of therapeutic carrier particles in a micro vessel. The flow of blood in the micro vessel is described by a two phase Herschel-Bulkley fluid model. The Brinkmann model is used to characterize the permeable nature of the inner wall of the micro-vessel. The fluidic force on the carrier traversing the micro-vessel and the magnetic force due to the external magnetic field is taken into account. The model enables rapid parametric analysis of magnetic targeting as a function of key variables including the size of the carrier particle, the properties and volume fraction of the imbedded magnetic nanoparticles, the properties of the magnet, the micro vessel and the permeability of the micro vessel.

scholarly journals Mathematical Analysis of Casson Fluid Model for Blood Rheology in Stenosed Narrow Arteries

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
J. Venkatesan ◽  
D. S. Sankar ◽  
K. Hemalatha ◽  
Yazariah Yatim
Keyword(s):  
Skin Friction ◽  
Yield Stress ◽  
Newtonian Fluid ◽  
Mathematical Analysis ◽  
Fluid Model ◽  
Blood Rheology ◽  
Casson Fluid ◽  
Casson Fluid Model ◽  
Stenosed Artery ◽  
Normal Artery

The flow of blood through a narrow artery with bell-shaped stenosis is investigated, treating blood as Casson fluid. Present results are compared with the results of the Herschel-Bulkley fluid model obtained by Misra and Shit (2006) for the same geometry. Resistance to flow and skin friction are normalized in two different ways such as (i) with respect to the same non-Newtonian fluid in a normal artery which gives the effect of a stenosis and (ii) with respect to the Newtonian fluid in the stenosed artery which spells out the non-Newtonian effects of the fluid. It is found that the resistance to flow and skin friction increase with the increase of maximum depth of the stenosis, but these flow quantities (when normalized with non-Newtonian fluid in normal artery) decrease with the increase of the yield stress, as obtained by Misra and Shit (2006). It is also noticed that the resistance to flow and skin friction increase (when normalized with Newtonian fluid in stenosed artery) with the increase of the yield stress.

scholarly journals Significance of MHD Radiative Non-Newtonian Nanofluid Flow towards a Porous Channel: A Framework of the Casson Fluid Model

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
N. Thamaraikannan ◽  
S. Karthikeyan ◽  
Dinesh Kumar Chaudhary
Keyword(s):  
Volume Fraction ◽  
Fluid Model ◽  
Perturbation Technique ◽  
Fluid Velocity ◽  
Darcy Number ◽  
Casson Fluid ◽  
Temperature Fields ◽  
Porous Channel ◽  
Flow Parameters ◽  
Casson Fluid Model

The effect of various parameters in the unsteady pulsating flow of radiative hydromagnetic Casson nanofluid through a porous channel is investigated. The governing equations were nondimensionalized by applying suitable transformations. The perturbation technique was employed to solve the resulting similarity equations. The velocity and temperature fields are illustrated for several pertinent flow parameters. The fluid velocity has been enhancing for higher values of the frequency parameter, Casson fluid parameter, nanoparticle volume fraction, and Darcy number. The reverse impact is observed for larger values of the Hartmann number. The result reveals that adding the nanoparticles has enhanced the heat transfer of the base fluid as the nanoparticles increase the heat conductivity. Furthermore, it is noticed that the temperature profile decreases rapidly for higher values of the cross Reynolds number and the radiation parameter. Finally, an excellent agreement between the current results and previous results is obtained by comparing with the available limiting results in the literature.

Fluidization by lift of 300 circular particles in plane Poiseuille flow by direct numerical simulation

2001 ◽  
Vol 438 ◽  
pp. 101-128 ◽  
Author(s):  
HYOUNG G. CHOI ◽  
DANIEL D. JOSEPH
Keyword(s):  
Reynolds Number ◽  
Single Particle ◽  
Poiseuille Flow ◽  
Volume Fraction ◽  
Effective Properties ◽  
Fluid Model ◽  
Fluid Velocity ◽  
Density Ratio ◽  
Steady Motion ◽  
Lift Off

We study the transport of a slurry of heavier-than-liquid circular particles in a plane pressure-driven flow in a direct simulation. The flow is calculated in a periodic domain containing 300 circular particles. The study leads to the concept of fluidization by lift in which all the particles are suspended by lift forces against gravity perpendicular to the flow. The study is framed as an initial-value problem in which a closely packed cubic array of particles resting on the bottom of the channel is lifted into suspension. All the details of the flow are resolved numerically without model assumptions. The fluidization of circular particles first involves bed inflation in which liquid is driven into the bed by high pressure at the front and low pressure at the back of each circle in the top row. This kind of bed inflation occurs even at very low Reynolds numbers but it takes more time for the bed to inflate as the Reynolds number is reduced. It appears that the bed will not inflate if the shear Reynolds number is below the critical value for single particle lift-off. The flows with a single particle are completely determined by a shear Reynolds number and a gravity parameter when the density ratio and aspect ratio parameters are specified. In the multi-particle case, the volume fraction and distribution also matters. The transition to a fully fluidized slurry by waves is discussed.An analytical model of the steady motion of a single particle dragged forward in a Poiseuille flow is derived and compared with a simulation. The undisturbed fluid velocity is always larger than the particle velocity, producing a fluid hold-up. The effect of the hold-up in the many particle case is to greatly reduce the velocity of the mixture which may be described by a two-fluid model in which the solid laden mixture is regarded as a second fluid with effective properties.

Effects of Transpiration and Internal Heat Generation/Absorption on the Unsteady Flow of a Maxwell Fluid at a Stretching Surface

2012 ◽  
Vol 79 (4) ◽  
Author(s):  
Swati Mukhopadhyay ◽  
Kuppalapalle Vajravelu
Keyword(s):  
Differential Equations ◽  
Newtonian Fluid ◽  
Fluid Model ◽  
Fluid Velocity ◽  
Internal Heat ◽  
Maxwell Fluid ◽  
Shear Thinning ◽  
Stretching Surface ◽  
Flow Features ◽  
Two Dimensional Flow

The effect of transpiration on unsteady two-dimensional flow of an MHD non-Newtonian Maxwell fluid over a stretching surface in the presence of a heat source/sink is investigated. The upper convected Maxwell fluid model is used to characterize the non-Newtonian fluid behavior. Using a similarity transformation the governing partial differential equations of the problem are reduced to a system of ordinary differential equations (ODEs), and the ODEs are solved numerically by a shooting method. The flow features and the heat transfer characteristics are analyzed and discussed in detail for several sets of values of the governing parameters. Though the velocity of the fluid initially decreases with increasing unsteady parameter but it increases finally. Quite the opposite is true with the temperature. Furthermore, the velocity of the fluid decreases with an increasing magnetic or Maxwell parameter. But the temperature is enhanced with an increasing Maxwell parameter. It is observed that the effect of the transpiration is to decrease the fluid velocity as well as the temperature. The results obtained reveal many interesting behaviors that warrant further study of the equations related to non-Newtonian fluid phenomena, especially the shear-thinning phenomena. Shear thinning reduces the wall shear stress.

A Complete Solution for Thermal-Elastohydrodynamic Lubrication of Line Contacts Using Circular Non-Newtonian Fluid Model

1992 ◽  
Vol 114 (3) ◽  
pp. 540-551 ◽  
Author(s):  
Hsing-Sen S. Hsiao ◽  
Bernard J. Hamrock
Keyword(s):  
Boundary Conditions ◽  
Newtonian Fluid ◽  
Energy Equation ◽  
Control Volume ◽  
Fluid Model ◽  
Complete Solution ◽  
Circular Model ◽  
Line Contacts ◽  
Stress Boundary Conditions ◽  
Stress Boundary

A complete solution is obtained for elastohydrodynamically lubricated conjunctions in line contacts considering the effects of temperature and the non-Newtonian characteristics of lubricants with limiting shear strength. The complete fast approach is used to solve the thermal Reynolds equation by using the complete circular non-Newtonian fluid model and considering both velocity and stress boundary conditions. The reason and the occasion to incorporate stress boundary conditions for the circular model are discussed. A conservative form of the energy equation is developed by using the finite control volume approach. Analytical solutions for solid surface temperatures that consider two-dimensional heat flow within the solids are used. A straightforward finite difference method, successive over-relaxation by lines, is employed to solve the energy equation. Results of thermal effects on film shape, pressure profile, streamlines, and friction coefficient are presented.

Vibration and Stability Behaviour of Sandwiched Viscoelastic Pipes Conveying a Non-Newtonian Fluid

2010 ◽  
Author(s):  
Vincent O. S. Olunloyo ◽  
Charles A. Osheku ◽  
Sidikat I. Kuye
Keyword(s):  
Newtonian Fluid ◽  
Fluid Velocity ◽  
Linear Equations ◽  
Steel Pipes ◽  
Flow Parameters ◽  
Internal Fluid ◽  
Reduction Mechanisms ◽  
Internal Fluid Flow ◽  
Flow Induced Vibrations ◽  
Flow Variables

Internal fluid flow parameters in conjunction with elastomechanical properties of conveyance systems have significantly modulated flow induced vibrations in pipeline and riser systems. Recent advances on the mechanics of sandwich elastic systems as effective vibration and noise reduction mechanisms have simulated the possibility of replacing traditional steel pipes with sandwich pipes in deepwater environment. The dynamic behaviour and stability of sandwich elastic pipes conveying a non-Newtonian fluid are investigated in this paper. For this problem, a set of generalised non-linear equations governing the vibration of sandwich pipes held together in pressurised environment and conveying a non-Newtonian fluid is presented. By linearizing the governing partial differential equation matching the problem physics, under slight perturbation of the internal fluid velocity and other flow variables closed form analytical results for the system dual natural frequencies and stability under external excitation are computed for field designs and applications. Results show that for a given length of pipe, beyond the critical velocity, instability increases with the velocity of conveyance.

Permeability in the Mushy Zone

2010 ◽  
Vol 649 ◽  
pp. 399-408 ◽  
Author(s):  
R.G. Erdmann ◽  
D.R. Poirier ◽  
A.G. Hendrick
Keyword(s):  
Mushy Zone ◽  
Volume Fraction ◽  
Primary Dendrite ◽  
Fluid Velocity ◽  
Interdendritic Liquid ◽  
Creeping Flow ◽  
Liquid Region ◽  
Local Volume ◽  
Local Volume Fraction ◽  
Deterministic Function

When modeled at macroscopic length scales, the complex dendritic network in the solid-plus-liquid region of a solidifying alloy (the “mushy zone”) has been modeled as a continuum based on the theory of porous media. The most important property of a porous medium is its permeability, which relates the macroscopic pressure gradient to the throughput of fluid flow. Knowledge of the permeability of the mushy zone as a function of the local volume-fraction of liquid and other morphological parameters is thus essential to successfully modeling the flow of interdendritic liquid during alloy solidification. In current continuum models, the permeability of the mushy zone is given as a deterministic function of (1) the local volume fraction of liquid and (2) a characteristic length scale such as the primary dendrite arm spacing or the reciprocal of the specific surface area of the solid-liquid interface. Here we first provide a broad overview of the experimental data, mesoscale numerical flow simulations, and resulting correlations for the deterministic permeability of both equiaxed and columnar mushy zones. A extended view of permeability in mushy zones which includes the stochastic nature of permeability is discussed. This viewpoint is the result of performing extensive numerical simulations of creeping flow through random microstructures. The permeabilities obtained from these simulations are random functions with spatial autocorrelation structures, and variations in the local permeability are shown to have dramatic effects on the flow patterns observed in such microstructures. Specifically, it is found that “lightning-like” patterns emerge in the fluid velocity and that the flows in such geometries are strongly sensitive to small variations in the solid structure. We conclude with a comparison of deterministic and stochastic permeabilities which suggests the importance of incorporating stochastic descriptions of the permeability of the mushy zone in solidification modeling.

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