### Browsing by Author "Afkhami, Shahriar"

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- A comparison of viscoelastic stress wakes for two-dimensional and three-dimensional Newtonian drop deformations in a viscoelastic matrix under shearAfkhami, Shahriar; Yue, Pengtao; Renardy, Yuriko Y. (American Institute of Physics, 2009-07)
Show more A recent experimental study of a Newtonian drop suspended in a viscoelastic matrix undergoing simple shear displays a transient overshoot in drop deformation which is qualitatively similar to two-dimensional (2D) numerical simulation results. Despite the similarity, an interpretation in light of the 2D result is misleading because the overshoot is absent in the fully three-dimensional (3D) simulation. This motivates a study of regimes where qualitatively different and interesting features such as overshoots in deformation occur for a 2D drop but not for a 3D drop. The influence of viscoelastic "wakes" that emanate from the drop tips is reported. The viscoelastic wakes are larger and of higher magnitude in 3D than in 2D, and lead to more deformation in 3D. During drop evolution, the less deformed drop is found to be aligned more with the flow direction. As the drop-to-matrix viscosity ratio increases from 1 to past 3, drop rotation is promoted, with accompanying retraction when the capillary number is sufficiently high. Thus, a 3D overshoot in deformation is promoted with increasing viscosity ratio.Show more - Deformation of a hydrophobic ferrofluid droplet suspended in a viscous medium under uniform magnetic fieldsAfkhami, Shahriar; Tyler, A. J.; Renardy, Yuriko Y.; Renardy, Michael J.; St Pierre, T. G.; Woodward, R. C.; Riffle, Judy S. (Cambridge University Press, 2010-11)
Show more The effect of applied magnetic fields on the deformation of a biocompatible hydrophobic ferrofluid drop suspended in a viscous medium is investigated numerically and compared with experimental data. A numerical formulation for the time-dependent simulation of magnetohydrodynamics of two immiscible non-conducting fluids is used with a volume-of-fluid scheme for fully deformable interfaces. Analytical formulae for ellipsoidal drops and near-spheroidal drops are reviewed and developed for code validation. At low magnetic fields, both the experimental and numerical results follow the asymptotic small deformation theory. The value of interfacial tension is deduced from an optimal fit of a numerically simulated shape with the experimentally obtained drop shape, and appears to be a constant for low applied magnetic fields. At high magnetic fields, on the other hand, experimental measurements deviate from numerical results if a constant interfacial tension is implemented. The difference can be represented as a dependence of apparent interfacial tension on the magnetic field. This idea is investigated computationally by varying the interfacial tension as a function of the applied magnetic field and by comparing the drop shapes with experimental data until a perfect match is found. This estimation method provides a consistent correlation for the variation in interfacial tension at high magnetic fields. A conclusion section provides a discussion of physical effects which may influence the microstructure and contribute to the reported observations.Show more - Editorial for Special Issue “Drop, Bubble and Particle Dynamics in Complex Fluids”Afkhami, Shahriar; Yue, Pengtao (MDPI, 2020-01-02)
Show more The presence of drops, bubbles, and particles affects the behavior and response of complex multiphase fluids [...]Show more - Ferrofluids and magnetically guided superparamagnetic particles in flows: a review of simulations and modelingRenardy, Yuriko Y.; Afkhami, Shahriar (Springer Netherlands, 2017-08-18)
Show more Ferrofluids are typically suspensions of magnetite nanoparticles, and behave as a homogeneous continuum. The ability of the ferrofluid to respond to an external magnetic field in a controllable manner has made it emerge as a smart material in a variety of applications, such as seals, lubricants, electronics cooling, shock absorbers and adaptive optics. Magnetic nanoparticle suspensions have also gained attraction recently in a range of biomedical applications, such as cell separation, hyperthermia, MRI, drug targeting and cancer diagnosis. In this review, we provide an introduction to mathematical modeling of three problems: motion of superparamagnetic nanoparticles in magnetic drug targeting, the motion of a ferrofluid drop consisting of chemically bound nanoparticles without a carrier fluid, and the breakage of a thin film of a ferrofluid.Show more - Field-induced motion of ferrofluid droplets through immiscible viscous mediaAfkhami, Shahriar; Renardy, Yuriko Y.; Renardy, Michael J.; Riffle, Judy S.; St Pierre, T. (Cambridge University Press, 2008-09)
Show more The motion of a hydrophobic ferrofluid droplet placed in a viscous medium and driven by an externally applied magnetic field is investigated numerically in an axisymmetric geometry. Initially, the drop is spherical and placed at a distance away from the magnet. The governing equations are the Maxwell equations for a non-conducting flow, momentum equation and incompressibility. A numerical algorithm is derived to model the interface between a magnetized fluid and a non-magnetic fluid via a volume-of-fluid framework. A continuum-surface-force formulation is used to model the interfacial tension force as a body force, and the placement of the liquids is tracked by a volume fraction function. Three cases are Studied. First, where inertia is dominant, the magnetic Laplace number Is varied while the Laplace number is fixed. Secondly, where inertial effects are negligible, the Laplace number is varied while the magnetic Laplace number is fixed. In the third case, the magnetic Bond number and inertial effects are both small, and the magnetic force is of the order of the viscous drag force. The time taken by the droplet to travel through the medium and the deformations in the drop are investigated and compared with a previous experimental study and accompanying simpler model. The transit times are found to compare more favourably than with the simpler model.Show more - Modeling Superparamagnetic Particles in Blood Flow for Applications in Magnetic Drug TargetingRukshin, Iris; Mohrenweiser, Josef; Yue, Pengtao; Afkhami, Shahriar (MDPI, 2017-06-04)
Show more Magnetic drug targeting is a technique that involves the binding of medicine to magnetizable particles to allow for more specific transport to the target location. This has recently come to light as a method of drug delivery that reduces the disadvantages of conventional, systemic treatments. This study developed a mathematical model for tracking individual superparamagnetic nanoparticles in blood flow in the presence of an externally applied magnetic field. The model considers the magnetic attraction between the particles and the external magnet, influence of power law flow, diffusive interaction between the particles and blood, and random collisions with red blood cells. A stochastic system of differential equations is presented and solved numerically to simulate the paths taken by particles in a blood vessel. This study specifically focused on localized cancer treatment, in which a surface tumor is accessed through smaller blood vessels, which are more conducive to this delivery method due to slower flow velocities and smaller diameters. The probability of the particles reaching the tumor location is found to be directly dependent on ambient factors; thus, diffusion through Brownian motion and red blood cell collisions, different magnetic field and force models, blood viscosities, and release points are considered.Show more - Numerical investigation of elongated drops in a microfluidic T-junctionAfkhami, Shahriar; Leshansky, A. M.; Renardy, Yuriko Y. (American Institute of Physics, 2011-02)
Show more We present a combined numerical and asymptotic approach for modeling droplets in microchannels. The magnitude of viscous forces relative to the surface tension force is characterized by a capillary number, Ca, which is assumed to be small. The numerical results successfully capture existing asymptotic solutions for the motion of drops in unconfined and confined flows; examples include the analytic Stokes flow solution for a two-dimensional inviscid bubble placed in an unbounded parabolic flow field and asymptotic formulas for slender bubbles and drops in confined flows. An extensive investigation of the accuracy of the computations is presented to probe the efficacy of the methodology and algorithms. Thereafter, numerical simulations are presented for droplet breakup in a symmetric microfluidic T-junction. The results are shown to support a proposed mechanism for breakup, driven by a pressure drop in a narrow gap between the droplet and the outer channel wall, which was formally derived in the limit Ca(1/5) << 1 [A. M. Leshansky and L. M. Pismen, "Breakup of drops in a microfluidic T junction," Phys. Fluids 21, 023303 (2009)]. (C) 2011 American Institute of Physics.Show more - A volume-of-fluid formulation for the study of co-flowing fluids governed by the Hele-Shaw equationsAfkhami, Shahriar; Renardy, Yuriko Y. (American Institute of Physics, 2013-08)
Show more We present a computational framework to address the flow of two immiscible viscous liquids which co-flow into a shallow rectangular container at one side, and flow out into a holding container at the opposite side. Assumptions based on the shallow depth of the domain are used to reduce the governing equations to one of Hele-Shaw type. The distinctive feature of the numerical method is the accurate modeling of the capillary effects. A continuum approach coupled with a volume-of-fluid formulation for computing the interface motion and for modeling the interfacial tension in Hele-Shaw flows is formulated and implemented. The interface is reconstructed with a height-function algorithm. The combination of these algorithms is a novel development for the investigation of Hele-Shaw flows. The order of accuracy and convergence properties of the method are discussed with benchmark simulations. A microfluidic flow of a ribbon of fluid which co-flows with a second liquid is simulated. We show that for small capillary numbers of O(0.01), there is an abrupt change in interface curvature and focusing occurs close to the exit.Show more