arXiv subjects

S. Afkhami

Publications and source records attributed to S. Afkhami.

8 recordsLinked to original sources

arXiv2021

Numerical Simulation of Superparamagnetic Nanoparticle Motion in Blood Vessels for Magnetic Drug Delivery

A numerical model is developed for the motion of superparamagnetic nanoparticles in a non-Newtonian blood flow under the influence of a magnetic field. The rheological properties of blood are modeled by the Carreau flow and viscosity, and the stochastic effects of Brownian motion and red blood cell collisions are considered. The model is validated with existing data and good agreement with experimental results is shown. The effectiveness of magnetic drug delivery in various blood vessels is assessed and found to be most successful in arterioles and capillaries. A range of magnetic field strengths are modeled using equations for both a bar magnet and a point dipole: it is shown that the bar magnet is effective at capturing nanoparticles in limited cases while the point dipole is highly effective across a range of conditions. A parameter study is conducted to show the effects of changing the dipole moment, the distance from the magnet to the blood vessel, and the initial release point of the nanoparticles. The distance from the magnet to the blood vessel is shown to play a significant role in determining nanoparticle capture rate. The optimal initial release position is found to be located within the tumor radius in capillaries and arterioles to prevent rapid diffusion to the edges of the blood vessel prior to arriving at the tumor, and near the edge of the magnet when a bar magnet is used.

physics.bio-ph↗

arXiv2018

Transition in a numerical model of contact line dynamics and forced dewetting

We investigate the transition to a Landau-Levich-Derjaguin film in forced dewetting using a quadtree adaptive solution to the Navier-Stokes equations with surface tension. We use a discretization of the capillary forces near the receding contact line that yields an equilibrium for a specified contact angle $θ_Δ$ called the numerical contact angle. Despite the well-known contact line singularity, dynamic simulations can proceed without any explicit additional numerical procedure. We investigate angles from $15^\circ$ to $110^\circ$ and capillary numbers from $0.00085$ to $0.2$ where the mesh size $Δ$ is varied in the range of $0.0035$ to $0.06$ of the capillary length $l_c$. To interpret the results, we use Cox's theory which involves a microscopic distance $r_m$ and a microscopic angle $θ_e$. In the numerical case, the equivalent of $θ_e$ is the angle $θ_Δ$ and we find that Cox's theory also applies. We introduce the scaling factor or gauge function $ϕ$ so that $r_m = Δ/ϕ$ and estimate this gauge function by comparing our numerics to Cox's theory. The comparison provides a direct assessment of the agreement of the numerics with Cox's theory and reveals a critical feature of the numerical treatment of contact line dynamics: agreement is poor at small angles while it is better at large angles. This scaling factor is shown to depend only on $θ_Δ$ and the viscosity ratio $q$. In the case of small $θ_e$, we use the prediction by Eggers [Phys. Rev. Lett., vol. 93, pp 094502, 2004] of the critical capillary number for the Landau-Levich-Derjaguin forced dewetting transition. We generalize this prediction to large $θ_e$ and arbitrary $q$ and express the critical capillary number as a function of $θ_e$ and $r_m$. An analogy can be drawn between $r_m$ and the numerical slip length.

physics.flu-dyn↗

arXiv2018

Breakup of finite-size liquid filaments: Transition from no-breakup to breakup including substrate effects

This work studies the breakup of finite-size liquid filaments, when also including substrate effects, using direct numerical simulations. The study focuses on the effects of three parameters: Ohnesorge number, the ratio of the viscous forces to inertial and surface tension forces, the liquid filament aspect ratio, and where there is a substrate, a measure of the fluid slip on the substrate, i.e. slip length. Through these parameters, it is determined whether a liquid filament breaks up during the evolution toward its final equilibrium state. Three scenarios are identified: a collapse into a single droplet, the breakup into one or multiple droplets, and recoalescence into a single droplet after the breakup (or even possibly another breakup after recoalescence). The results are compared with the ones available in the literature for free-standing liquid filaments. The findings show that the presence of the substrate promotes breakup of the filament. The effect of the degree of slip on the breakup is also discussed. The parameter domain regions are comprehensively explored when including the slip effects. An experimental case is also carried out to illustrate the collapse and breakup of a finite-size silicon oil filament supported on a substrate, showcasing a critical length of the breakup in a physical configuration. Finally, direct numerical simulations reveal striking new details into the breakup pattern for low Ohnesorge numbers, where the dynamics are fast and the experimental imaging is not available; our results therefore significantly extend the range of Ohnesorge number over which filament breakup has been considered.

physics.flu-dyn↗

arXiv2017

Ferrofluids and magnetically guided superparamagnetic particles in flows: A review of simulations and modeling

Ferrofluids are typically suspensions of magnetite nanoparticles, and behave as a homogeneous continuum. The production of nanoparticles with a narrow size distribution and the achievement of colloidal stability are important technological issues. 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.

physics.flu-dyn↗

arXiv2016

A numerical approach for the direct computation of flows including fluid-solid interaction: modeling contact angle, film rupture, and dewetting

In this paper, we present a computationally efficient method for including fluid-solid interactions into direct numerical simulations of the Navier-Stokes equations. This method is found to be as powerful as our earlier formulation [J. Comp. Phys., vol. 249: 243 (2015)], while outperforming the earlier method in terms of computational efficiency. The performance and efficacy of the presented method are demonstrated by computing contact angles of droplets at equilibrium. Furthermore, we study the instability of films due to destabilizing fluid-solid interactions, and discuss the influence of contact angle and inertial effects on film breakup. In particular, direct simulation results show an increase in the final characteristic length scales when compared to the predictions of a linear stability analysis, suggesting significant influence of nonlinear effects. Our results also show that emerging length scales differ, depending on a number of physical dimensions considered.

physics.flu-dyn↗

arXiv2016

On the capillary self-focusing in a microfluidic system

A computational framework is developed to address capillary self-focusing in Step Emulsification. The microfluidic system consists of a single shallow and wide microchannel that merges into a deep reservoir. A continuum approach coupled with a volume of fluid method is used to model the capillary self-focusing effect. The original governing equations are reduced using the Hele-Shaw approximation. We show that the interface between the two fluids takes the shape of a neck narrowing in the flow direction just before entering the reservoir, in agreement with our experimental observations. Our computational model relies on the assumption that the pressure at the boundary, where the fluid exits into the reservoir, is the uniform pressure in the reservoir. We investigate this hypothesis by comparing the numerical results with experimental data. We conjecture that the pressure boundary condition becomes important when the width of the neck is comparable to the depth of the microchannel. A correction to the exit pressure boundary condition is then proposed, which is determined by comparison with experimental data. We also present the experimental observations and the numerical results of the transitions of breakup regimes.

physics.flu-dyn↗

arXiv2014

Capillary focusing close to a topographic step: Shape and instability of confined liquid filaments

Step-emulsification is a microfluidic technique for droplet generation which relies on the abrupt decrease of confinement of a liquid filament surrounded by a continuous phase. A striking feature of this geometry is the transition between two distinct droplet breakup regimes, the "step-regime" and "jet-regime", at a critical capillary number. In the step-regime, small and monodisperse droplets break off from the filament directly at a topographic step, while in the jet-regime a jet protrudes into the larger channel region and large plug-like droplets are produced. We characterize the breakup behavior as a function of the filament geometry and the capillary number and present experimental results on the shape and evolution of the filament for a wide range of capillary numbers in the jet-regime. We compare the experimental results with numerical simulations. Assumptions based on the smallness of the depth of the microfluidic channel allow to reduce the governing equations to the Hele-Shaw problem with surface tension. The full nonlinear equations are then solved numerically using a volume-of-fluid based algorithm. The computational framework also captures the transition between both regimes, offering a deeper understanding of the underlying breakup mechanism.

physics.flu-dyn↗

arXiv2013

Numerical simulation of ejected molten metal-nanoparticles liquefied by laser irradiation: Interplay of geometry and dewetting

Metallic nanoparticles, liquefied by fast laser irradiation, go through a rapid change of shape attempting to minimize their surface energy. The resulting nanodrops may be ejected from the substrate when the mechanisms leading to dewetting are sufficiently strong, as in the experiments involving gold nanoparticles [Habenicht et al., Science 309, 2043 (2005)]. We use a direct continuum-level approach to accurately model the process of liquid nanodrop formation and the subsequent ejection from the substrate. Our computations show a significant role of inertial effects and an elaborate interplay of initial geometry and wetting properties: e.g., we can control the direction of ejection by prescribing appropriate initial shape and/or wetting properties. The basic insight regarding ejection itself can be reached by considering a simple effective model based on an energy balance. We validate our computations by comparing directly with the experiments specified above involving the length scales measured in hundreds of nanometers, and with molecular dynamics simulations on much shorter scales measured in tens of atomic diameters, as in [M. Fuentes-Cabrera et al., Phys. Rev. E 83, 041603 (2011)]. The quantitative agreement, in addition to illustrating how to controlling particle ejection, shows utility of continuum-based simulation in describing dynamics on nanoscale quantitatively, even in a complex setting as considered here.

physics.flu-dyn↗