This article describes the equilibrium shape of a liquid drop under applied fields such as gravity and electrical fields, taking into account material properties such as dielectric constants, resistivities, and surface tension coefficients. The analysis is based on an energy minimization framework. A rigorous and exact link is provided between the energy function corresponding to any given physical phenomena, and the resulting shape and size dependent force term in Young's equation. In particular, the framework shows that a physical effect, such as capacitive energy storage in the liquid, will lead to 1/R ''line-tension''-type terms if and only if the energy of the effect is proportional to the radius of the liquid drop: EϰR. The effect of applied electric fields on shape change is analyzed. It is shown that a dielectric solid and a perfectly conducting liquid are all that is needed to exactly recover the Young-Lippmann equation. A dielectric liquid on a conducting solid gives rise to line tension terms. Finally, a slightly resistive liquid on top of a dielectric, highly resistive solid gives rise to contact angle saturation and accurately matches the experimental data that we observe in our electro-wetting-on-dielectric devices.

In magnetic drug delivery, therapeutic magnetizable particles are typically injected into the blood stream and magnets are then used to concentrate them to disease locations. The behavior of such particles in-vivo is complex and is governed by blood convection, diffusion (in blood and in tissue), extravasation, and the applied magnetic fields. Using physical first-principles and a sophisticated vessel-membrane-tissue (VMT) numerical solver, we comprehensively analyze in detail the behavior of magnetic particles in blood vessels and surrounding tissue. For any blood vessel (of any size, depth, and blood velocity) and tissue properties, particle size and applied magnetic fields, we consider a Krogh tissue cylinder geometry and solve for the resulting spatial distribution of particles. We find that there are three prototypical behaviors (blood velocity dominated, magnetic force dominated, and boundary-layer formation) and that the type of behavior observed is uniquely determined by three non-dimensional numbers (the magneticRichardson number, mass Péclet number, and Renkin reduced diffusion coefficient). Plots and equations are provided to easily read out which behavior is found under which circumstances (Figures 5,6,7,and 8). We compare our results to previously published in-vitro and in-vivo magnetic drug delivery experiments. Not only do we find excellent agreement between our predictions and prior experimental observations, but we are also able to qualitatively and quantitatively explain behavior that was previously not understood. IntroductionMagnetic drug targeting refers to the attachment of therapeutics to magnetizable particles, and then applying magnetic fields to concentrate them to disease locations such as to solid tumors, regions of infection, or blood clots [4,[8][9][10][11][12][13][14]. Though in some cases the magnetizable particles can be introduced into the body outside the blood flow, e.g. as in magnetic treatment of the inner-ear where a small gel containing nano-particles is placed on the round window membrane [19,20], usually ferromagnetic particles are injected into a vein or artery [4][5][6][7]9,13,16,[21][22][23][24][25][26][27][28][29]. Particles so injected will circulate throughout the vasculature as the applied magnetic field is used to attempt confinement at target locations. Two main considerations arise from the in-vivo use of these particles. First, the particles must be small * Corresponding author, alek@umd.edu.Publisher's Disclaimer: This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. NIH Public Access NIH-PA Author ManuscriptNIH-PA Author Manuscript NIH-PA...

Abstract-This paper discusses the modeling and simulation of a parallel-plate Electrowetting On Dielectric (EWOD) device that moves fluid droplets through surface tension effects. We model the fluid dynamics by using Hele-Shaw type equations with a focus on including the relevant boundary phenomena. Specifically, we show that contact angle saturation and hysteresis are needed to predict the correct shape and time scale of droplet motion. We demonstrate this by comparing our simulation to experimental data for a splitting droplet. Without these boundary effects, the simulation shows the droplet splitting into three pieces instead of two and the motion is over 15 times faster than the experiment. We then show how including the saturation characteristics of the device, and a simple model of contact angle hysteresis, allows the simulation to better predict the splitting experiment. The match is not perfect and suffers mainly because contact line pinning is not included. This is followed by a comparison between our simulation, whose parameters are now frozen, and a new experiment involving bulk droplet motion. Our numerical implementation uses the level set method, is fast, and is being used to design algorithms for the precise control of microdroplet motion, mixing, and splitting.[1439]

The principle of magnetic drug targeting, wherein therapy is attached to magnetically responsive carriers and magnetic fields are used to direct that therapy to disease locations, has been around for nearly two decades. Yet our ability to safely and effectively direct therapy to where it needs to go, for instance to deep tissue targets, remains limited. To date, magnetic targeting methods have not yet passed regulatory approval or reached clinical use. Below we outline key challenges to magnetic targeting, which include designing and selecting magnetic carriers for specific clinical indications, safely and effectively reaching targets behind tissue and anatomical barriers, real-time carrier imaging, and magnet design and control for deep and precise targeting. Addressing these challenges will require interactions across disciplines. Nanofabricators and chemists should work with biologists, mathematicians and engineers to better understand how carriers move through live tissues and how to optimize carrier and magnet designs to better direct therapy to disease targets. Clinicians should be involved early on and throughout the whole process to ensure the methods that are being developed meet a compelling clinical need and will be practical in a clinical setting. Our hope is that highlighting these challenges will help researchers translate magnetic drug targeting from a novel concept to a clinically-available treatment that can put therapy where it needs to go in human patients.