Drug targeting promises to substantially enhance future therapies, for example through the focussing of chemotherapeutic drugs at the site of a tumor, thus reducing the exposure of healthy tissue to unwanted damage. Promising work on the steering of medication in the human body employs magnetic fields acting on nanoparticles made of paramagnetic materials. We develop a computational tool to aid in the optimization of the physical parameters of these particles and the magnetic configuration, estimating the fraction of particles reaching a given target site in a large patient-specific vascular system for different physiological states (heart rate, cardiac output, etc.). We demonstrate the excellent computational performance of our model by its application to the simulation of paramagnetic-nanoparticle-laden flows in a circle of Willis geometry obtained from an MRI scan. The results suggest a strong dependence of the particle density at the target site on the strength of the magnetic forcing and the velocity of the background fluid flow.

We develop and apply an efficient multiscale method for simulating a large class of low-speed internal rarefied gas flows. The method is an extension of the hybrid atomistic-continuum approach proposed by Borg et al. (2013) [28] for the simulation of micro/nano flows of high-aspect ratio. The major new extensions are: (1) incorporation of fluid compressibility; (2) implementation using the direct simulation Monte Carlo (DSMC) method for dilute rarefied gas flows, and (3) application to a broader range of geometries, including periodic, non-periodic, pressure-driven, gravity-driven and shear-driven internal flows. The multiscale method is applied to micro-scale gas flows through a periodic converging-diverging channel (driven by an external acceleration) and a non-periodic channel with a bend (driven by a pressure difference), as well as the flow between two eccentric cylinders (with the inner rotating relative to the outer). In all these cases there exists a wide variation of Knudsen number within the geometries, as well as substantial compressibility despite the Mach number being very low. For validation purposes, our multiscale simulation results are compared to those obtained from full-scale DSMC simulations: very close agreement is obtained in all cases for all flow variables considered. Our multiscale simulation is an order of magnitude more computationally efficient than the full-scale DSMC for the first and second test cases, and two orders of magnitude more efficient for the third case

Murray's law states that the volumetric flow rate is proportional to the cube of the radius in a cylindrical channel optimized to require the minimum work to drive and maintain the fluid. However, application of this principle to the biomimetic design of micro/nano fabricated networks requires optimization of channels with arbitrary cross-sectional shape (not just circular) and smaller than is valid for Murray's original assumptions. We present a generalized law for symmetric branching that (a) is valid for any cross-sectional shape, providing that the shape is constant through the network; (b) is valid for slip flow and plug flow occurring at very small scales; and (c) is valid for networks with a constant depth, which is often a requirement for lab-on-a-chip fabrication procedures. By considering limits of the generalized law, we show that the optimum daughter-parent area ratio C, for symmetric branching into N daughter channels of any constant cross-sectional shape, is C ¼ N À2=3 for large-scale channels, and C ¼ N À4=5 for channels with a characteristic length scale much smaller than the slip length. Our analytical results are verified by comparison with a numerical optimization of a two-level network model based on flow rate data obtained from a variety of sources, including Navier-Stokes slip calculations, kinetic theory data, and stochastic particle simulations.

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