Theory of Particle Focusing in Inertial Microfluidic Devices

Microfluidic devices are tiny circuits that flow fluids instead of electrons. Because they are inexpensive and portable, microfluidic devices are ideal for use in areas where medical resources are scarce. Inertial microfluidic devices represent a new direction in microfluidic device design in which high flow speeds are used to exert nonlinear inertial effects on the fluid and on fluid-suspended particles. While inertial microfluidic devices are finding applications in fields such as fluid mixing, particle filtration, flow cytometry (the counting, sorting, and analyzing of cells), the devices are built with essentially no theoretical input due to a lack of models for the nonlinear inertial effects.Why is there so little theory for inertial microfluidic devices? While there are many numerical methods for simulating inertial migration, because most devices have multiple moving boundaries and rely on three-dimensional effects, simulations are computationally intensive. In many cases, the computational time far exceeds the time needed to build and test a device experimentally. In contrast, asymptotic studies of inertial migration are only valid in limited cases, such as vanishingly small particle sizes.This thesis is concerned with developing a theory for inertial effects in microfluidic devices for a wide range of complicated geometries. This theory is achieved through the combination of both asymptotic and numerical methods. First, a theory is developed for the inertial lift force on a particle in a square channel. Second, this theory for the inertial lift force is validated against experiment. Third, a theory is developed for the formation of particle chains in a rectangular channel. Finally, a theory is developed for the number of focusing positions in a given channel

Theory of Particle Focusing in Inertial Microfluidic Devices

Microfluidic devices are tiny circuits that flow fluids instead of electrons. Because they are inexpensive and portable, microfluidic devices are ideal for use in areas where medical resources are scarce. Inertial microfluidic devices represent a new direction in microfluidic device design in which high flow speeds are used to exert nonlinear inertial effects on the fluid and on fluid-suspended particles. While inertial microfluidic devices are finding applications in fields such as fluid mixing, particle filtration, flow cytometry (the counting, sorting, and analyzing of cells), the devices are built with essentially no theoretical input due to a lack of models for the nonlinear inertial effects.Why is there so little theory for inertial microfluidic devices? While there are many numerical methods for simulating inertial migration, because most devices have multiple moving boundaries and rely on three-dimensional effects, simulations are computationally intensive. In many cases, the computational time far exceeds the time needed to build and test a device experimentally. In contrast, asymptotic studies of inertial migration are only valid in limited cases, such as vanishingly small particle sizes.This thesis is concerned with developing a theory for inertial effects in microfluidic devices for a wide range of complicated geometries. This theory is achieved through the combination of both asymptotic and numerical methods. First, a theory is developed for the inertial lift force on a particle in a square channel. Second, this theory for the inertial lift force is validated against experiment. Third, a theory is developed for the formation of particle chains in a rectangular channel. Finally, a theory is developed for the number of focusing positions in a given channel

Marine crustaceans with hairy appendages: Role of hydrodynamic boundary layers in sensing and feeding

Decapod crustaceans have appendages with an array of rigid hairs covered in chemoreceptors, used to sense and track food. Crustaceans directly influence the flow behavior by changing the speed of flow past the hairy surface, thereby manipulating the Reynolds number (Re). Hairs act either as a rake, diverting flow around the hair array, or as a sieve, filtering flow through the hairs. In our experiments, we uncover a third transitional phase: deflection, where the flow partially penetrates the hair array and is deflected laterally. We develop a reduced-order model that predicts the flow phase based on the depth of the boundary layer on a single hair. This model with no fitting parameters agrees very well with our experimental data. Additionally, our model agrees well with measurements of both chemosensing and suspension-feeding crustaceans and can be generalized for many different geometries. ©2019 American Physical Society.NSF Grant (DMS-1606487

Fluid flow in the sarcomere

A highly organized and densely packed lattice of molecular machinery within the sarcomeres of muscle cells powers contraction. Although many of the proteins that drive contraction have been studied extensively, the mechanical impact of fluid shearing within the lattice of molecular machinery has received minimal attention. It was recently proposed that fluid flow augments substrate transport in the sarcomere, however, this analysis used analytical models of fluid flow in the molecular machinery that could not capture its full complexity. By building a finite element model of the sarcomere, we estimate the explicit flow field, and contrast it with analytical models. Our results demonstrate that viscous drag forces on sliding filaments are surprisingly small in contrast to the forces generated by single myosin molecular motors. This model also indicates that the energetic cost of fluid flow through viscous shearing with lattice proteins is likely minimal. The model also highlights a steep velocity gradient between sliding filaments and demonstrates that the maximal radial fluid velocity occurs near the tips of the filaments. To our knowledge, this is the first computational analysis of fluid flow within the highly structured sarcomere.Army Research Office (Contract W911NF-14-1-0396)NIH (Grant P30AR074990