Standard tissue culture of adherent cells is known to poorly replicate physiology and often entails suspending cells in solution for analysis and sorting, which modulates protein expression and eliminates intercellular connections. To allow adherent culture and processing in flow, we present 3D-shaped hydrogel cell microcarriers, which are designed with a recessed nook in a first dimension to provide a tunable shear-stress shelter for cell growth, and a dumbbell shape in an orthogonal direction to allow for self-alignment in a confined flow, important for processing in flow and imaging flow cytometry. We designed a method to rapidly design, using the genetic algorithm, and manufacture the microcarriers at scale using a transient liquid molding optofluidic approach. The ability to precisely engineer the microcarriers solves fundamental challenges with shear-stress-induced cell damage during liquid-handling, and is poised to enable adherent cell culture, in-flow analysis, and sorting in a single format.

We deploy the immersogeometric approach for tracking moving objects. The method immerses objects into non-boundary-fitted meshes and weakly enforces Dirichlet boundary conditions on the object boundaries. The object motion is driven by the integrated surface force and external body forces. A residual-based variational multiscale method is employed to stabilize the finite element formulation for incompressible flows. Adaptively refined quadrature rules are used to better capture the geometry of the immersed boundaries by accurately integrating the intersected background elements. Treatment for the freshly-cleared nodes (i.e. background mesh nodes that are inside the object at one time step, but are in the fluid domain at the next time step) is considered. We assess the accuracy of the method by analyzing object motion in different flow structures including objects freely dropping in viscous fluids and particle focusing in unobstructed and obstructed micro-channels. We show that key quantities of interest are in very good agreements with analytical, numerical and experimental solutions. We also show a much better computational efficiency of this framework than current commercial codes using adaptive boundary-fitted approaches. We anticipate deploying this framework for applications of particle inertial migration in microfluidic channels.

We consider inertial focusing of particles in channels with triangular cross sections. The number and the location of inertial focusing positions in isosceles triangular channels can change with varying blockage ratios (a/H) and Reynolds numbers (Re). In triangular channels, asymmetric velocity gradient induced by the sloped sidewalls leads to changes in the direction and the strength of the inertial lift forces. Therefore, varying the configuration (specifically, angle) of the triangular cross section is expected to lead to a better understanding of the nature of the inertial lift forces. We fabricated triangular microchannels with various apex angles using channel molds that were shaped by a planing process, which provides precise apex angles and sharp corners. The focusing position shift was found to be affected by the channel cross section, as expected. It was determined that the direction of the focusing position shift can be reversed depending on whether the vertex is acute or obtuse. More interestingly, corner focusing modes and splitting of the corner focusing were observed with increasing Re, which could explain the origin of the inertial focusing position changes in triangular channels. We conducted fluid dynamic simulations to create force maps under various conditions. These force maps were analyzed to identify the basins of attraction of various attractors and pinpoint focusing locations using linear stability analysis. Calculating the relative sizes of the basins of attractions and exhaustively identifying the focusing positions, which are very difficult to investigate experimentally, provided us a better understanding of trends in the focusing mechanism.

Design of microparticles which stabilize at the centerline of a channel flow when part of a dilute suspension is examined numerically for moderate Reynolds numbers (10 ≤ Re ≤ 80). This problem is motivated by the need for design of shaped particle carriers for use in next generation cell cytometry devices. Stability metrics for particles with arbitrary shapes are formulated based on linear-stability theory. Particle shape is parametrized by a compact, Non-Uniform Rational B-Spline (NURBS)-based representation. Shape-design is posed as an optimization problem and solved using adaptive Bayesian optimization. We focus on designing particles for maximal stability at the channel-centerline robust to perturbations. Our results indicate that centerline-focusing particles are families of characteristic "fish"/"bottle"/"dumbbell"-like shapes, exhibiting fore-aft asymmetry. A parametric exploration is then performed to identify stable particle-designs at different k's (particle chord-to-channel width ratio) and Re's (0.1 ≤ k ≤ 0.4, 10 ≤ Re ≤ 80). Particles at high-k's and Re's are highly stabilized when compared to those at low-k's and Re's. A comparison of the modified dumbbell designs from the current framework also shows better performance to perturbations in Fluid-Structure Interaction (FSI) when compared to the rod-disk model-dumbbell reported previously (Uspal & Doyle, 2014) for low-Re Hele-Shaw flow. We identify a basin of attraction around the centerline, within which any arbitrary release results in rotationally stable centerline-focusing. We find that this basin spans larger release-angle-ranges and lateral locations (tending to the channel width) for narrower channels. This effectively standardizes the notion of global focusing using the current stability-paradigm in narrow channels, which eliminates the need for an independent design for global-focusing in such configurations. The framework detailed in this work is illustrated for 2D cases and is generalizable to stability in 3D flow-fields. The current formulation is agnostic to Re and particle/channel geometry which indicates substantial potential for integration with imaging flow-cytometry tools and microfluidic biosensing-assays.

Identifying focusing patterns in arbitrarily cross-sectioned channels is an interesting, significant, and, complex problem in applications involving microfluidic sorting, separation, and ordering. Current computational approaches involve construction of cross-sectional "force-maps" followed by a visual identification to confirm the presence of experimentally-observed stable points [D. Di Carlo et. al., Physical review letters, 102, 094503 (2009)]. Such visual inspections are naturally prone to misinterpreting stable locations and focusing shifts in the case of non-trivial focusing patterns. We develop and deploy an approach for automating the calculation of focusing patterns for a general channel geometry, and thereby reduce the dependence on empirical/visual procedures to confirm the presence of stable locations. We utilize concepts from interpolation theory (to represent continuous force-fields using discrete points), and stability theory to identify "basins of attraction" and quantitatively identify stable equilibrium points. Our computational experiments reveal that predicting equilibrium points accurately requires upto ×10-20 times more refined force-maps that conventionally used, which highlights the spatial resolution required for an accurate representation of cross-sectional forces. These focusing patterns are validated using experimental results for a rectangular channel, and triangular channel with an apex angle of 90 • . We then apply the approach to predict and explain focusing patterns and shifts for a 90 • -isosceles triangular channel across a range of Reynolds numbers for a H = 0.4 (particle-to-channel size ratio). We observe that the predicted focusing patterns match experiments well. The force-maps also re-