Microvascular multinozzle arrays are designed and fabricated for high-throughput printing of functional materials. Ink-flow uniformity within these multigeneration, bifurcating microchannel arrays is characterized by computer modeling and microscopic particle image velocimetry (micro-PIV) measurements. Both single and dual multinozzle printheads are produced to enable rapid printing of multilayered periodic structures over large areas (≈1 m(2)).

Numerical computations are performed to evaluate the resistance functions for low Reynolds number flow past spherical particles, droplets and bubbles in cylindrical domains. Spheres of arbitrary radius a and radial position b move with arbitrary velocity U within a cylinder of radius R. The undisturbed fluid may be at rest, or subject to a pressure-driven flow with maximum velocity U0. The spectral boundary element method is employed to compute the resistance force for torque-free bodies in three cases: rigid solids, fluid droplets with viscosity ratio λ = 1, and bubbles with viscosity ratio λ = 0. A lubrication theory is developed to predict the limiting resistance of bodies near contact with the cylinder walls. Compact algebraic expressions are developed which accurately represent the numerical data over the entire range of particle positions 0 < b/(R − a) < 1 for all particle sizes in the range 0 < a/R < 0.9. The resistance functions are consistent with known analytical results and are presented in a form suitable for further studies of particle migration in cylindrical vessels.

A novel method is introduced for solving the three-dimensional Stokes equations via a spectral element approach to the boundary integral method. The accuracy and convergence of the method are illustrated through applications involving rigid particles, deformable droplets and interacting particles. New physical results are obtained for two applications in low Reynolds number flow: the permeability of periodic models of a porous membrane and the instability of a toroidal droplet subject to non-axisymmetric perturbations. Further applications are described in the companion paper (Higdon & Muldowney 1995).