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Motivated by the problem of microfluidic mixing, optimal control of advective mixing in Stokes fluid flows is considered. The velocity field is assumed to be induced by a finite set of spatially distributed force fields that can be modulated arbitrarily with time, and a passive material is advected by the flow. To quantify the degree of mixedness of a density field, we use a Sobolev space norm of negative index. We frame a finite-time optimal control problem for which we aim to find the modulation that achieves the best mixing for a fixed value of the action (the time integral of the kinetic energy of the fluid body) per unit mass. We derive the first-order necessary conditions for optimality that can be expressed as a two-point boundary value problem (TPBVP) and discuss some elementary properties that the optimal controls must satisfy. A conjugate gradient descent method is used to solve the optimal control problem and we present numerical results for two problems involving arrays of vortices. A comparison of the mixing performance shows that optimal aperiodic inputs give better results than sinusoidal inputs with the same energy.

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Preliminary tests have been carried out on short circular cylinders with both ends free. Drag force is measured across the range 6 × 104 < Re < 2.6 × 105 for cylinders of length to diameter ratio L/D between 1 and 10. The effect of hemispherical ends is also investigated. A kind of periodic vortex shedding is found in the range 2 < L/D < 8. The oil-film surface flow visualization shows that the ‘eyes’ near the free ends (regions of low pressure) gradually disappear as L/D is reduced to 3. An asymmetric flow pattern is established for very short cylinders (L/D < 3). The detailed measurements of pressure distribution along and across models shows asymmetries of minimum and base pressures along the span. The asymmetric flow produces yawing and rolling moments which are also measured.

The performance of plasma surface modified silica filler in styrene‐butadiene rubber (SBR) matrix has been analyzed. The conditions of plasma modification have been optimized by taking secant modulus as a standard parameter and the occurrence of the modification has been confirmed by surface area determination and Fourier transform infrared spectroscopy. The plasma‐modified surface of silica has been found to be composed of carbon–carbon double bonds and carbon–hydrogen bonds. Silane treatment also has been carried out on silica filler surface for a comparative assessment of its influence in the curing behavior and filler–rubber interaction. The cure reactions of all the rubber compounds have been found to be proceeded according to first‐order kinetics. A reduction in the cure reaction rate constant has been observed with the loading of unmodified and surface modified silica, emphasizing the cure deactivation of the matrix rubber by the silica filler. The filler dispersion, as revealed by scanning electron microscopy, has been found to be greatly improved by the plasma as well as silane treatment. The filler–rubber interaction has been found to be greatly improved by both surface treatments, but the best balance of mechanical properties has been observed with plasma surface modification only. Copyright © 2004 John Wiley & Sons, Ltd.

This work describes the effect of the speed of drum-type rotating collector in an electrospinning process on the orientation of electrospun poly(butylene terephthalate) fiber mats, and its effect on the tensile properties. The degree of orientation increased with the increase in the drum speed (surface velocity) up to a critical level, and thereafter, wavy fibers were observed. The average diameter reduced and its distribution became narrower with increase in the velocity. The mechanical properties in a parallel direction improved about three times with increase in the surface velocity. The anisotropic mechanical behavior could be predicted with a simple classical equation.