We present a versatile high-level programming-language implementation of nonlinear topology optimization. Our implementation is based on the commercial software package Femlab, and it allows a wide range of optimization objectives to be dealt with easily. We exemplify our method by studies of steady-state Navier-Stokes flow problems, thus extending the work by Borrvall and Petersson on topology optimization of fluids in Stokes flow [Int. J. Num. Meth. Fluids 2003; 41:77-107]. We analyze the physical aspects of the solutions and how they are affected by different parameters of the optimization algorithm. A complete example of our implementation is included as Femlab code in an appendix.

We consider pressure-driven, steady state Poiseuille flow in straight channels with various crosssectional shapes: elliptic, rectangular, triangular, and harmonic-perturbed circles. A given shape is characterized by its perimeter P and area A which are combined into the dimensionless compactness number C = P 2 /A, while the hydraulic resistance is characterized by the well-known dimensionless geometrical correction factor α. We find that α depends linearly on C, which points out C as a single dimensionless measure characterizing flow properties as well as the strength and effectiveness of surface-related phenomena central to lab-on-a-chip applications. This measure also provides a simple way to evaluate the hydraulic resistance for the various shapes.

We confront, quantitatively, the theoretical description of the reaction-diffusion process of a second-order reaction to experiment. The reaction at work is Ca(2+)/CaGreen, a fluorescent tracer for calcium. The reactor is a T-shaped microchannel, 10 microm deep, 200 microm wide, and 2 cm long. The experimental measurements are compared with the two-dimensional numerical simulation of the reaction-diffusion equations. We find good agreement between theory and experiment. From this study, one may propose a method of measurement of various quantities, such as the kinetic rate of the reaction, in conditions yet inaccessible to conventional methods.

In this article we concentrate on a particular micromixer that exploits chaotic trajectories to achieve mixing. The micromixer we consider here is a cross-channel intersection, in which a main stream is perturbed by an oscillatory flow, driven by an external source. Depending on the amplitude and frequency of the oscillatory flow, one obtains wavy and chaotic regimes, reminiscent of a tendril-whorl mapping. The chaotic states, in which material lines are stretched and folded, favour mixing. A spatiotemporal resonance phenomenon, in which the material-line deformation is transient, is shown. An experiment using soft lithography and integrated valves, in which the resonant states are revealed, is described. From a practical viewpoint, the cross-channel micromixer offers a variety of regimes, which can be exploited to mix fluids or separate particles of different sizes. In the context of microsystems, it can be viewed as a 'smart' elementary system.

Until now, the planar Hall effect has been studied in samples with cross-shaped Hall geometry. We demonstrate theoretically and experimentally that the planar Hall effect can be observed for an exchange-biased ferromagnetic material in a Wheatstone bridge topology and that the sensor signal can be significantly enhanced by a geometric factor. For the samples in the present study, we demonstrate an enhancement of the sensor output by a factor of about 100 compared to cross-shaped sensors. The presented construction opens a new design and application area of the planar Hall effect, which we term planar Hall effect bridge sensors.