Laurits Højgaard Olesen

A high‐level programming‐language implementation of topology optimization applied to steady‐state Navier–Stokes flow

We present a versatile high-level programming-language implementation of non-linear 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 analyse 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. Copyright

Flow reversal at low voltage and low frequency in a microfabricated ac electrokinetic pump.

Microfluidic chips have been fabricated in Pyrex glass to study electrokinetic pumping generated by a low-voltage ac bias applied to an in-channel asymmetric metallic electrode array. A measurement procedure has been established and followed carefully resulting in a high degree of reproducibility of the measurements over several days. A large coverage fraction of the electrode array in the microfluidic channels has led to an increased sensitivity allowing for pumping measurements at low bias voltages. Depending on the ionic concentration a hitherto unobserved reversal of the pumping direction has been measured in a regime, where both the applied voltage and the frequency are low, V(rms)<1.5 V and f<20 kHz , compared to previously investigated parameter ranges. The impedance spectrum has been thoroughly measured and analyzed in terms of an equivalent circuit diagram to rule out trivial circuit explanations of our findings. Our observations agree qualitatively, but not quantitatively, with theoretical electrokinetic models published in the literature.

Electrohydrodynamics of binary electrolytes driven by modulated surface potentials.

We study the electrohydrodynamics of the Debye screening layer that arises in an aqueous binary solution near a planar insulating wall when applying a spatially modulated ac voltage. Combining this with first order perturbation theory we establish the governing equations for the full nonequilibrium problem and obtain analytic solutions in the bulk for the pressure and velocity fields of the electrolyte and for the electric potential. We find good agreement between the numerics of the full problem and the analytics of the linear theory. Our work provides the theoretical foundations of circuit models discussed in the literature. The nonequilibrium approach also reveals unexpected high-frequency dynamics not predicted by circuit models.

Transport coefficients for electrolytes in arbitrarily shaped nano- and microfluidic channels

We consider laminar flow of incompressible electrolytes in long, straight channels driven by pressure and electro-osmosis. We use a Hilbert space eigenfunction expansion to address the general problem of an arbitrary cross-section and obtain general results in linear-response theory for the hydraulic and electrical transport coefficients which satisfy Onsager relations. In the limit of non-overlapping Debye layers, the transport coefficients are simply expressed in terms of parameters of the electrolyte as well as the geometrical correction factor for the Hagen–Poiseuille part of the problem. In particular, we consider the limits of thin non-overlapping as well as strongly overlapping Debye layers, respectively, and calculate the corrections to the hydraulic resistance due to electro-hydrodynamic interactions.

Pulsatile microfluidics as an analytical tool for determining the dynamic characteristics of microfluidic systems

An understanding of all fluid dynamic time scales is needed to fully understand and hence exploit the capabilities of fluid flow in microfluidic systems. We propose the use of harmonically oscillating microfluidics as an analytical tool for the deduction of these time scales. Furthermore, we suggest the use of system-level equivalent circuit theory as an adequate theory of the behavior of the system. A novel pressure source capable of operation in the desired frequency range is presented for this generic analysis. As a proof of concept, we study the fairly complex system of water-filled interconnected elastic microfluidic tubes containing a large, trapped air bubble and driven by a pulsatile pressure difference. We demonstrate good agreement between the system-level model and the experimental results, allowing us to determine the dynamic time scales of the system. However, the generic analysis can be applied to all microfluidic systems, both ac and dc.

Mass and Charge Transport in Micro and Nanofluidic Channels

We consider laminar flow of incompressible electrolytes in long, straight channels driven by pressure and electroosmosis. We use a Hilbert space eigenfunction expansion to address the general problem of an arbitrary cross section and obtain general results in linear-response theory for the mass and charge transport coefficients that satisfy Onsager relations. In the limit of nonoverlapping Debye layers the transport coefficients are simply expressed in terms of parameters of the electrolyte as well as the hydraulic radius with and being the cross-sectional area and perimeter, respectively. In particular, we consider the limits of thin nonoverlapping as well as strongly overlapping Debye layers, respectively, and calculate the corrections to the hydraulic resistance due to electrohydrodynamic interactions.