Fridolin Okkels

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

Reexamination of Hagen-Poiseuille flow: Shape dependence of the hydraulic resistance in microchannels

We consider pressure-driven, steady-state Poiseuille flow in straight channels with various cross-sectional 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= P2/A, while the hydraulic resistance is characterized by the well-known dimensionless geometrical correction factor alpha. We find that alpha 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.

Topology and shape optimization of induced-charge electro-osmotic micropumps

For a dielectric solid surrounded by an electrolyte and positioned inside an externally biased parallel-plate capacitor, we study numerically how the resulting induced-charge electro-osmotic (ICEO) flow depends on the topology and shape of the dielectric solid. In particular, we extend existing conventional electrokinetic models with an artificial design field to describe the transition from the liquid electrolyte to the solid dielectric. Using this design field, we have succeeded in applying the method of topology optimization to find system geometries with non-trivial topologies that maximize the net induced electro-osmotic flow rate through the electrolytic capacitor in the direction parallel to the capacitor plates. Once found, the performance of the topology-optimized geometries has been validated by transferring them to conventional electrokinetic models not relying on the artificial design field. Our results show the importance of the topology and shape of the dielectric solid in ICEO systems and point to new designs of ICEO micropumps with significantly improved performance.

Scaling behavior of optimally structured catalytic microfluidic reactors.

In this study of catalytic microfluidic reactors we show that, when optimally structured, these reactors share underlying scaling properties. The scaling is predicted theoretically and verified numerically. Furthermore, we show how to increase the reaction rate significantly by distributing the active porous material within the reactor using a high-level implementation of topology optimization.

Topology optimization of viscoelastic rectifiers

An approach for the design of microfluidic viscoelastic rectifiers is presented based on a combination of a viscoelastic model and the method of topology optimization. This presumption free approach yields a material layout topologically different from experimentally realized rectifiers, and simulations indicate superior performance for the optimized design in the regime of moderate elasticity.

Topology optimized microbioreactors

This article presents the fusion of two hitherto unrelated fields—microbioreactors and topology optimization. The basis for this study is a rectangular microbioreactor with homogeneously distributed immobilized brewers yeast cells (Saccharomyces cerevisiae) that produce a recombinant protein. Topology optimization is then used to change the spatial distribution of cells in the reactor in order to optimize for maximal product flow out of the reactor. This distribution accounts for potentially negative effects of, for example, by‐product inhibition. We show that the theoretical improvement in productivity is at least fivefold compared with the homogeneous reactor. The improvements obtained by applying topology optimization are largest where either nutrition is scarce or inhibition effects are pronounced. Biotechnol. Bioeng. 2011; 108:786–796.

Parametric optimization of inverse trapezoid oleophobic surfaces.

In this paper, we introduce a comprehensive and versatile approach to the parametric shape optimization of oleophobic surfaces. We evaluate the performance of inverse trapezoid microstructures in terms of three objective parameters: apparent contact angle, maximum sustainable hydrostatic pressure, and mechanical robustness (Im, M.; Im, H:; Lee, J.H.; Yoon, J.B.; Choi, Y.K. A robust superhydrophobic and superoleophobic surface with inverse-trapezoidal microstructures on a large transparent flexible substrate. Soft Matter 2010, 6, 1401-1404; Im, M.; Im, H:; Lee, J.H.; Yoon, J.B.; Choi, Y.K. Analytical Modeling and Thermodynamic Analysis of Robust Superhydrophobic Surfaces with Inverse-Trapezoidal Microstructures. Langmuir 2010, 26, 17389-17397). We find that each of these parameters, if considered alone, would give trivial optima, while their interplay provides a well-defined optimal shape and aspect ratio. The inclusion of mechanical robustness in combination with conventional performance characteristics favors solutions relevant for practical applications, as mechanical stability is a critical issue not often addressed in idealized models.

Experimental characterisation of a novel viscoelastic rectifier design

A planar microfluidic system with contractions and obstacles is characterized in terms of anisotropic flow resistance due to viscoelastic effects. The working mechanism is illustrated using streak photography, while the diodicity performance is quantified by pressure drop measurements. The point of maximum performance is found to occur at relatively low elasticity levels, with diodicity around 3.5. Based on a previously published numerical work [Ejlebjerg et al., Appl. Phys. Lett. 100, 234102 (2012)], 2D simulations of the FENE-CR differential constitutive model are also presented, but limited reproducibility and uncertainties of the experimental data prevent a direct comparison at low elasticity, where the flow is essentially two-dimensional.

HistoFlex—a microfluidic device providing uniform flow conditions enabling highly sensitive, reproducible and quantitative in situ hybridizations

A microfluidic device (the HistoFlex) designed to perform and monitor molecular biological assays under dynamic flow conditions on microscope slide-substrates, with special emphasis on analyzing histological tissue sections, is presented. Microscope slides were reversibly sealed onto a cast polydimethylsiloxane (PDMS) insert, patterned with distribution channels and reaction chambers. Topology optimization was used to design reaction chambers with uniform flow conditions. The HistoFlex provided uniform hybridization conditions, across the reaction chamber, as determined by hybridization to microscope slides of spotted DNA microarrays when applying probe concentrations generally used in in situ hybridization (ISH) assays. The HistoFlexs novel ability in online monitoring of an in situ hybridization assay was demonstrated using direct fluorescent detection of hybridization to 18S rRNA. Tissue sections were not visually damaged during assaying, which enabled adapting a complete ISH assay for detection of microRNAs (miRNA). The effects of flow based incubations on hybridization, antibody incubation and Tyramide Signal Amplification (TSA) steps were investigated upon adapting the ISH assay for performing in the HistoFlex. The hybridization step was significantly enhanced using flow based incubations due to improved hybridization efficiency. The HistoFlex device enabled a fast miRNA ISH assay (3 hours) which provided higher hybridization signal intensity compared to using conventional techniques (5 h 40 min). We further demonstrate that the improved hybridization efficiency using the HistoFlex permits more complex assays e.g. those comprising sequential hybridization and detection of two miRNAs to be performed with significantly increased sensitivity. The HistoFlex provides a new histological analysis platform that will allow multiple and sequential assays to be performed under their individual optimum assay conditions. Images can subsequently be recorded either in combination or sequentially through the ability of the HistoFlex to monitor assays without disassembly.

Topology optimization of robust superhydrophobic surfaces

In this paper we apply topology optimization to micro-structured superhydrophobic surfaces for the first time. It has been experimentally observed that a droplet suspended on a brush of micrometric posts shows a high static contact angle and low roll-off angle. To keep the fluid from penetrating the space between the posts, we search for an optimal post cross-section that minimizes the vertical displacement of the liquid–air interface at the base of the drop when a pressure difference is applied. Topology optimisation proves effective in this framework, showing that posts with a branching cross-section are optimal, which is consistent with several biologic strategies to achieve superhydrophobicity. Through a filtering technique, we can also control the characteristic length scale of the optimal design, thus obtaining geometries feasible via standard lithography.