Topology optimization of microfluidic mixers

Abstract

This paper demonstrates the application of the topology optimization method as a general and systematic approach for microfluidic mixer design. The mixing process is modeled as convection dominated transport in low Reynolds number incompressible flow. The mixer performance is maximized by altering the layout of flow/non-flow regions subject to a constraint on the pressure drop between inlet and outlet. For a square cross-sectioned pipe the mixing is increased by 70% compared with a straight pipe at the cost of a 2.5 fold increase in pressure drop. Another example where only the bottom profile of the channel is a design domain results in intricate herring bone patterns that confirm findings from the literature. TOPOLOGY OPTIMIZATION OF MICROFLUIDIC MIXERS 499 diffusive properties, one can alter the geometry such that the flow distributes the matter more evenly in the solvent. By doing so, convection of matter is used as a mechanism to enhance mixing which; however, comes at the cost of an increased pressure drop between inlet and outlet. Stroock et al. [2] presented a mixer that induces chaotic advection by sequencing asymmetric microchannel sections containing staggered herringbones. For the systematic design of such microchannel mixers, topology optimization could be useful since no prerequisites are taken with respect to the geometry, only a design domain and boundary conditions need to be specified a priori.The material distribution method for topology optimization was first presented by Bendsøe and Kikuchi [3] for solid mechanics problems. Since then, topology optimization has been introduced in several other branches of physics such as optics, acoustics and flows (see e.g. Bendsøe and Sigmund [4] for an overview of the subject).Optimal design in fluid mechanics has been studied long before topology optimization was invented and optimal shapes minimizing the dissipated power for different profiles subjected to Stokes flow were already determined analytically in the 1970s by Pironneau [5] using shape optimization. As opposed to shape optimization, however, topology optimization allows introduction of new boundaries as the optimization progresses. This allows the topology to change several times during the optimization, which is impossible in shape optimization where the topology (i.e. the number of boundaries and connectivity) is predetermined.In topology optimization the geometry is represented as a gray-scale image. The color in each pixel (finite element) represents a value of a physical parameter, e.g. permeability, such that black pixels represent small permeability (no-flow regions with 'solid-like' material) and white pixels represent large permeability (fluid regions). Computationally, the gray-scale in each element is a design variable. Based on repeated finite element analyses the design variables are updated using gradient driven math programming tools as described in e.g. [4].Topology optimization in fluid mechanics was introduced by Borrvall and Petersson [6] modeling 2D flow in a Brinkman med...

Design of passive coolers for light-emitting diode lamps using topology optimisation

“…Topology optimisation for fluid systems began with the treatment of Stokes flow by Borrvall and Petersson [11] and has since been applied to Navier-Stokes flow [12], as well as passive transport problems [13,14], reactive flows [15], transient flows [16,17,18], fluid-structure interaction [19,20], amongst many others. The extension of topology optimisation to turbulent fluid flow is still in its infancy [21,22].…”

Topology optimization of inertia driven dosing units

“…A few works on flow components that are able to pump a fluid and have been designed by topology optimization have been promoted. Impeller designs for flow machines have been studied by Romero and Silva (2014) and Andreasen et al (2014) for 2D and 3D designs, respectively. An alternative unsteady pump design is promoted by Nørgaard et al (2016).…”

“…On top of the flow problems different transport phenomena have been considered i.e. passive transport (Andreasen et al, 2009), reacting flows (Okkels and Bruus, 2007), buoyancy problems (Alexandersen et al, 2014), active transport e.g. heat (Yoon, 2010a;Marck et al, 2013;Alexandersen et al, 2016).…”

“…However, even for 3D problems a proper mixing would have a cost in terms of increased internal friction due to the needed secondary motion. The problem of optimizing the mixing was studied in Andreasen et al (2009). It is therefore not expected that the presented formulation would ensure proper mixing in a 3D context either.…”

Convergence of Cell Based Finite Volume Discretizations for Problems of Control in the Conduction Coefficients

“…Presently, FVMs represent a standard choice of discretization within engineering communities dealing with computational fluid dynamics, transport, and convection-reaction problems. This is particularly important as control in the coefficients is being applied in these application domains, see for example [2,6,12,[16][17][18][19][20]27,28,30,31,[33][34][35][36][37][40][41][42]46]. Among various flavours of FVMs, cell based approaches, where all variables are associated only with cell centers, are particularly attractive.…”