Viscoelastic fluids, PhD: Structural...

Structural Optimization of Non-Newtonian Microfluidics

Ph.d. student: Kristian Ejlebjerg Jensen

Group: Theoretical MicroSystems Optimization

Supervisor: Fridolin Okkels

Duration: 1/8/2010 – 1/8/2013

Project Description

The main objective of this project is to combine a state of the art numerical method for viscoelastic flow calculation with the topology optimisation method to improve on existing- as well as to discover novel non-Newtonian microfluidic devices.

Perspective

Novel microfluidic devices relying on non-Newtonian working fluids have been experimentally realised. Topology optimization is the ideal tool to investigate the non-intuitive relation between the geometry of these devices and their performance.

Microfluidic Rectifiers

Lab-on-a-chip systems can be applied for analysis and separation purposes with reduction in cost, analysis time, and sample volumes as major advantages compared to conventional laboratory methods. Micropumps can be used in lab-on-a-chip systems, but the lack of robust valves on the microscale is a critical limitation. In fact, the smallest experimentally realized pumps rely on passive valves, which are quite leaky in the sense that the resistance only differs slightly between the two flow directions. This anisotropic flow resistance is due to inertial effects but it is well-known that inertial effects decrease when devices are scaled down, making this mechanism a questionable candidate for a pump on the microscale. Many working fluids, however, contain large flexible molecules, e.g., biological fluids or polymers, and these can give rise to viscoelastic properties. Therefore, leaky valves/rectifiers relying on viscoelastic effects have been suggested, as this working mechanism not only survives, when the valve is scaled down, but also gives rise to significantly higher diodicity, and thus, potentially larger flow rates. The working mechanism is related to elastic instabilities, which can also be used in the context of micromixing.

Topology Optimization [1]

We find that it is possible to combine recent model developments with a high level implementation of topology optimization to determine the optimal material layout that maximizes the flow rate ratio in a rectifier device. We have presented results for topology optimization of a viscoelastic rectifier and found a design that promises superior performance in the regime of moderate elasticity.

Experiments [2]

We successfully characterized a viscoelastic rectifier with a contraction-obstacle design and found a maximum diodicity of 3.5 at a Weissenberg number of 27, which is a verification of previous simulations in the sense that these predicted the design to be optimal at moderate elasticity. Streak photography illustrated that the working mechanism can be attributed to elastic recirculations upstream of the contraction.

The Bistable Cross-Slot [3]

The cross-slot exhibits bistability beyond a critical point. We wish to optimize the cross-slot for early bistability, but this property does not appear explicitly in the solution. It is however well-known that the asymmetric flow of the bifurcated solution gives rise to extra resistance compared to the unstable symmetric solution. Therefore we opt for a heuristic approach based on the resistance ratio between these two solutions. Note that the resistance ratio is equivalent to the ratio of dissipations.