Optimization of capillary flow through square micropillar arrays

This work compares several models for fluid flow through micropillar arrays to numerical simulations and uses them to optimize pillar dimensions for maximum fluid flow in a heat pipe application. Micropillar arrays are important for controlling capillary flow in microfluidic devices, and array permeability is a key parameter in determining fluid flow rate. Several permeability models are considered, including the Brinkman equation, numerical simulations, inverse reciprocal sums of a cylinder bank and open flow over a flat plate, and an analytical solution developed by the authors derived from a 2-dimensional velocity profile with appropriately varying boundary conditions. The comparison seeks to identify the models that are reliable over a wide range of porosities yet flexible enough to accommodate new pillar configurations. Numerical simulations of pillar permeability are the most desirable due to their accuracy. For pillars arranged in a square pattern, the 2-D analytical solution proposed in this study performs well at short pillar heights while the Brinkman equation is more accurate at tall pillar heights. Therefore, a hybrid model is formulated that uses the 2-D solution for h/d ⩽ 5 and the Brinkman model for h/d > 5. The 2-D solution, the Brinkman equation using specifically the permeability derived by Tamayol and Bahrami (2009), and numerical simulations are easily adapted to alternative pillar arrangements. A comparison of these models for pillars arranged in a rectangular pattern demonstrated that the authors' proposed solution is an excellent match to numerical results. These findings are applied to capillary fluid flow in heat pipes to explore the effects of pillar spacing, diameter, and height on the maximum fluid flow rate through the wick. At a given height aspect ratio, there is an optimum pillar spacing that balances the viscous losses and driving capillary pressure such that the flow rate reaches a maximum. In addition, the flow rate is increased by increasing pillar height if the pillar spacing is maintained at the corresponding optimum point.