Macro-models (also called “reduced-order-models”, “lumped parameter models”, etc.) are convenient and efficient design tools that afford reasonable simulation accuracy by replacing the governing physical equations with behavioral models. Such models are easy to implement, usually do not require grid formulations, employ simple numerical schemes (systems of ordinary differential equations or algebraic equations), and have robust numerical convergence. In this study macro-models were developed for predicting the filling of micro-chambers for capillary driven flows as a function of geometric parameters and fluid properties (viscosity, surface tension and contact angle). It was found that bubble formation in filling of micro-chambers is a strong function of wall contact angles. A region of wall influence parameter was identified which was found to be relatively insensitive to flow parameters (flow rate, viscosity, etc.) and depends strongly on the wettability of the side walls of the micro-chambers.

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