Biocompatible polymers, such as polydimethylsiloxane (PDMS), are the materials of choice for creating organ-on-a-chip microfluidic platforms. Desirable qualities include ease of fabrication, optical clarity, and hydrophobicity, the latter of which facilitates oxygen transport to encased cells. An emerging and important application of organ-on-a-chip technology is drug discovery; however, a potential issue for polymer-based microfluidic devices has been highlighted by recent studies with PDMS, which have demonstrated absorption (and thus loss) of hydrophobic drugs into PDMS under certain experimental conditions. Absorption of drug in the polymer can also lead to undesirable transfer of drug between adjacent microfluidic lines. Given the benefits of polymers, it is essential to develop a comprehensive understanding of drug absorption. In this study, we considered convection, dissolution, and diffusion of a drug within a polymer-based microfluidic device to characterize the dynamics of drug loss in a quantitative manner. We solved Fick's 2nd law of diffusion (unsteady diffusion-convection) by finite element analysis in COMSOL®, and experimentally validated the numerical model for loss of three hydrophobic molecules (rhodamine B, cyanine NHS ester, and paclitaxel) in PDMS. Drug loss, as well as the unintended mixing of drugs by adjacent microfluidic channels, depends strongly on platform design parameters, experimental conditions, and the physico-chemical properties of the drug, and can be captured in a simple quantitate relationship that employs four scalable dimensionless numbers. This simple quantitative framework can be used in the design of a wide range of polymer-based microfluidic devices to minimize the impact of drug absorption.