Peclet Number Dependence of Mass Transfer in Microscale Segmented Gas–Liquid Flow

Abstract

A detailed understanding of the scaling behavior associated with the fluid flow and the transport of gas molecules from a train of elongated gas plugs into neighboring liquid segments is of great importance for a broad range of microscale applications. The indirect dependence of the parameters affecting the <i>Capillary</i> and <i>Peclet</i> numbers and thereby scaling behavior (i.e., the velocity and length of the gas plugs, and the length of the liquid segments) on the directly adjustable experimental inputs (i.e., flow rate or pressure of each phase) has hindered the systematic investigation of scaling behavior in microscale gas–liquid flows. Here, we take advantage of an image-based feedback strategy that allows us to directly impose Capillary and Peclet numbers. We custom fabricated a long, straight microchannel (width 300 μm, length-to-width ratio 700) in a gas impermeable silicon–glass substrate. We automatically determined the length reduction of initially uniformly sized gas plugs at different positions along the microchannel and elucidated the gas concentration within adjacent liquid segments. In accordance with penetration theory, we analytically estimated the gas–liquid mass transfer time to scale with the Peclet number, <i>Pe</i>, to the power of −0.5. The experimentally measured scaling exponent −0.55 ± 0.5 for carbon dioxide dissolution in methanol and ethanol at <i>Pe</i> = 2060–16500 compared favorably with the analytical prediction and provides a guideline for predicting physical transport for a wide range microscale gas–liquid flow processes