Abstract
A mathematical model is developed to predict the effect of motion of a liquid plug in a capillary tube on the dynamic contact angles including the effects of driving pressure, liquid plug length, tube diameter, and operating temperature. Results show that the advancing contact angle significantly affects the flow resistance of the liquid plug occurring in a capillary tube. For a given driving pressure difference, the pressure difference due to the increase of the advancing contact angle is the primary contribution to the flow resistance of capillary flow in a capillary tube. For example, when the liquid plug length is equal to 5 mm at a driving pressure difference of 10 Pa and a tube radius of 500 μm, the flow resistance caused by the dynamic contact angle can be 92% of the total flow resistance at an operating temperature of 60°C. It can be concluded that the effect of the dynamic contact angle on the fluid flow of a liquid plug in a capillary tube must be considered.
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