Effect of contact-angle hysteresis on the pressure drop under slug flow conditions in minichannels and microchannels

The effect of the difference between the advancing and receding contact angles (the phenomenon known as contact-angle hysteresis or wetting hysteresis) on the pressure drop in capillaries (minichannels and microchannels) for liquid-liquid and gas-liquid systems is analyzed. It is shown that, in microchannels, for cases of a continuous medium that both does and does not wet the walls, the pressure drop has a positive sign. A relationship is proposed for estimating the dynamic receding contact angle, which is the monotone extension of a similar relationship for the advancing contact angle. The region of the allowable values of the capillary numbers for these equations is found. The fraction of the pressure drop in capillaries due to contact-angle hysteresis in the total pressure drop is estimated.