Numerical study of the thermocapillary droplet migration in a microchannel under a blocking effect from the heated upper wall

This study presents a numerical computation to investigate the transient thermocapillary migration of a small liquid droplet in a microchannel. When the upper wall of the microchannel is set to be a constant temperature higher than the lower wall, subjected to a uniform temperature gradient, the evolution of the temperature distribution both inside and outside the droplet affects the migration behavior of the droplet. During the initial stage, the smallest temperature on the free interface shifts from near the mid-plane to the advancing side. The imbalance in the surface tension along the free surface causes two pairs of thermocapillary vortices both inside and outside the liquid droplet which create a net thermocapillary momentum that pushes the droplet to migrate. With the passage of time, they decrease in magnitude due to a reduction of the net thermocapillary momentum. The highest temperature appears on the free interface after the lowest temperature reaches the advancing side. During this period, the net thermocapillary momentum turns to go against the droplet migration. As a consequence, the droplet first accelerates and then decelerates to zero velocity. With a higher upper wall temperature, the time taken for the migration of the droplet to stop is shorter. When the static contact angle is less than 90°, the migration of the droplet is assisted by the capillary force. Therefore, the time it takes to block the movement of the droplet becomes longer. On the other hand, the blocking time is shortened due to the negative effect of the capillary force when the static contact angle is greater than 90°.