Dynamic behavior of immiscible gas bubble attached to the wall in channel flow plays very important role in many engineering applications. Special attention has been paid to micro direct methanol fuel cell(${mu}$DMFC) where surface tension becomes dominant factor with minor gravitational effect due to its reduced size. Therefore, displacement of $CO_2$ bubble generating on a cathode side in ${mu}$DMFC can be very difficult and efficient removal of $CO_2$ bubbles will affect the overall machine performance considerably. We have focused our efforts on studying the dynamic behavior of immiscible bubble attached to the one side of the wall on 2D rectangular channel subject to external shear flow. We used Level Contour Reconstruction Method(LCRM) which is the simplified version of front tracking method to track the bubble interface motion. Effects of Reynolds number, Weber number, advancing/receding contact angle and property ratio on bubble detachment characteristic has been numerically identified.