The movement of water from one cell of the cortex to the adjacent one in roots is due to

The movement of water from one cell of the cortex to the adjacent one in the roots is due to the Water potential gradient.
Water always moves from a higher energy state to a lower energy state. Water moves from soil to and through roots, through the xylem of plants, to the leaves, and eventually evaporates in the substomatal cavities of the leaf. The driving force for this flow is a water potential gradient.