  Contact angle hysteresis of a macroscopic droplet on a heterogeneous but flat
substrate is studied using the interface displacement model. First, the
apparent contact angle of a droplet on a heterogeneous surface under the
condition of constant volume is considered. By assuming a cylindrical
liquid-vapor surface (meniscus) and minimizing the total free energy, we derive
an equation for the apparent contact angle, which is similar but different from
the well-known Cassie's law. Next, using this modified Cassie's law as a guide
to predict the behavior of a droplet on a heterogeneous striped surface, we
examine several scenarios of contact angle hysteresis using a periodically
striped surface model. By changing the volume of the droplet, we predict a
sudden jump of the droplet edge, and a continuous change of the apparent
contact angle at the edge of two stripes. Our results suggest that as drop
volume is increased (advancing contact lines), the predominant drop
configuration observed is the one whose contact angle is large; whereas,
decreasing drop volume from a large value (receding contact lines) yields drop
configuration that predominantly exhibit the smaller contact angle.
