A flow promotes mixing by separating neighboring fluid particles. This separation occurs because of velocity  gradients, a phenomenon called shearing. Let  and  be two neighboring fluid particles, separated by  at time t. When the particles are advected by a flow , at time  the approximate separation between the particles can be found through Taylor expansion : 
hence
and
The rate of growth of the separation is therefore given by the gradient of the velocity field in the direction of the separation. The plane shear flow is a simple example of large-scale stationary flow that deforms fluid elements because of a uniform shear.