Micro and Nano Scale Hydrodynamics with and without Free Surfaces

When studying free surface flows, the dynamics of interfaces comes into play. So the equations of motion are important here. These equations are mentioned below.

Equation of continuity

(3.1)

Navier-Stokes equation

(3.2)

There are four unknowns – pressure field and three components of the velocity vector, and four equations. Therefore, theoretically, this system of equations can be solved. But due to their complexity, these equations have not been analytically solved yet.

Figure 3.1. Free surface flow