Bernoulli's theorem states that when an incompressible and non-viscous liquid flows in a stream lined motion from one place to another then at every point its total energy per unit volume is conserved. Atomizer is based on this principle.
When the rubber ball is squeezed it sends a stream of air which passes over the tube. The velocity is very large in the constricted part so that pressure in that part is lowered. Consequently, liquid rises in the tube and is mixed with air and comes out in the form of fine spray.
