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The flow of a viscous incompressible fluid between two parallel plates due to the normal motion of the plates is investigated. The unsteady Navier-Stokes equations are reduced to a nonlinear fourth-order differential equation by using similarity solutions. Homotopy analysis method (HAM) is used to solve this nonlinear equation analytically. The convergence of the obtained series solution is carefully analyzed. The validity of our solutions is verified by the numerical results obtained by fourth-order Runge-Kutta.

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The numerical results showed good agreement with high-speed video recordings. Monodispersed droplets were produced in the dripping regime when the ratio of the continuous phase flow rate to dispersed phase flow rate was 5-20 and the Weber number of the dispersed phase was less than 0.01. The porosity of polycaprolactone particles increased from 8 to 62% when 30 wt% of the water phase was incorporated in the organic phase prior to emulsification. The inner water phase was loaded with 0.156 wt% lidocaine hydrochloride to achieve a sustained drug release. 26% of lidocaine was released after 1 h and more than 93% of the drug was released after 130 h.