Translocation of a vesicle through a narrow hole across a membrane

We study the translocation process of a vesicle through a hole in a solid membrane separating two chambers by using the Onsager principle. By considering the stretching energy of the vesicle and the driving force due to pressure difference, we derive a free energy that shows clearly a decrease in the energy barrier as the pressure difference between two sides of the membrane increases. The difference between the reaction path obtained from the string method and the actual kinetic paths obtained from the Onsager principle is discussed when the friction parameter changes. The translocation time decreases as the pressure difference increases or the initial size of the vesicle decreases.