  Translocation of a daughter vesicle from a mother vesicle through a pore is
experimentally studied by many groups using a model system of self-reproducing
vesicles. However, the theoretical formulation of the problem is not fully
understood. In the present study, we present a theoretical formulation of the
process based on our previous work [P. Khunpetch et al., Phys. Fluids 33,
077103 (2021)]. In our previous work, we considered the daughter vesicle as a
rigid body. In the present work, however, we allow the daughter vesicle to
deform during the expulsion process. We thus derive the free energy
constituting of the elastic moduli of both the mother and daughter vesicles,
and of pressure-driven contribution. The minimum energy path of the
translocation is searched by using the string method. Our improved model
successfully suggests the disappearance of the energy barrier where all the
elastic moduli are in agreement with the experimental reports, while the
previous work is unsuccessful to do so. The equations of motion of the daughter
vesicle have been derived within the framework of the Onsager principle. We
found that the translocation time of the daughter vesicle can be reduced when
the pressure inside the mother vesicle increases, or the initial size of the
daughter vesicle decreases.
