Forced transport of deformable containers through narrow constrictions

We study, numerically and analytically, the forced transport of deformable containers through a narrow constriction. Our central aim is to quantify the competition between the constriction geometry and the active forcing, regulating whether and at which speed a container may {\em pass} through the constriction and under what conditions it gets {\em stuck}. We focus, in particular, on the interrelation between the force that propels the container and the radius of the channel, as these are the external variables that may be directly controlled in both artificial and physiological settings. We present Lattice-Boltzmann simulations that elucidate in detail the various phases of translocation, and present simplified analytical models that treat two limiting types of these membrane containers: deformational energy dominated by the {\em bending} or {\em stretching} contribution. In either case we find excellent agreement with the full simulations, and our results reveal that not only the radius but also the length of the constriction determines whether or not the container will pass.