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The driven transport of fluid vesicles through narrow, cylindrical pores in a linear external potential is studied using Monte Carlo simulations, scaling arguments, and mean-field theory. The mobility of the vesicles increases sharply when the strength f of the driving field exceeds a threshold value f*. For f>f*, the mobility saturates at a value that is essentially independent of the strength of the driving field. The threshold field strength f* is found to scale with the membrane bending rigidity {κ}, the vesicle area A₀, and the pore size rₚ as f*/kBT{~} ({κ}/kBT)^1+β{A}₀^{{{-}}3/2+{{η}}}rₚ^-2η. An analysis of the zero-temperature limit yields the exponents {β}=0 and {η}=1.55, while the Monte Carlo simulations of low-bending-rigidity vesicles are well described by the (effective) exponents {β}{}0.2 and {η}{}2.4.
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D. M. Kroll (1995) studied this question.
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