Entropic Pressure Between Fluctuating Membranes With Surface Tension Available to Purchase

Entropic pressure, a longstanding topic of interest in biophysics and biomechanics, has been studied for over four decades. Similar to an ideal gas, fluctuating surfaces can generate entropic pressure through thermally driven motions. These thermal fluctuations impact a wide range of biological activities, including but not limited to vesicle fusion, cell adhesion, exocytocis, and endocytocis among many others. It has been proposed (and validated) by many researchers that the entropic pressure near a fluctuating confined fluid membrane without surface tension scales as $p∝1/d3$⁠, where $d$ is the confining distance, and this power law is size independent. In this article, we show that entropic pressure near a fluctuating fluid membrane could be strongly affected by the membrane’s size and surface tension. We show that while for membranes of size $L=1μm$ and larger, the pressure is size independent, for smaller membranes, the pressure does indeed depend on the membrane’s size. Our findings also shows that the surface tension changes this scaling law and at larger distance makes the pressure decay exponentially. Our work provides insights into how surface tension enhances biological vesicles fusion by suppressing membrane fluctuations, and consequently, the repulsive entropic force, and impacts biomembranes interactions with external objects at the early stage of approaching.