Revisiting the entropic force between fluctuating biological membranes

The complex interplay between the various attractive and repulsive forces that mediate between biological membranes governs an astounding array of biological functions: cell adhesion, membrane fusion, self-assembly, binding-unbinding transition among others. In this work, the entropic repulsive force between membranes---which originates due to thermally excited fluctuations---is critically reexamined both analytically and through systematic Monte Carlo simulations. A recent work by Freund \cite {Freund13} has questioned the validity of a well-accepted result derived by Helfrich \cite{Helfrich78}. We find that, in agreement with Freund, for small inter-membrane separations ($d$), the entropic pressure scales as $p\sim 1/d$, in contrast to Helfrich's result: $p\sim 1/d^3$. For intermediate separations, our calculations agree with that of Helfrich and finally, for large inter-membrane separations, we observe an exponentially decaying behavior.