Adhesion between a rigid cylindrical particle and a soft fluid membrane tube

We investigate the structure of a tubular membrane adhering to a rigid cylindrical particle, in various radius ratios. Through a theoretical and numerical analysis of a free-energy model that uses Helfrich energy for the description of the membrane, we show that three distinct phases exist, depending on the ratio between radii of the membrane tube and the rigid cylinder and an adsorption parameter describing the attraction between the cylinder and tube surface. The adhesion transition from the desorbed to weakly adhered states is identified as a second-order phase transition; the wrapping transition from the weakly adhered to strongly adhered states is identified as a first-order phase transition.