Interface mechanics: the shape of membrane cylinder

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Abstract
We determined the shape of membrane cylinder adherent to a flat support and derived the relationship between the energy of membrane adhesion and the geometrical characteristics of membrane contour. The obtained theoretical results allow an alternative method of adhesion energy measurement in addition to the method which includes the measurement of contact angle. Two different cases are analytically analysed : zero transmembrane pressure differential at which the shape of the membrane is determined entirely by the bending effects; second, high transmembrane pressure differential whose action surpasse the effect of bending elasticity. In the first case the adhesion energy is expressed only through the lengths of adsorbed and free parts of membrane contour which can be readly measured by optical methods. In second case the expression for adhesion energy includes the additional geometrical characteristic - the curvature of membrane contour in the pole which can be also calculated from the results of optical experiments. The distribution of force factors along the membrane is analysed

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