We discuss a closed system of field equations for a semipermeable membrane which has particle and heat exchange with its surroundings. In this case we consider a surface with an arbitrary shape for specific quantities and mechanical properties. A representation of the constitutive equations follows from the principle of material objectivity in space as well as on surfaces. The constitutive equations can be restricted by an entropy principle. We present both the Gibbs equation and the entropy flux. Furthermore, we obtain the surface stress and the chemical potential in terms of the specific free energy of the membrane. Both the heat flux and the particle flux normal to the membrane depend on the mean curvature and the friction between the particle across the membrane. The interaction tangential to the interface is dependent up on gradients of the surface stress as well as the chemical potential of the interface.
