with the partial molar enthalpy of component j in the bulk phase h b j , the composition of the bulk phase x j , the internal energy of the fluid in the porous medium U , the number of particles in the porous medium N j . The solid material is assumed to be rigid and therefore, the volume of the porous medium is not considered a variable. Using h b j = T s b j + µ i and dU = T dS + i µ i dN i the chemical potential can be canceled out from the contributions of the bulk phase and the inhomogeneous system, leading to: