A membrane structure is provided. A membrane structure has a top surface and a bottom surface. The membrane structure includes a plurality of sintered layers including an inner layer disposed between two outer layers. The membrane structure further includes a nonmonotonic gradient in pore size extending between the top surface and the bottom surface. A method of making a membrane structure is provided. The method includes the steps of providing at least one inner layer; providing a plurality of outer layers; and laminating the inner layer and the outer layers to obtain a membrane structure.