A method for forming a filter membrane, comprising: bonding two or more PTFE layers (52, 54) and co-stretching the two or more PTFE layers (52, 54), after bonding, to form the filter membrane having porosities and pore sizes that change from one layer to another, the method comprising the following steps: a first PTFE mixture is prepared configured to provide a first pore size; a second PTFE mixture is prepared configured to provide a second pore size, wherein the first and second PTFE mixtures have different amounts of lubricating agents such that the first and second pore sizes after co-stretching are different; the first PTFE mixture is extruded into a first preform and the second PTFE mixture is extruded into a second preform; the first preform and the second preform are combined into a double-layered PTFE sheet, wherein combining the first preform and the second preform comprises: pressing the first preform into a first sheet, pressing the second preform into a second sheet, wherein each preform is pressed separately, drying the first and second sheets, and pressurizing the first dried sheet and the second dried sheet together during co-stretching; and the double-layered PTFE sheet is further co-stretched to form the filter membrane comprising a first layer that includes pores of the first pore size and a second layer that includes pores of the second pore size. bonding two or more PTFE layers (52, 54) and co-stretching the two or more PTFE layers (52, 54), after bonding, to form the filter membrane having porosities and pore sizes that change from one layer to another, the method comprising the following steps: a first PTFE mixture is prepared configured to provide a first pore size; a second PTFE mixture is prepared configured to provide a second pore size, wherein the first and second PTFE mixtures have different amounts of lubricating agents such that the first and second pore sizes after co-stretching are different; the first PTFE mixture is extruded into a first preform and the second PTFE mixture is extruded into a second preform; the first preform and the second preform are combined into a double-layered PTFE sheet, wherein combining the first preform and the second preform comprises: pressing the first preform into a first sheet, pressing the second preform into a second sheet, wherein each preform is pressed separately, drying the first and second sheets, and pressurizing the first dried sheet and the second dried sheet together during co-stretching; and the double-layered PTFE sheet is further co-stretched to form the filter membrane comprising a first layer that includes pores of the first pore size and a second layer that includes pores of the second pore size. a first PTFE mixture is prepared configured to provide a first pore size; a second PTFE mixture is prepared configured to provide a second pore size, wherein the first and second PTFE mixtures have different amounts of lubricating agents such that the first and second pore sizes after co-stretching are different; the first PTFE mixture is extruded into a first preform and the second PTFE mixture is extruded into a second preform; the first preform and the second preform are combined into a double-layered PTFE sheet, wherein combining the first preform and the second preform comprises: pressing the first preform into a first sheet, pressing the second preform into a second sheet, wherein each preform is pressed separately, drying the first and second sheets, and pressurizing the first dried sheet and the second dried sheet together during co-stretching; and pressing the first preform into a first sheet, pressing the second preform into a second sheet, wherein each preform is pressed separately, drying the first and second sheets, and pressurizing the first dried sheet and the second dried sheet together during co-stretching; and the double-layered PTFE sheet is further co-stretched to form the filter membrane comprising a first layer that includes pores of the first pore size and a second layer that includes pores of the second pore size.