(US9010547) We claim: 1. A membrane comprising: (a) a coating layer having a thickness from about 0.1 to about 1 mu m comprising cellulose or a cellulose derivative; (b) a porous support layer comprising nanofibers having a core-shell structure, the core and shell formed of different polymers; wherein the membrane is prepared by a process comprising coating a solution comprising cellulose or a cellulose derivative dissolved in an ionic liquid onto the porous support layer, and removing the ionic liquid, thereby forming the coating layer, and wherein the porous support layer further comprises a plurality of layers each comprising nanofibers, and wherein the average diameter of the nanofibers in the layer contacting the coating layer is less than the average diameter of the nanofibers disposed below the layer contacting the coating layer. 2. The membrane of claim 1, wherein the concentration of the cellulose or a cellulose derivative in the ionic liquid is in the range of about 0.002% (w/w) to 10% (w/w). 3. The membrane of claim 1, wherein the coating layer has a thickness from about 0.3 microns to about 1.0 microns, and wherein the concentration of cellulose or cellulose derivative in the ionic liquid is in the range of from about 0.01% (w/w) to about 2.5% (w/w). 4. The membrane of claim 1, wherein the ionic liquids comprise N-alkylimidazolonium cations having the general formula 1-CnH2n+1-3-methylimidazolonium wherein n is an integer from 1-12. 5. The membrane of claim 4, wherein the anion for the N-alkylimidazolonium cation is selected from the group consisting of halogens, perchlorates, pseudohalogens, and carboxylates. 6. The membrane of claim 5, wherein the anion comprises Cl-, or Br-. 7. The membrane of claim 1, wherein the ionic liquid comprises 1-ethyl-3-methylimidazolium acetate or 1-butyl-3-methylimidazolium chloride. 8. The membrane of claim 1, wherein the porous support layer comprising nanofibers has a thickness of about 50 nm to about 50 mu m. 9. The membrane of claim 1, wherein the porous support has a thickness of about 5 mu m to about 50 mu m. 10. The membrane of claim 1, wherein the average diameter of the nanofibers in the layer contacting the coating layer ranges from about 2 nm to about 100 nm, and the average diameter of the nanofibers disposed below the layer contacting the coating layer ranges from about 100 nm to about 2000 nm. 11. The membrane of claim 1, wherein the coating layer has a thickness in the range of about 0.3 to about 0.5 microns, and the thickness of the porous support layer is in the range of about 20 mu m to about 50 mu m. 12. The membrane of claim 1, wherein the nanofibers comprise a polymer selected from the group consisting of polyolefins, polysulfones, polyethersulfones, fluoropolymers, polyvinylidene fluorides, polyesters, polyamides, polycarbonates, polystyrenes, polyacrylamides, polyacrylates, polyacrylonitriles, poly(meth)acrylates, polyvinyl acetates, polyvinyl alcohols, polysaccharides, chitosan, proteins, polyalkyleneoxides, polyurethanes, polyrureas, polyvinyl chlorides, polyimines, polyvinylpyrrolidones, polyacrylic acids, polymethacrylic acids, polysiloxanes, poly(ester-co-glycol) polymers, poly(ether-co-amide) polymers, cross-linked forms thereof, derivatives thereof, and copolymers thereof. 13. The membrane of claim 12, wherein the membrane is an ultrafiltration membrane, a nanofiltration membrane, a reverse osmosis membrane, or a forward osmosis membrane. 14. The membrane of claim 1, wherein the nanofibers comprise polyamide, polyacrylonitrile, polysulfone, polyvinyl alcohol, polyethersulfone, or derivatives thereof. 15. The membrane of claim 1, wherein the porous support further comprises a substrate layer disposed on the surface of the porous support opposite the surface in contact with the cellulose coating. 16. The membrane of claim 15, wherein the substrate layer is either woven or non woven. 17. The membrane of claim 15, wherein the substrate layer comprises poly(ethylene terephthalate). 18. The membrane of claim 1, having a permeation flux for water filtration of about 400 L/m2h to about 700 L/m2h at a pressure of about 15 psi, and wherein the coating layer has a thickness of about 0.3 microns. 19. The membrane of claim 1, wherein the thickness of the coating layer is in the range of about 0.3 micron to about 1.0 micron. 20. The membrane of claim 1, wherein the volume of the core of the nanofibers having the core-shell structure occupies from about 1% to about 90% of the total effective volume of the nanofiber.
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