Besides, electrospinning method as mentioned Daniel, I would fill the pores with PEG or whatsoever, the after coating PVA on the top surface remove the pore filling agent (i.e. PEG).
If you wish to physically modify the material of UF membrane with adsorbed PVA without filling the pores, I would suggest to use low concentrations of PVA (1-5 mg/mL) in water-acetone or water-ethanol mixture close to (but not above) the cloud point, in order to increase the polymer adsorption. Let the solution of polymer go through the membrane by suction. Keep them in contact overnight, wash the membrane with the same solvent to remove non-adsorbed PVA, and then with a small amount of water to remove solvent. Physically adsorbed PVA will be slowly desorbed by aqueous filtrates, but there is a chance to make a successful filtration through the modified membrane once or twice. Drying on air may make the coating more stable, if the membrane is not distorted.
I suggest to use a intermediate (flexible) substrate to transfer the PVA polymer over the membranes. In literature this method is also calles 'stamp and stick'. A transparancy sheet can be used on which the PVA 'sticks'. Then you 'stamp' it on the membrane substrate to transfer the PVA polymer. The thickness of the PVA should not be larger then the pore depth.
I have a similar problem. I am casting a polymer onto a porous membrane using spin-coating. I think I am minimizing the effect by using higher viscosity concentrations, but I am open to suggestions as well. Ali Nematollahzadeh Daniel Wijnperle