Fibers with diameters less than a micron can be formed using electrospinning processes where a droplet of polymer solution or melt is elongated by a strong electrical field. The resulting fibers are collected as non-woven mats with extremely large surface to volume ratio; which are useful for various applications including filtration. Most previous studies on electrospinning have focused on fibers from polymer solutions, i.e., are directed to solution electrospinning. Current solution electrospinning apparatus and processes have the disadvantages of requiring a dissolving step, of requiring solvent recovery and disposal or complete recycling if the process is to be environmentally friendly, of having low production rates because of the dissolving and solvent recovery/recycling steps detracting from obtaining high throughput, of not being adaptable to polymers such as polyethylene, polypropylene, polyethylene terephthalate and polybutylene terephthalate, which are not dissolvable in acceptable solvents at room temperature, of requiring regulation of a plurality of parameters to adjust molecular properties and solidification and of requiring apparatus not readily provided by adaptation of conventional existing facilities for fiber/non-woven production for most polymers since these are based on melt treatment. Melt electrospinning apparatus and process which would avoid these disadvantages and provide useful production of fibers/non-wovens have not heretofore been developed. Moreover, no attempts have been made to provide solution electrospinning apparatus and processes which are suitable for operation on polymers which are not dissolvable in acceptable solvents at room temperature.