A method, apparatus, and system for fabricating buckypaper or similar sheets of nanostructures having relatively high aspect ratios. A dispersion of nanostructures such as nanotubes is subjected to fluid dynamics/forces which promote alignment of their axes of elongation while in suspension in the flow. An agglomeration of better aligned nanostructures is isolated from the carrier fluid into a useable form. In the case of nanotubes, one form is buckypaper. One example of alignment forces is Taylor-Couette flow shear forces. One example of isolation is filtering the flowing dispersion to collect better aligned nanostructures across the filter into a sheet or film. The degree of alignment can produce anisotropic material properties that can be beneficially used in application of the sheet or film.