The dynamics of imbibition into the roughness of a surface was investigated with hexagonal arrays of anisotropic nanofins fabricated with interference lithography and metal assisted chemical etching. It was found that viscous drag caused by the nanofins is similar to that caused by open nano-channels of equal length and height containing the same volume of liquid. In addition, the energy dissipated by form drag for a given driving pressure was determined to be directly proportional to the volume of fluid between nanofin planes that are flat and normal to the imbibition direction.