We have studied fine-scale temporal variations in the arrival profiles of approximately 20 keV nucleon-1 to approximately 2 MeV nucleon-1 ions from impulsive solar flares using instrumentation on board the Advanced Composition Explorer spacecraft at 1 AU between 1997 November and 1999 July. The particle events often had short-timescale ( approximately 3 hr) variations in their intensity that occurred simultaneously across all energies and were generally not in coincidence with any local magnetic field or plasma signature. These features appear to be caused by the convection of magnetic flux tubes past the observer that are alternately filled and devoid of flare ions even though they had a common flare source at the Sun. Thus, we have used the particles to study the mixing of the interplanetary magnetic field that is due to random walk. We deduce an average timescale of 3.2 hr for these features, which corresponds to a length of approximately 0.03 AU.