Methods of maintaining narrow residence time distributions in continuous flow systems, particularly applicable to virus inactivation such as during a protein purification process. Fluid sample is introduced into an axial flow channel and caused to flow therein in discrete packets or zones to minimize residence time distribution and axial dispersion. Embodiments described herein obviate or minimize the need for using large tanks or reservoirs for performing virus inactivation during a protein purification process; reduce the overall time required for virus inactivation, and/or reduce the overall physical space required to perform the virus inactivation operation during a protein purification process, which in turn reduces the overall footprint for the purification process.