Column efficiency (as described by Van Deemter) in HPLC is largely a function of dispersion, column particle size and the flow rate of the mobile phase. Flow rate should be optimized for all methods (linear velocity). Once the optimum flow rate range is achieved, little to no advantage in analysis time or solvent savings is found by increasing it (as column efficiency normally decreases at higher flow rates).
From a practical point of view, columns packed with porous 3 to 5 micron diameter supports show only small differences in efficiency as flow rate is varied above the initial, optimum level. Running at too low a flow rate serves no purpose, increases dispersion/diffusion and delays the peaks from eluting off the column in a timely manner. Once the flow rate has been set within the 'optimized zone', it no longer becomes a variable in HPLC method development.
Many 3 micron supports do demonstrate some ability to maintain optimum efficiency at slightly higher flow rates (e.g. with linear velocities > 1 mm/second), but significant advantages in using higher flow rates to save time and solvent are not obvious.
However, with the much smaller diameter ~ 2 micron particles, column efficiency can be further optimized using higher than "typical" flow rates on standard columns. Columns packed with these smaller porous particles show optimized flow rates at higher linear velocities (2x normal or ~ 2 mm/second for standard analytical sized columns. If your method currently runs at 1.000 mL/min, you may be able to run the same method at 2.000 mL/min using one of the very small particles). This increased available efficiency coupled with proper optimization of the flow path to reduce dispersion allows for a doubling of the flow rate without a loss of efficiency (or loss of resolution). Depending on the scaling used, a two-fold savings in analysis time over conventional methods using larger particles may be observed. There may be a corresponding increase in system back-pressure too (if only the particle size is changed, but the column dimensions are unchanged. *Some of this can be countered using proper scaling of the column dimensions too. Optimization of method resolution, overall time and solvent usage should be considered). The increased efficiency gained from the smaller particle size also allows for scaling down the column dimensions (i.e. length, ID or both) too, though a trade-off between overall column efficiency vs analysis time and/or back-pressure must be addressed to optimize the method to meet the application goals.
Summary: HPLC analytical column flow rate is often ignored in method development (esp after it has been adjusted to the initial optimum, often 1.0 mL/min for a 4.6 mm ID column), but IF you are using porous HPLC particles that are smaller than 3.5 micron diameter, please be sure to re-optimize the flow rate for your application so you can take advantage of any increases in column efficiency and/or scaling. As with ALL applications using these small particles, pre-optimization of the HPLC flow path is often needed to achieve any of the possible benefits.