This question has several possible answers depending on what the definition of mixing is and how much of a change has been made to the agitator.  If one of the changes has been to change the impeller type, as for instance a change from a pitched-blade turbine to a hydrofoil impeller, the "backtracking" becomes more complicated.  The following are some possible answers to the question, starting with the simplest:
 
If the only change has been the rotational speed, the blend time will have been reduced in proportion to the increase in rotational speed.  To a first approximation, the length of time required for uniform blending is proportional to the number of revolutions of the mixer, for the same type and size impeller.  Similarly, the local velocities and apparent agitation intensity will be in proportion to the speed change.  This answer is much too obvious for the question.
 
If the change to the agitator has been to increase the diameter of the same type of impeller.  The power input will have increased by the ratio of the new to old impeller diameters raised to the fifth power.  For instance, a 10% increase in the impeller diameter will make a 61% increase in the power.  Power input might be important for some reactions.  Blend time is less sensitive to the impeller diameter, with the same impeller type, so an increase in impeller diameter of 10% would reduce blend time by 20% or be only about 80% of the original blend time.  Fluid velocity is often the motion most commonly associated with the appearance of mixing intensity and should change approximately in proportion to the impeller diameter squared.  Thus, an increase in impeller diameter of 10% would appear to increase the mixing intensity by about 20%.
 
To reduce the speed, the change needs to be in opposite proportion to the increase associated with a diameter increase for the same type, geometrically similar impeller.  For instance to adjust the mixer speed to compensate for increased impeller diameter, the speed ratio needs to be in inverse proportion to the diameter ratio to the five thirds.  Thus to compensate for a 10% increase in impeller diameter, the speed needs to be reduced by 15% to match the original power.  If the mixing intensity or fluid velocity need to be matched, then the mixer speed needs to be adjusted in proportion to the diameter ratio to the four thirds.  Thus for a 10% increase in impeller diameter, the speed be reduced by 12%.  All of these adjustments assume that the same type of impeller is involved.  If a different type of impeller is used many other combinations of corrections are possible.
 
In addition, different adjustments may be needed if the process is other than single phase liquid blending.  The simplest, and least elegant solution to the problem is to keep the tip speed of the impeller constant.  If the impeller diameter increased by 10%, then reduce the speed by 10%.  This approach can be used to a first approximation for any type of impeller and any type of application.  Of course, a tip speed change does not necessarily reflect actual changes to power, torque, blend time, or process result, especially for different types of impellers.  In many ways the answer to the question is "it depends."

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