text: The number of theoretical plates, or separation efficiency, in capillary electrophoresis is given by:
  where  is the number of theoretical plates,  is the apparent mobility in the separation medium and  is the diffusion coefficient of the analyte.  According to this equation, the efficiency of separation is only limited by diffusion and is proportional to the strength of the electric field, although practical considerations limit the strength of the electric field to several hundred volts per centimeter.  Application of very high potentials (>20-30 kV) may lead to arcing or breakdown of the capillary.  Further, application of strong electric fields leads to resistive heating (Joule heating) of the buffer in the capillary.  At sufficiently high field strengths, this heating is strong enough that radial temperature gradients can develop within the capillary.  Since electrophoretic mobility of ions is generally temperature-dependent (due to both temperature-dependent ionization and solvent viscosity effects), a non-uniform temperature profile results in variation of electrophoretic mobility across the capillary, and a loss of resolution.  The onset of significant Joule heating can be determined by constructing an "Ohms Law plot", wherein the current through the capillary is measured as a function of applied potential.  At low fields, the current is proportional to the applied potential (Ohms Law), whereas at higher fields the current deviates from the straight line as heating results in decreased resistance of the buffer.  The best resolution is typically obtained at the maximum field strength for which Joule heating is insignificant (i.e. near the boundary between the linear and nonlinear regimes of the Ohm's Law plot).  Generally capillaries of smaller inner diameter support use of higher field strengths, due to improved heat dissipation and smaller thermal gradients relative to larger capillaries, but with the drawbacks of lower sensitivity in absorbance detection due to shorter path length, and greater difficulty in introducing buffer and sample into the capillary (small capillaries require greater pressure and/or longer times to force fluids through the capillary).
  The efficiency of capillary electrophoresis separations is typically much higher than the efficiency of other separation techniques like HPLC.  Unlike HPLC, in capillary electrophoresis there is no mass transfer between phases.  In addition, the flow profile in EOF-driven systems is flat, rather than the rounded laminar flow profile characteristic of the pressure-driven flow in chromatography columns as shown in figure 5. As a result, EOF does not significantly contribute to band broadening as in pressure-driven chromatography.  Capillary electrophoresis separations can have several hundred thousand theoretical plates.
  The resolution () of capillary electrophoresis separations can be written as:
  According to this equation, maximum resolution is reached when the electrophoretic and electroosmotic mobilities are similar in magnitude and opposite in sign.  In addition, it can be seen that high resolution requires lower velocity and, correspondingly, increased analysis time.
  Besides diffusion and Joule heating (discussed above), factors that may decrease the resolution in capillary electrophoresis from the theoretical limits in the above equation include, but are not limited to, the finite widths of the injection plug and detection window; interactions between the analyte and the capillary wall; instrumental non-idealities such as a slight difference in height of the fluid reservoirs leading to siphoning; irregularities in the electric field due to, e.g., imperfectly cut capillary ends; depletion of buffering capacity in the reservoirs; and electrodispersion (when an analyte has higher conductivity than the background electrolyte).  Identifying and minimizing the numerous sources of band broadening is key to successful method development in capillary electrophoresis, with the objective of approaching as close as possible to the ideal of diffusion-limited resolution.