text: The separation of compounds by capillary electrophoresis is dependent on the differential migration of analytes in an applied electric field. The electrophoretic migration velocity () of an analyte toward the electrode of opposite charge is:
  The electrophoretic mobility can be determined experimentally from the migration time and the field strength:
  where  is the distance from the inlet to the detection point,  is the time required for the analyte to reach the detection point (migration time),  is the applied voltage (field strength), and  is the total length of the capillary. Since only charged ions are affected by the electric field, neutral analytes are poorly separated by capillary electrophoresis.
  The velocity of migration of an analyte in capillary electrophoresis will also depend upon the rate of electroosmotic flow (EOF) of the buffer solution. In a typical system, the electroosmotic flow is directed toward the negatively charged cathode so that the buffer flows through the capillary from the source vial to the destination vial.  Separated by differing electrophoretic mobilities, analytes migrate toward the electrode of opposite charge. As a result, negatively charged analytes are attracted to the positively charged anode, counter to the EOF, while positively charged analytes are attracted to the cathode, in agreement with the EOF as depicted in figure 3.
  The velocity of the electroosmotic flow,  can be written as:
  where  is the electroosmotic mobility, which is defined as:
  where  is the zeta potential of the capillary wall, and  is the relative permittivity of the buffer solution.  Experimentally, the electroosmotic mobility can be determined by measuring the retention time of a neutral analyte.  The velocity () of an analyte in an electric field can then be defined as:
  Since the electroosmotic flow of the buffer solution is generally greater than that of the electrophoretic mobility of the analytes, all analytes are carried along with the buffer solution toward the cathode.  Even small, triply charged anions can be redirected to the cathode by the relatively powerful EOF of the buffer solution.  Negatively charged analytes are retained longer in the capillary due to their conflicting electrophoretic mobilities. The order of migration seen by the detector is shown in figure 3: small multiply charged cations migrate quickly and small multiply charged anions are retained strongly.
  Electroosmotic flow is observed when an electric field is applied to a solution in a capillary that has fixed charges on its interior wall.  Charge is accumulated on the inner surface of a capillary when a buffer solution is placed inside the capillary.  In a fused-silica capillary, silanol (Si-OH) groups attached to the interior wall of the capillary are ionized to negatively charged silanoate (Si-O) groups at pH values greater than three.  The ionization of the capillary wall can be enhanced by first running a basic solution, such as NaOH or KOH through the capillary prior to introducing the buffer solution. Attracted to the negatively charged silanoate groups, the positively charged cations of the buffer solution will form two inner layers of cations (called the diffuse double layer or the electrical double layer) on the capillary wall as shown in figure 4.  The first layer is referred to as the fixed layer because it is held tightly to the silanoate groups.  The outer layer, called the mobile layer, is farther from the silanoate groups.  The mobile cation layer is pulled in the direction of the negatively charged cathode when an electric field is applied.  Since these cations are solvated, the bulk buffer solution migrates with the mobile layer, causing the electroosmotic flow of the buffer solution. Other capillaries including Teflon capillaries also exhibit electroosmotic flow.  The EOF of these capillaries is probably the result of adsorption of the electrically charged ions of the buffer onto the capillary walls. The rate of EOF is dependent on the field strength and the charge density of the capillary wall.  The wall's charge density is proportional to the pH of the buffer solution.  The electroosmotic flow will increase with pH until all of the available silanols lining the wall of the capillary are fully ionized.
  In certain situations where strong electroosmotic flow toward the cathode is undesirable, the inner surface of the capillary can be coated with polymers, surfactants, or small molecules to reduce electroosmosis to very low levels, restoring the normal direction of migration (anions toward the anode, cations toward the cathode).  CE instrumentation typically includes power supplies with reversible polarity, allowing the same instrument to be used in "normal" mode (with EOF and detection near the cathodic end of the capillary) and "reverse" mode (with EOF suppressed or reversed, and detection near the anodic end of the capillary).  One of the most common approaches to suppressing EOF, reported by Stellan Hjertén in 1985, is to create a covalently attached layer of linear polyacrylamide.  The silica surface of the capillary is first modified with a silane reagent bearing a polymerizable vinyl group (e.g. 3-methacryloxypropyltrimethoxysilane), followed by introduction of acrylamide monomer and a free radical initiator.  The acrylamide is polymerized in situ, forming long linear chains, some of which are covalently attached to the wall-bound silane reagent.  Numerous other strategies for covalent modification of capillary surfaces exist.  Dynamic or adsorbed coatings (which can include polymers or small molecules) are also common.  For example, in capillary sequencing of DNA, the sieving polymer (typically polydimethylacrylamide) suppresses electroosmotic flow to very low levels.  Besides modulating electroosmotic flow, capillary wall coatings can also serve the purpose of reducing interactions between "sticky" analytes (such as proteins) and the capillary wall.  Such wall-analyte interactions, if severe, manifest as reduced peak efficiency, asymmetric (tailing) peaks, or even complete loss of analyte to the capillary wall.