= Capillary electrophoresis
\b[<Capillary electrophoresis>] separates species by their motion in an <electric field> inside a narrow liquid-filled tube. In its free-solution form, different <electrophoretic mobilities> produce different drift speeds; a detector at a fixed position records the arriving bands as an <electropherogram>. The liquid itself can also move by <electroosmotic flow>, so arrival order is not determined by molecular charge alone.
A simple apparatus places the ends of a capillary in two buffer reservoirs containing electrodes. An applied <electric potential difference> drives migration along the tube; a detection window interrogates the passing material. In the uniform-field model, with total capillary length $L$, detector distance $L_d$ and signed applied potential $U$,
$$
E=\frac UL,\qquad v_i=(\mu_{{\rm ep},i}+\mu_{\rm eo})E,\qquad t_i=\frac{L_dL}{(\mu_{{\rm ep},i}+\mu_{\rm eo})U}.
$$
The last expression requires net motion towards the detector. Thus a neutral marker can move with <electroosmotic flow> even though its <electrophoretic mobility> is zero. The instrument's distinction between total length and detector distance matters when converting migration times into apparent <mobility>.<Processing Methods - CE data by Waters>[Procedure, Step 2 and Step 5, item 6]{ref}
For an original ideal example, take $L=0.50\,\mathrm m$, $L_d=0.40\,\mathrm m$ and $U=20\,\mathrm{kV}$. Two net mobilities $(4,5)\times10^{-8}\,\mathrm{m^2\,V^{-1}\,s^{-1}}$ give speeds $1.6$ and $2.0\,\mathrm{mm\,s^{-1}}$ and migration times 250 and 200 s. These are model values, not assigned chemical identities. Band widths from <diffusion>, injection and other dispersion mechanisms determine whether the time difference is actually resolved.
Narrow tubes also help remove <Joule heating>. For a uniform cylindrical liquid conductor, heat generation per volume is $\sigma E^2$, with <electrical conductivity> $\sigma$, while wall area per liquid volume is $2/a$ for tube radius $a$. This geometric scaling motivates small bores, although temperature control still depends on heat transfer through the wall and surroundings. Increasing the <electric field> indefinitely is therefore not a free route to perfect separation.
A primary 1981 demonstration used a 1 m glass capillary with 75 micrometre internal diameter, a 30 kV applied potential and a <fluorescence> detector. It resolved fluorescent derivatives of <amino acids>, <peptides> and urinary amines. The observed result was separated fluorescent zones; the need to derivatize the samples was an explicit detection limitation.<Free-zone electrophoresis in glass capillaries by J. W. Jorgenson and K. D. Lukacs>[Abstract, apparatus and demonstrated separations]{ref}
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