A 2-D finite-volume model is developed to simulate nonlinear IEF in complex microgeometries. This mathematical model is formulated based on the mass conservation and ionic dissociation relations of amphoteric macromolecules, charge conservation, and the electroneutrality condition. Based on the 2-D model, three different separation cases are studied: an IPG in a planar channel, an ampholyte-based pH gradient in a planar channel, and an ampholyte-based pH gradient in a contraction-expansion channel. In the IPG case, cacodylic acid (pK(1) = 6.21) and Tris (pK(1) = 8.3) are used as the acid and base, respectively, to validate the 2-D IEF model. In the ampholyte-based pH gradient cases, IEF is performed in the pH range, 6.21-8.3 using 10 ampholytes in the planar channel and 20 ampholytes in the contraction-expansion channel. The numerical results reveal different focusing efficiencies and resolution in the narrow and wide sections of the contraction-expansion channel. To explain this, the expressions for separation resolution and peak concentrations of separands in the contraction-expansion channel are presented in terms of the channel shape factor. In a 2-D planar channel, a focused band remains straight all the time. However, in a contraction-expansion channel, initially straight bands take on a crescent profile as they pass through the trapezoidal sections joining the contraction and expansion sections.