find the quadratic polynomial if α + β = ¼ and α.β = -1.
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When analytes containing cationic components, such as proteins, are separated in fused silica capillaries or micro-chips, they adsorb strongly to the negatively charged channel walls. Broadened and highly asymmetric peaks in the detector signal is symptomatic of the presence of such wall interactions. Band broadening is caused by the introduction of shear into the electroosmotic flow which leads to Taylor dispersion. The shearing flow in turn is caused by axial variations in zeta-potential due to adsorbed analytes. In this paper, numerical solutions of the coupled electro-hydrodynamic equations for fluid flow and the advection-diffusion equation for analyte concentration are presented in the limit of thin Debye layers. The simulations reproduce many of the qualitative effects of wall adsorption familiar from observation. Further, the simulation results are compared, and found to agree very well (to within a percent for characteristic values of the parameters) with a recently developed asymptotic theory.