Analytic Theory for Dilute Colloids in a Charged Slit

Nanofluidic devices can now be manufactured with a slit-like geometry whose charged walls are 50-1000 nm wide. Through these slits, large charged macromolecules at very low concentration suspended in electrolytes can flow and be analyzed and separated based on their charge and other properties. To study such a system and to compute the flow of these colloidal macromolecules, the equilibrium distribution across the slit (perpendicular to the flow) is needed. Here, an analytic theory for such a concentration distribution of dilute colloid particles in a charged slit is presented. The theory is based on classical density functional theory (DFT) of fluids with the colloid particles described as large, charged, hard spheres and the background electrolyte described as point charges. In the limit of a very dilute colloid, low surface charge on the slit walls, and noninteracting electrical double layers at these walls, the approximate theory is quantitatively correct when compared to numerical solutions of the DFT equations. Outside of this regime of parameters, the approximate theory is generally qualitatively correct, especially when the colloid particles and the slit have the same sign charge.