Depletion force between two large spheres suspended in a bath of small spheres: Onset of the Derjaguin limit
Abstract
We analyze the depletion interaction between two hard colloids in a hardsphere solvent and pay special attention to the limit of large size ratio between colloids and solvent particles which is governed by the wellknown Derjaguin approximation. For separations between the colloids of less than the diameter of the solvent particles (defining the depletion region), the solvent structure between the colloids can be analyzed in terms of an effective twodimensional gas. Thereby we find that the Derjaguin limit is approached more slowly than previously thought. This analysis is in good agreement with simulation data which are available for a moderate size ratio of 10. Small discrepancies in results from density functional theory (DFT) at this size ratio become amplified for larger size ratios. Therefore we have improved upon previous DFT techniques by imposing testparticle consistency which connects DFT to integral equations. However, the improved results show no convergence towards the Derjaguin limit and thus we conclude that this implementation of DFT together with previous ones which rely on testparticle insertion become unreliable in predicting the force in the depletion region for size ratios larger than 10.
 Publication:

Physical Review E
 Pub Date:
 April 2004
 DOI:
 10.1103/PhysRevE.69.041404
 arXiv:
 arXiv:condmat/0310523
 Bibcode:
 2004PhRvE..69d1404O
 Keywords:

 83.80.Hj;
 05.20.Jj;
 Suspensions dispersions pastes slurries colloids;
 Statistical mechanics of classical fluids;
 Condensed Matter  Soft Condensed Matter
 EPrint:
 17 pages