Following the approach of Kuhnen et al. (2000), determine the rate coefficient for aggregation of the E. coli cells.  Calculate the theoretical rate coefficient (k_fast. m³ s^-1) for cell-cell collisions using the aggregation rate coefficient spreadsheet.

Calculate the collision efficiency for cell-cell collisions for the three highest ionic strengths tested by Redman et al., I = 31.6, 100, and 300 mM.  To calculate the collision efficiency, use the relationship between N_DLVO (the dimensionless parameter introduced by Elimelech (ref. 38 in Redman et al.) and the collision efficiency a derived in Redman et al. (2004).  For N_DLVO, you will need values of k, the ionic strength-dependent inverse Debye length parameter (watch out for the units of I), a Hamaker constant A for cell-cell interactions, the dielectric permittivity of water and a vacuum, and the cell surface potential, which you can approximate at the cell zeta potential at the appropriate ionic strength.

With these collision efficiencies for three ionic strengths, calculate three rate coefficients (k, m³ s^-1) for cell-cell aggregation and three stability ratios (W).

Compare the calculated values of the cell-cell collision efficiencies with those determined for hematite-hematite aggregation determined by Kuhnen et al. (2000) and decide if multi-layer deposition of E. coli cells would have occurred in the Redman et al. (2004) experiments.

Finally, calculate the DLVO potential energy between the cells for the three ionic strengths for the cases of constant potential and constant charge.  Does a secondary energy minimum exist between cells in any of these cases?  How would this secondary minimum affect cell-cell aggregation?