Estimating depletion layer thickness in colloidal systems: Correlation with oil-in-water emulsion composition

In emulsions, slippage due to wall depletion effects is well known in rheological investigations. This effect can be overcome by using geometries with serrated surfaces. However, we present here an easily practicable calculation that allows the slip data to be manipulated in order to determine the depletion layer thickness when data from both smooth and serrated surfaces is obtained. When studies are performed over a range of concentrations we show that there is a strong correlation between depletion layer thickness and emulsion composition. The experimental system used as the test case for the method was the ternary system triton X-100/water/tetradecane. Calculations were performed using data obtained for oil-in-water emulsions with the parallel plate geometry for a range of different gap sizes. The depletion layer thickness (≤1 μm) decreased on increasing the amount of dispersed phase, until at a sufficiently high concentration of dispersed phase (φmax = 0.73) slippage was no longer observed. The maximum depletion layer thickness was found to be a quadratic function of the relative volume fraction of the dispersed phase. The data coincide with those reported in the literature for a latex particle suspension if plotted using the same representation. Moreover, the proportionality constant was found to be of the order of the radius of the largest droplets in the dispersion. It is these droplets, which are chiefly responsible for the three-dimensional arrangement of the dispersed phase. This leads to the conclusion that the thickness of the depletion layer is controlled by the volume fraction and the size of the dispersed droplets.