Capillary Force and Water Retention between Two Uneven-Sized Particles

Capillary force and water retention between two uneven-sized spherical particles are investigated. Previous studies have been limited to systems with even-sized particles. The appropriate definition of the boundary value problem for a water lens between two uneven-sized particles is presented under the consideration of thermodynamic free energy at the microscopic level. Capillary force and water retention under the consideration of toroidal approximation are also derived for a system with two uneven-sized particles. Comparison of normalized capillary force and water retention calculated by the free energy approach and toroidal approximation are conducted. The quantitative analysis shows that for a system with two identical particles, the behavior of water retention and normalized capillary force is very similar to some recent studies by others, confirming that the toroidal approximation provides reasonably good estimations for both capillary force and water retention. For a system with uneven-sized particles, it is shown that error in normalized capillary force could be significant as the matric suction approaches zero and the particle sizes become very different. The errors for the mean curvature of the meniscus for the toroidal approximation are significant where the matric suction is near zero. Thus for soils with varying particle sizes, it may be necessary to employ the exact solution to meniscus shape in order to accurately quantify normalized capillary force and water retention. The induced normalized capillary force increases inversely with the particle size, and is generally insensitive to the water content. For soil assembly with particle size of $0.01\mathrm{mm}$ , the normalized capillary force could reach $10\mathrm{kPa}$ , whereas for soil assembly with particle size of $1\mathrm{mm}$ , the normalized capillary force is on the order of $100\mathrm{Pa}$ .