Measurement of Capillary Force Between Uneven-Sized Spheres by Micro-Mechanical Manipulation

Bulk constitutive relations for unsaturated soils should be based upon and not violate the fundamental micro-mechanical interactions that occur. Thus, knowledge of these basic interactions is required in order to fully derive or assess a given constitutive relation. In particular, at low water contents liquid bridges can be assumed to exist between pairs of particles; knowledge of the interactions due to these bridges of varying liquid volume is necessary. To this end, a micro-mechanical experimental method to determine the capillary forces between individual soil particles at varying liquid content is proposed. A rough glass sphere (160–325 μm diameter) is glued to a glass fiber cantilever (30 μm) while another is glued to a rigid capillary tube. A small drop of liquid is applied, and the capillary force is measured by the deflection of the fiber cantilever as the particles are brought together and separated. The position of the base of the cantilever is fixed, while the movement of the particle attached to the rigid capillary tube is controlled by a high precision micro-manipulator. Displacements are tracked using high-speed digital video microscopy under an inverted light microscope. Image processing is used to analyze the frames taken during the experiments. Experiments with unevenly-sized spheres compare well to known analytic results. Liquid volume and mean curvature of the meniscus as functions of filling angle are well described analytically. Forces measured range from 25 to 50 micro-Newtons depending on the liquid content. A force characteristic curve is presented to describe this dependence. Viscosity effects are as yet undetermined as are detailed measurements of the liquid-solid contact angle hysteresis.