Thermal Conductivity of an Array of Unsaturated Solid Spheres.
Robert Ewing, Iowa State University, Department of Agronomy, Iowa State University, Ames, IA 50011-1010, Allen Hunt, Wright State University, Wright State, Dayton, OH 45321, and Robert Horton, Department of Agronomy, Iowa State University, Ames, IA 50011-1010.
The thermal conductivity of soil increases with increasing saturation, but the shape of the relationship changes with soil texture and other factors. For example, in some soils the addition of a small amount of water produces no increase at all in the thermal conductivity, while in others the increase is immediate. This investigation was initiated to clarify the contribution of small amounts of water to system conductivity. The soil was modeled as locally homogeneous regions of equal-sized spheres in a cubic array, with a contact angle of zero. Water collects at the contact points, forming capillary bridges that increase the effective thermal contact between the grains. Within a given region, as long as the air phase is continuous, the thermal conductivity increases with approximately the one-fourth power of the water content, with the precise value of the exponent varying according to the relative conductivities of the solid and liquid phases. At higher water contents, once the air phase is discontinuous, the relationship becomes nearly linear. Using this relationship to model the thermal conductivity of a soil with a power-law particle-size distribution gives results in good agreement with measured values.