Figure 1 - Schematic of a TPA experiment with a) plate or b) cylinder. The schematic shows the formation of a pressure gradient in the pore fluid between the sample interior and the sample surface.

A TPA experiment consists of submerging a saturated porous body and observing the dilation of the body as it is exposed to a temperature cycle. Upon heating, the liquid phase expands much more than the solid phase so it tends to flow out of the body. If the heating rate is fast, or the permeability is low, the liquid does not have time to escape, so it is forced to expand in the pores. Thermal expansion of the confined fluid places the fluid in compression and the network in tension, causing the network to stretch like a spring. In addition, a gradient in pore pressure forms between the interior of the solid network and its surface. During a subsequent isotherm, the solid network will force liquid out of its pores until ambient pressure is restored throughout the pore space, and the solid retracts to a dimension dictated by its thermal expansion coefficient. Analyzing the kinetics of the dilation permits extraction of the permeability coefficient of the solid network, and the thermal expansion coefficient of the solid phase.

Figure 2 - Results from a TPA experiment with a cylinder. The plot shows the overshoot in the strain caused by the confined pore fluid, and, during the isotherm, relaxation to the plateau.

Figure 2 shows results from a TPA experiment with a cylinder. The strain rate is greatest at the beginning of the heating ramp. The curvature in the dilation, the height of the peak, and the kinetics of relaxation to the plateau are governed by the transport properties of the porous body. The dotted line represents a fit of the analytical expression for the strain to the experimental data. When fitting this expression to the data the only free paramter is the characteristic time for hydrodnamic relaxation, τ. The value of τ; that yields the best fit of the analytical solution to the data is then used to determine the fluid permeability. Details concerning the theoretical analysis and fitting routine can be found here. To substantiate the TPA technique, comparative measurements where performed with beam bending. These measurements uncovered the occurrence of anomalous thermal expansion of water in fine pores (rp < 10 nm). In addition, the comparison indicated that ignoring the occurrence of VE stress relaxation during the experiment resulted in an underestimation of the permeability of our cement paste by ~ 30%. The results of this comparionson and the corresponding analysis can be found here.