Visions of a single mobile substance present as two rival phases more or less cleanly segregated by capillarity between rival strata of a serially porous medium (a discontinuum) imply explicit testable equations for externally measured capillary thermo-osmotic pressures and capillary thermo-osmosis, with implications for thermomechanical consolidation, dilation, and cracking. Underlying equations assume fluid phases governed by the laws of surface tension and viscous flow, moderated by an appropriate form of the Clapeyron equation. Derived phenomenological coefficients in macroscopic equations for steady coupled transports of mass and heat include only path-length-weighted fluid and heat conductances for rival domains and the heat of phase transformation. Expressions emphasize the phase-specific nature of Onsager's reciprocity principle and apply to serial media held within permeameters set up for measuring either isothermal or adiabatic mass transport or held within sealed containers intended for measurements of thermal conductivities. Results clarify unmet challenges facing modelers of similar processes and attributes in randomly porous media. ¿ 1998 American Geophysical Union