Self-Potential Studies in Volcanic Environments: A Cheap and Efficient Method for Multiscale Fluid-Flow Investigations

Table 1

Onsager matrix displaying the types of coupled flow that can occur in a porous medium. The main diagonal represents direct flow phenomena, i.e., the actuating force and the corresponding flow are of the same type. The off-diagonal entries represent the coupled flow phenomena. Onsager reciprocity is reflected by the symmetrical entries across the main diagonal (e.g., streaming potential vs. electroosmosis). Bear in mind that this table is a highly simplified representation. Table 1 is modified from [48].

Flux	Driving force: gradient of the actuating phenomenon
	Hydraulic	Electric	Chemical	Thermal
Fluid	Darcy’s law	Electroosmosis	Chemical osmosis	Thermoosmosis
Charge	Streaming potential	Ohm’s law	Dorn potential	Seebeck effect
Solute	Ultrafiltration	Electrophoresis	Fick’s law	Soret effect
Heat	Isothermal heat	Peltier effect	Dufour effect	Fourier’s law