Relationship between flux and resident concentrations for anomalous dispersion

A concentration measurement in the field or laboratory will be most closely related to either the resident or the flux concentration. The former describes all solute particles present at some point while the latter describes solute particles that have moved irrevocably past some point. In addition, either measurement may preferentially sample a relatively mobile phase ( say, by drawing a water sample) or both the mobile and immobile phases ( say, by measuring in- situ electrical conductivity). The relationship between the resident and flux concentrations for anomalous, fractional-order, transport equations is developed analytically using an integral transform and explored further using a random walk model. The late- time resident and flux concentrations may differ by several orders- of- magnitude, so that the relationships developed here are critical for making predictions of flux based on resident concentration measurements and vice- versa.