Mechanical equilibrium of particles attached to rock during flow is defined as torque balance of attaching and detaching forces. Oversaturated state of fines means that detaching torque exceeds the attaching torque, and fines detach as the flow starts. In undersaturation, the attaching torque dominates the detaching torque, and fines mobilisation can occur only if there is either additional detaching torque or a weakening of the attaching torque. Preliminary laboratory tests determine the mechanical equilibrium velocity and salinity, to ensure that oversaturation or undersaturation can be readily reproduced in further corefloods. We formulate the basic governing equations and derive exact solutions for over and undersaturated cases. The exact solutions allow formulating the fingerprints for transport of oversaturated and undersaturated fines in porous media. The coreflood results reveal the characteristic features of the oversaturated case of fines migration. Moreover, the analytical modelling results are found to be in high agreement with the experimental data, under the typical values of the fitted model coefficients. (C) 2019 Elsevier Ltd. All rights reserved.