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We consider the equation of the Jeffreys type as the basic one in threedifferent models of mass transfer, namely, the Jeffreys type and two-phasemodels, and the $D_1$ approximation to the linear Boltzmann equation. We studytwo classic 1 + 1D problems in the framework of each model. The first problemis the transfer of a substance initially confined in a point. The secondproblem is the transfer of a substance from a stationary point source. Wecalculate the mean-square displacement (MSD) for the solutions of the firstproblem. The temporal behaviour of the MSD in the framework of the first andthird models is found to be the same as that in the Brownian motion describedby the standard Langevin equation. Besides, we find a remarkable phenomenonwhen a portion of the substance does not move.

Local immobilization of particles in mass transfer described by the equation of the Jeffreys type