A modification of the single-fluid MHD approach for modeling a mass-lo
aded plasma is proposed. The well known source terms in the single-flu
id equations remain unchanged in the model. The finite time-duration o
f the new ions assimilation is taken into account via introduction of
additional currents and charges, considered as external to the basic f
luid substance. These external currents and charges are caused by non-
picked up new ions in the frame of time and length scales, smaller tha
n the infinitesimal scales of the considered continuum. Possible quasi
-quantitative estimates for so introduced parameters, based on additio
nal knowledge of relaxation time, are considered. A kinematic analysis
of the fluid and magnetic field lines reveals that the magnetic field
is not frozen in. There are two velocity components of the obtained m
agnetic held diffusion: diffusion component directed against the flow
of the neutral particles, and pseudo-diffusion along the magnetic fiel
d line. A generalization of the solution for solar wind flow past a co
metary exosphere, containing two shocks and contact surface, is consid
ered qualitatively in terms of this approach. Such a consideration pre
dicts that the interplanetary magnetic field penetrates through the co
ntact surface, reaching the inner shock, which becomes a diamagnetic b
oundary.