  We investigate flow-driven amoeboid motility as exhibited by microplasmodia
of Physarum polycephalum. A poroelastic two-phase model with rigid boundaries
is extended to the case of free boundaries and substrate friction. The
cytoskeleton is modeled as an active viscoelastic solid permeated by a fluid
phase describing the cytosol. A feedback loop between a chemical regulator,
active mechanical deformations, and induced flows gives rise to oscillatory and
irregular motion accompanied by spatio-temporal contraction patterns. We cover
extended parameter regimes of active tension and substrate friction by
numerical simulations in one spatial dimension and reproduce experimentally
observed oscillation periods and amplitudes. In line with experiments, the
model predicts alternating forward and backward ectoplasmatic flow at the
boundaries with reversed flow in the center. However, for all cases of periodic
and irregular motion, we observe practically no net motion. A simple
theoretical argument shows that directed motion is not possible with a
spatially independent substrate friction.
