  Soft living tissues like cartilage can be considered as biphasic materials
comprised of a fibrous complex biopolymer network and a viscous background
liquid. Here, we show by a combination of experiment and theoretical analysis
that both the hydraulic permeability and the elastic properties of (bio)polymer
networks can be determined with simple ramp compression experiments in a
commercial rheometer. In our approximate closed-form solution of the
poroelastic equations of motion, we find the normal force response during
compression as a combination of network stress and fluid pressure. Choosing
fibrin as a biopolymer model system with controllable pore size, measurements
of the full time-dependent normal force during compression are found to be in
excellent agreement with the theoretical calculations. The inferred elastic
response of large-pore ($\mathrm{\mu m}$) fibrin networks depends on the strain
rate, suggesting a strong interplay between network elasticity and fluid flow.
Phenomenologically extending the calculated normal force into the regime of
nonlinear elasticity, we find strain-stiffening of small-pore (sub-$\mathrm{\mu
m}$) fibrin networks to occur at an onset average tangential stress at the
gel-plate interface that depends on the polymer concentration in a power-law
fashion. The inferred permeability of small-pore fibrin networks scales
approximately inverse squared with the fibrin concentration, implying with a
microscopic cubic lattice model that the thickness of the fibrin fibers
decreases with protein concentration. Our theoretical model provides a new
method to obtain the hydraulic permeability and the elastic properties of
biopolymer networks and hydrogels with simple compression experiments, and
paves the way to study the relation between fluid flow and elasticity in
biopolymer networks during dynamical compression.
