Biopolymer gels such as fibrin and collagen networks are known to develop
tensile axial stress when subject to torsion. This negative normal stress is
opposite to the classical Poynting effect observed for most elastic solids
including synthetic polymer gels, where torsion provokes a positive normal
stress. As recently shown, this anomalous behavior in fibrin gels depends on
the open, porous network structure of biopolymer gels, which facilitates
interstitial fluid flow during shear and can be described by a phenomenological
two-fluid model with viscous coupling between network and solvent. Here we
extend this model and develop a microscopic model for the individual diagonal
components of the stress tensor that determine the axial response of
semi-flexible polymer hydrogels. This microscopic model predicts that the
magnitude of these stress components depends inversely on the characteristic
strain for the onset of nonlinear shear stress, which we confirm experimentally
by shear rheometry on fibrin gels. Moreover, our model predicts a transient
behavior of the normal stress, which is in excellent agreement with the full
time-dependent normal stress we measure.Comment: 12 pages, 8 figure