Soft living tissues like cartilage can be considered as biphasic materials comprising 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 (μm) 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-μm) 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 number of protofibrils per fibrin fiber cross-section 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.

中文翻译：

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压缩过程中（生物）聚合物网络的孔隙弹性：理论和实验。

诸如软骨之类的柔软的活组织可以被认为是包含纤维复合生物聚合物网络和粘性背景液体的两相材料。在这里，我们通过实验和理论分析的结合表明，（生物）聚合物网络的水力渗透率和弹性特性都可以通过商业流变仪中的简单斜率压缩实验来确定。在多孔运动方程的近似闭合形式解中，我们发现压缩过程中的法向力响应是网络应力和流体压力的组合。选择纤维蛋白作为具有可控孔径的生物聚合物模型系统，发现压缩过程中与时间有关的全时法向力的测量与理论计算非常吻合。大孔径（μm）纤维蛋白网络的推断弹性响应取决于应变率，表明网络弹性与流体流动之间存在很强的相互作用。从现象学上，将计算出的法向力扩展到非线性弹性范围内，我们发现小孔（亚微米）纤维蛋白网络的应变刚度发生在凝胶板界面的平均切向应力开始时，该切向应力取决于聚合物中的浓度。幂律法。小孔血纤蛋白网络的渗透率与血纤蛋白浓度成反比，这与微观立方晶格模型有关，即每血纤蛋白纤维横截面的原纤维数目随着蛋白质浓度的增加而减少。