Thermo-Mechanical Gel Dynamics

To describe the spatially distributed strain of the PVME gel system, the THB equation of motion [5] can be used. Even if is an oversimplified version of the Biot s poroelastic model [7], it adequately describes the diffusion kinetics of gel matrices [3, 5-7] and reads  

In the case of an uncharged polymer network (i.e. K12 = K21 = 0), the friction coefficient results f=(Kn) [7], where Kn is the gel hydraulic permeability. 

Generally speaking, the material parameters in Equation (4.1) and Equation (4.2) are functions of the physical variables of the material (e.g. temperature, strain itself, etc.) as well as of the chemical ones (e.g. pH, ionic strength and type of solvent). Because the dependence of the material parameters on the mechanical deformation is weak, p, k and f can be assumed constants in the thermal gel readjustment, where the temperamre is held constant for t 0. Moreover, since the temperamre change can be approximately assumed uniform over the sample, the thermal stress (a) is only a function of time. 

Given ot(x, t s O) = the application of a sudden change of temperature (AT) at time t = 0 that is held constant as a function of time, leads to the following thermal stress function  

By choosing the null reference thermal stress state at t 0 so that  

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