分散系にみられる非線形粘弾性の解析法

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In our resent studies, it has been found that a sinusoidal strain is applied to the disperse system such as emulsions and suspension, results in a stress including not only first but also higher odd order harmonics. Extending Boltzmann's superposition principle, we write [numerical formula] (1) where,γ(t) is the time dependent strain, σ(t) is stressed and φ_m(t) is the response function extended by the authors. when the strain is sinusoidal and given by γ(t)=γ_0^<e^<iwt>>, Eq. (1) becomes [numerical formula] (2) where G_m*(miω) and η_m*(miω) are defined as follows; [numerical formula] (3) [numerical formula] (4) Thus the mth harmonics (m is a odd number) are included in the stress. Since G_m* and η_m* are complex, we can write [numerical formula] (5) [numerical formula] (6) When a sinusoidal vibration θ(t)=θ_0sin ωt is given to the outer cylinder of a rotating cylinder type rheometer, the true deformation of the sample is given by [numerical formula] (7) where ξ(t) is the deflextion of the inner cylinder suspended by a torsion wire having the torsion constant k'. When ξ(t)≪θ(t), the equation of the motion of the rheometer is given by [numerical formula] (8) where Z_m is an apparatus constant and I is the moment of inertia of the vibrating system. On the other hand, the measureable stress on the surface of inner cylinder σ(t) is proportional to ξ(t). By the harmonic analysis, we can expand ξ(t) into Fourier series; [numerical formula] (9) where, φ_m is the phase angle and A_m and B_m are numerical constants. Substituting Eq. (9) for Eq. (8), we can derive a new equation which will enable us to determine G_m' and η_m'. Nonlinear viscoelasticity parameters G_1', G_3', η_1 and η_3' at several frequencies have been calculated fro vanishing cream at 28℃.
社団法人日本材料学会の論文
1968-04-15

分散系にみられる非線形粘弾性の解析法

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