Yamaue Tatsuya, Doi Masao
Department of Computational Science and Engineering, Nagoya University, Nagoya 464-8603, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Jul;70(1 Pt 1):011401. doi: 10.1103/PhysRevE.70.011401. Epub 2004 Jul 8.
We analyze the swelling kinetics of constrained thin-plate gels using the linearized stress-diffusion coupling model proposed in the previous paper [Phys. Rev. E 69, 041402 (2004)]]. The gel is chemically clamped on the disk-like glass plates at the top and the bottom surfaces and can swell and shrink only along the thickness direction. We analyze how the top plate moves when a force is applied at a certain point on the top plate while the bottom plate is fixed. We predict that (i) the translation and the rotation of the top plate are described by a single exponential relaxation process, that (ii) the rotational relaxation process is three times faster than the translational one, and that (iii) when the force is applied to the edge, the displacement by the rotation is four times larger than that by the translation at the edge point where the force is applied. We also analyze how the gel deforms when it is clamped on the flexible film on which external load is applied.
我们使用上一篇论文[《物理评论E》69, 041402 (2004)]中提出的线性化应力-扩散耦合模型，分析了受限薄板凝胶的溶胀动力学。凝胶在顶部和底部表面被化学固定在圆盘状玻璃板上，并且只能沿厚度方向膨胀和收缩。我们分析了在底部板固定的情况下，当在顶板上的某一点施加力时顶板如何移动。我们预测：(i)顶板的平移和旋转由单个指数弛豫过程描述；(ii)旋转弛豫过程比平移过程快三倍；(iii)当力施加在边缘时，在施加力的边缘点处，旋转引起的位移比平移引起的位移大四倍。我们还分析了凝胶在被固定在施加外部载荷的柔性薄膜上时如何变形。
