| 液滴对弹性梯度薄基变形的影响 |
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| 引用本文： | 杨勇林,王旭,李星.液滴对弹性梯度薄基变形的影响[J].应用数学和力学,2021,42(1):58-70. |
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| 作者姓名： | 杨勇林 王旭 李星 |
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| 作者单位： | 宁夏大学 数学统计学院, 银川 750021 |
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| 基金项目： | 国家自然科学基金(11762017)；宁夏自然科学基金(2019AAC03037) |
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| 摘 要： | 液滴润湿现象在细胞的变形和软器件的设计和制作中具有潜在的指导意义.该文在考虑三相接触线处线张力的情况下,研究了液滴引起的梯度薄基变形问题.首先，利用积分变换法求解了基底变形的本构方程,给出了变形的法向位移表达式.其次，讨论了基底弹性模量非梯度、指数型梯度和幂型梯度变化时基底的变形情况.最后，给出了液滴大小、弹性模量、线张力及梯度指数变化时位移的变化情况.数值结果表明弹性模量逐渐减小和梯度指数逐渐增大时,湿润脊逐渐变高,变形也越大；线张力和特征深度越小,位移的峰值越高,变形也越大；液滴半径较小时,湿润脊的对称性会变得更好.
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| 关 键 词： | 基底变形 线张力 梯度模量 积分变换 双重Bessel函数数值积分 |
| 收稿时间： | 2020-06-15 |
Effects of Proplet on the Deformation of Elastic Gradient Thin Substrate |
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| Affiliation: | School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, P.R.China |
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| Abstract: | The phenomenon of droplet wetting has potential significance in cell deformation research and design as well as fabrication of soft devices. In view of the linear tension at the 3-phase contact lines, the gradient thin substrate deformation caused by liquid droplets was studied. Firstly, the constitutive equations of the substrate deformation were solved with the integral transformation method, and the normal displacement expression of the deformation was given. Secondly, the substrate deformation was discussed with different types of elastic moduli of no gradient, the exponential gradient and the power gradient. Finally, the variations of the substrate displacement with the droplet size, the elastic modulus, the linear tension and the gradient index were given. The numerical results show that, with the increases of the elastic modulus and the gradient index, the wetting ridge will go higher and the deformation larger. The smaller the linear tension and the characteristic depth are, the higher the peak displacement value and the larger the deformation will be. When the droplet radius is smaller, the symmetry of the wetting ridge will be better. |
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