【摘要】 质量一定、受竖直简谐驱动的液体表面在一定条件下会产生稳定驻波图样,即法拉第斑图.对于黄原胶溶液斑图系统,朗道的经典表面重力张力波色散关系仅适用于低频区域.为了使更大频率范围内色散关系成立,需要考虑黏滞耗散及剪切稀化效应,作出理论修正.分析表明,黏滞耗散为斑图系统的色散关系引入了频率的四次方依赖项;剪切稀化效应在高频下弱化了黏滞耗散,采用幂律方程定量描述了该作用.基于圆柱形容器中的黄原胶溶液及配套测量器材,测量了较大频率范围内的色散关系,验证了理论修正的合理性.更多还原

【Abstract】 Stable standing wave patterns,termed Faraday waves,will appear on the free fluid surface subjected to a vertical harmonic oscillation under certain conditions.For xanthan gum solution,Landau’s classical dispersion relation of surface gravity-tension wave is applicable only for the low frequency region.In order to obtain the dispersion relation over a larger frequency range,a theoretical correction should be made considering viscous effect and shear thinning effect.The analysis showed that the viscous effect introduced a fourth power of frequency dependence to the dispersion relation.And the shear thinning effect,quantitatively described by power law equation,weakened the viscous effect at high frequencies.The dispersion relation over a wide frequency range was measured for the xanthan gum solution in a cylindrical container,and the rationality of the theoretical correction was verified quantitatively.更多还原