Flow induced instability of the interface between a fluid and a gel at low Reynolds number
Flow induced instability of the interface between a fluid and a gel at low Reynolds number
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低雷诺数下流体和凝胶之间的界面流动引起的不稳定性
DOI：
10.1051/jp2:1994173
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发表时间：
1994
期刊：
影响因子：
--
通讯作者：
P. Pincus
中科院分区：
文献类型：
--
作者：
V. Kumaran;G. Fredrickson;P. Pincus
研究了厚度为HR的凝胶与厚度为R的牛顿流体在线性剪切流作用下的界面稳定性，其中惯性效应可以忽略不计。凝胶的剪切应力包含依赖于局部位移场的弹性部分和依赖于速度场的粘性部分。表面剪切流动使表面波动趋于不稳定，临界应变率Γ c是不稳定波动所需的最小应变率，它是无因次量H的函数，ηr = (ηg/ηf), T = （Γ/ER）。其中ηg和ηf为凝胶和流体粘度，E为凝胶弹性，Γ为凝胶-流体界面的表面张力，应变率Γ用（E/ηf）表示。在极限H =∞时，γc与ηr和t成正比地减小，与ηr和t无关。但在有限H时，γc强烈依赖于ηr和t。当ηr≥1时，界面在任意应变速率下均稳定 $H \sqrt{\eta_{\rm r}}$． 当ηr = 1, H = 1时，我们发现当T=0时γc∝(H - 1)1/2，当T≠0时γc∝(H - 1)3/4T1/4。对于ηr >1，分析表明 $\gamma_{\rm c} \propto(H-\sqrt{\eta_{\rm r}})^{-1}$ 与T无关 $H \to \sqrt{\eta_{\rm r}}$． 当ηr < 1时，不稳定的开始强烈依赖于参数T。当T = 0时，临界应变率在极限H = 0时有限，而当T≠0时，临界应变率在有限值H处偏离，最小H值随着ηr的增大而减小。当T较大时，平均流的能量转移到平均流在界面处所做的功所引起的波动中。
The stability of the interface between a gel of thickness HR and a Newtonian fluid of thickness R subjected to a linear shear flow is studied in the limit where inertial effects are negligible. The shear stress for the gel contains an elastic part that depends on the local displacement field and a viscous component that depends on the velocity field. The shear flow at the surface tends to destabilize the surface fluctuations, and the critical strain rate γc, which is the minimum strain rate required for unstable fluctuations, is determined as a function of the dimensionless quantities H, ηr = (ηg/ηf), and T = (Γ/ER). Here ηg and ηf are the gel and fluid viscosities, E is the gel elasticity, Γ is the surface tension of the gel — fluid interface and the strain rate γ is scaled by (E/ηf). In the limit H ↦∞, we find that γc decreases proportional to H-1 independent of ηr and T. But at finite H, γc is strongly dependent on ηr and T. For ηr ≥1, the interface is stable for all values of the strain rate for $H \sqrt{\eta_{\rm r}}$. For ηr = 1 and H ↦1, we find that γc ∝(H - 1)1/2 for T=0 and γc ∝(H - 1)3/4T1/4 for T ≠0. For ηr > 1, the analysis indicates that $\gamma_{\rm c} \propto(H-\sqrt{\eta_{\rm r}})^{-1}$ independent of T for $H \to \sqrt{\eta_{\rm r}}$. For ηr < 1, the onset of instability depends strongly on the parameter T. For T = 0, the critical strain rate is finite in the limit H ↦0, while for T ≠0 the critical strain rate diverges at a finite value of H. This minimum H decreases proportional to ηr for large T. The instability is caused by the energy transfer from the mean flow to the fluctuations due to the work done by the mean flow at the interface.