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arXiv 2304.07902cond-mat.softmath.APmath.DSphysics.chem-phphysics.flu-dyn
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牛顿与非牛顿薄膜中有限时间细丝起源研究

Origin of filaments in finite-time in Newtonian and non-Newtonian thin-films

Saksham Sharma, D. Ian Wilson

AI总结:

本文通过线性稳定性分析和数值模拟,揭示了牛顿与非牛顿后退薄膜在范德华力主导下形成规则细丝的临界膜厚判据,并与实验观测吻合,证明细丝源于有限时间奇异性。

摘要:

猪笼草叶片导管中发现的粘性流体在从基底上退润湿时,会留下分形状的细丝。为理解这些细丝的起源,我们研究了部分润湿聚二甲基硅氧烷(PDMS)基底的水性聚环氧乙烷(PEO)溶液后退薄膜的动力学。在特定条件下,后退薄膜会产生规则间距的液体细丝。我们对退润湿的早期薄膜动力学进行了研究,以确定液体细丝形成的理论判据。从牛顿或简单非牛顿(幂律)薄膜的线性稳定性分析出发,确定了一个临界膜厚,该厚度取决于流体-基底对的Hamaker常数和流体的表面张力。当测得的膜厚小于该值时,薄膜不稳定,并因范德华力主导其行为而形成细丝。该临界膜高与实验测得的膜厚进行了比较,这些膜厚来自在相对于竖直方向倾斜0°、30°和60°的基底上生成的牛顿(甘油-水混合物)和非牛顿(PEO)溶液后退薄膜。细丝出现与否的观测结果与理论吻合良好。对薄膜形状演化的数值模拟表明,细丝的形成源于薄膜方程在有限时间后出现奇异解,因此被称为“有限时间奇异性”。

英文摘要:

The sticky fluids found in pitcher plant leaf vessels can leave fractal-like filaments behind when dewetting from a substrate. To understand the origin of these filaments, we investigate the dynamics of a retreating thin-film of aqueous polyethylene oxide (PEO) solutions which partially wet polydimethyl siloxane (PDMS) substrates. Under certain conditions the retreating film generates regularly-spaced liquid filaments. The early-stage thin-film dynamics of dewetting are investigated to identify a theoretical criterion for liquid filament formation. Starting with a linear stability analysis of a Newtonian or simple non-Newtonian (power-law) thin-film, a critical film thickness is identified which depends on the Hamaker constant for the fluid-substrate pair and the surface tension of the fluid. When the measured film thickness is smaller than this value, the film is unstable and forms filaments as a result of van der Waals forces dominating its behaviour. This critical film-height is compared with experimental measurements of film thickness obtained for receding films of Newtonian (glycerol-water mixtures) and non-Newtonian (PEO) solutions generated on substrates inclined at angles 0 $^{\circ}$, 30 $^{\circ}$, and 60 $^{\circ}$ to the vertical. The observations of filament and its absence show good agreement with the theory. The evolution of the thin-film shape is modelled numerically to show that the formation of filaments arises because the thin-film equation features a singular solution after a finite-time, hence termed a "finite-time singularity".

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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