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21.
在用毛细管测液体表面张力系数实验中,“上升法”液柱升不到“预期”的高度,是因为接触角并不近似为零。“下降法”使管壁充分浸润,不是补偿由于液体层间摩擦损失的能量。 相似文献
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The mathematical formulation of the dynamics of free liquid surfaces including the effects of surface tension is governed by a non-linear system of elliptic differential equations. The major difficulty of getting unique closed solutions only in trivial cases is overcome by numerical methods. This paper considers transient simulations of liquid–gas menisci in vertical capillary tubes and gaps in the presence of gravity. Therefore the CFD code FIDAP 7.52 based on the Galerkin finite element method (FEM) is used. Calculations using the free surface model are presented for a variety of contact angles and cross-sections with experimental and theoretical verification. The liquid column oscillations are compared for numerical accuracy with a mechanical mathematical model, and the sensitivity with respect to the node density is investigated. The efficiency of the numerical treatment of geometric non-trivial problems is demonstrated by a prismatic capillary. Present restrictions limiting efficient transient simulations with irregularly shaped calculational domains are stated. © 1998 John Wiley & Sons, Ltd. 相似文献
24.
Zero‐viscosity‐capillarity limit to rarefaction waves for the 1D compressible Navier–Stokes–Korteweg equations 下载免费PDF全文
In this paper, we study the zero viscosity and capillarity limit problem for the one‐dimensional compressible isentropic Navier–Stokes–Korteweg equations when the corresponding Euler equations have rarefaction wave solutions. In the case that either the effects of initial layer are ignored or the rarefaction waves are smooth, we prove that the solutions of the Navier–Stokes–Korteweg equation with centered rarefaction wave data exist for all time and converge to the centered rarefaction waves as the viscosity and capillarity number vanish, and we also obtain a rate of convergence, which is valid uniformly for all time. These results are showed by a scaling argument and elementary energy analysis. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
26.
The combination of substrate unevenness and capillarity is known to induce far‐reaching perturbations at the free surface of thin liquid films. These might be undesired and this paper explores the possibility to control the free surface of thin liquid films to give it a prescribed profile by a suitable design of the underlying substrate. This corresponds to the inverse of the widely studied forward problem, which considers the effect of substrate unevenness on a free surface. Assuming that the steady free surface profile can be described by the lubrication approximation, this optimal control problem is shown to be governed by a first‐order partial differential equation, which is solved numerically using the method of characteristics. The proposed method is successfully tested for a range of desired free surface profiles and the domain of existence of a solution to the inverse problem is probed. Expectedly, it is shown that, owing to surface tension, not all free surface profiles can be achieved but in some cases capillarity can be beaten and a prescribed free surface profile obtained. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
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In static wetting on an elastic substrate, force exerted by the liquid–vapour surface tension on a solid surface deforms the substrate, producing a capillary ridge along the contact line. This paper presents a finite element formulation for predicting elastic deformation, close to the static wetting line (with angle of contact=90o and σSV=σSL).The substrate deformation is modelled with the Mooney–Rivlin constitutive law for incompressible rubber‐like solids. At the contact line, a stress singularity is known to arise, due to the surface tension acting on a line of infinitesimal thickness. To relive the stress singularity, either (i) the surface tension is applied over a finite contact region (of macroscopic thickness), or (ii) the solid crease angle is fixed. These two options suggest that normal component of Neumann's triangle law of forces, for the three surface tensions, is not applicable for elastic substrates (as for rigid ones). The vertical displacement of the contact line is a strong function of liquid/vapour surface tension and shear modulus of the solid. Copyright 2004 John Wiley & Sons, Ltd. 相似文献
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A theoretical investigation of the EFG process working point based on the meniscus height control is carried out. The link between the two control parameters, which are the pulling rate and the upper die temperature, is found from the thermal equilibrium at the crystallization interface. Using the pressure equilibrium in the film and considering the meniscus shape, the change in meniscus height depending on the crystal radius is analyzed. Limited to small crystal radii, an algebraic formulation of the temperature gradient at the interface is established. Some die design parameters are taken into account and their impacts on the process working point are discussed. 相似文献
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C. Mihaila 《偏微分方程通讯》2013,38(12):1673-1701
AbstractA classical result of Wente, motivated by the study of sessile capillarity droplets, demonstrates the axial symmetry of every hypersurface which meets a hyperplane at a constant angle and has mean curvature dependent only on the distance from that hyperplane. An analogous result is proven here for the fractional mean curvature operator. 相似文献