capillary forcediffusion coefficientliquid meniscusYoung‐Laplace equationLaplace pressureKelvin equationCapillary condensationYoung's equationcircular approximationnodoidCapillary forces are not only caused by liquid menisci in gaseous environment but can also be caused by capillary bridges of one liquid in ...
Equation (2.58) characterizes the capillary rise; note that the capillary rise can be important. What is the corresponding capillary force? The capillary force balances the weight of the liquid in the tube. This weight is given by: F=ρgπR2h. Replacing h by its value from Eq. (2.54),...
A dynamic model of capillary force actuators was developed assuming small convective acceleration. The model consists of a nonlinear 2nd order fluid–structure model and a 1st order electrical model, coupled by the Young–Lippmann electrowetting equation. With a constant voltage input, the nonlinear mo...
Therefore, the fluid flow in the low-velocity measuring tube was in accordance with Darcy’s law, which could be described by the Naiver-Stokes equation. The Level-set method could be used to calculate the dynamic capillary force in the flow velocity measurement tube. Because the dynamic ...
challenges still remain. First, the capillaryforceis not presented in the Young's equation. Additionally, the Young's equation cannot be verified directly in experiments. Compared with its thermodynamic derivation, there are more obstacles to put forward the mechanical interpretation of the equation. ...
The capillary force balances the gravity force that is exerted on the weight of the water column, resulting in the following capillary rise equation for a rectangular cross-section groove21: $$h_{rec} = \frac{{\sigma \left[ {\left( {2D + W} \right)cos\theta - W} \right]}}{\rho...
In Sect. 2.4.3 a simple approximation ( F c = 4 πγR ) was introduced to calculate the capillary force between the ball and the flat sample. Throughout the book cases were shown where this equation did not hold. This appendix, therefore, presents a detailed derivation of this equation ...
Our findings not only provide a theoretical insight into the pinning force at the contact line, but also validate Young’s equation based on a mechanical interpretation . 中文翻译: 接触线处毛细管力平衡的微观起因 我们研究了接触线处毛细管力平衡的潜在机理。特别是,我们提供了一种新颖的方法来描述和...
The resulting equation cannot be written in terms of the total material derivative, and is significantly more difficult to solve. A benefit of the general equation formulation is its allowance for variable properties. Typical of compressible gas applications, the density is related to the temperature...
The drag force (\(F_d\)) from the translation of the capillary wave, is given by the Stokes’ drag equation61: $$\begin{aligned} F_{d}=6\pi \mu r v_t. \end{aligned}$$ (5) As a simplistic approximation, the Eqs. (4) and (5) are obtained considering Stokes flow and do ...