Analytical Model of Post-Impact Droplet Spreading on a Micro-Patterned Superhydrophobic Surface With Surface Slip

2014 ◽  
Author(s):  
Cristian E. Clavijo ◽  
Julie Crockett ◽  
Daniel Maynes
Keyword(s):  
Analytical Model ◽  
Contact Angles ◽  
Superhydrophobic Surfaces ◽  
Analytical Models ◽  
Impact Behavior ◽  
Droplet Deformation ◽  
Droplet Spreading ◽  
Surface Slip ◽  
Classical Energy ◽  
Dynamical Parameters

Several analytical models exist to predict droplet impact behavior on superhydrophobic surfaces. However, no previous model has rigorously considered the effect of surface slip on droplet spreading and recoiling that is inherent in many superhydrophobic surfaces. This paper presents an analytical model that takes into account surface slip at the solid-fluid interface during droplet deformation. The effects of slip are captured in terms that model the kinetic energy and viscous dissipation and are compared to a classical energy conservation model given by Attane et al. and experimental data from Pearson et al. A range of slip lengths, Weber numbers, Ohnesorge numbers, and contact angles are investigated to characterize the effects of slip over the entire range of realizable conditions. We find that surface slip does not influence normalized maximum spread diameter for low We but can cause a significant increase for We > 100. Surface slip affects dynamical parameters more profoundly for low Oh numbers (0.002–0.01). Normalized residence time and rebound velocity increase as slip increases for the same range of We and Oh. The influence of slip is more significantly manifested on normalized rebound velocity than normalized maximum spread diameter. Contact angles in the range of 150°–180° do not affect impact dynamics significantly.

Analytical Model for the Deformation of Viscoelastic Non-Newtonian Drops Undergoing Secondary Atomization

2016 ◽  
Author(s):  
Sharon E. Snyder ◽  
Varun Kulkarni ◽  
Paul E. Sojka
Keyword(s):  
Analytical Model ◽  
Xanthan Gum ◽  
Experimental Results ◽  
Analytical Models ◽  
Drop Diameter ◽  
Droplet Deformation ◽  
Secondary Atomization ◽  
Starting Point ◽  
Breakup Model ◽  
Xanthan Gum Solution

While there is no single analytical model that accurately predicts all stages and modes of secondary atomization, many groups have developed models that predict deformation and oscillation of a single, isolated drop. The TAB (Taylor Analogy Breakup) model was chosen for this investigation, mainly due to its widespread use by Liu and Reitz [1], Hwang et al. [2], Tanner [3], and Lee and Reitz [4], among others. Since the TAB model is also the foundation for many other analytical models, it will also be used here as a starting point for the development of a viscoelastic non-Newtonian model to predict droplet deformed radii, droplet deformation time, and velocity at deformation time for viscoelastic xanthan gum - DI water solutions. Three additional improvements are made to this viscoelastic TAB model: the first is a change to a TAB coefficient; the second to the equation for the drag coefficient, and the third modification is to the breakup criterion. This model uses Carreau rheology and Zimm relaxation time. Non-dimensional drop diameter and initiation times are plotted against We; model results are compared to experimental results for a range of xanthan gum solution concentrations. Results show fair agreement between experimental results and model results for non-dimensional drop diameter, with the best match at low XG concentration and low-to-medium We (10–30). It was also noted that increased viscoelasticity seems to increase this drop diameter. Good agreement between experimental data and model results has been seen for initiation time, with increased viscoelasticity increasing this parameter as well.

Novel, Gasketless, Interconnect Using Parallel Superhydrophobic Surfaces for Modular Microfluidic Systems

2011 ◽  
Author(s):  
Christopher R. Brown ◽  
Bahador Farshchian ◽  
Pin-Chuan Chen ◽  
Taehyun Park ◽  
Sunggook Park ◽  
...  
Keyword(s):  
Steady State ◽  
Analytical Model ◽  
Liquid Bridge ◽  
Contact Angles ◽  
Superhydrophobic Surfaces ◽  
Maximum Pressure ◽  
The Novel ◽  
Microfluidic Systems ◽  
Order Of Magnitude ◽  
State Pressure

A novel, modular, microfluidic interconnect was developed using parallel superhydrophobic interfaces to facilitate the transport of fluids between component chips in modular microfluidic systems. A static analytical model, derived from the Laplace equation [1], approximates the maximum steady-state pressure of the liquid at the liquid bridge which forms across the gap between the chips. Preliminary experiments using parallel superhydrophobic surfaces on PMMA validated the concept. Additional experiments controlled the gap distance, measured contact angles of the superhydrophobic surfaces, gradually increased the pressure of the novel, gasketless, interconnect until rupture to find the maximum pressure across the liquid bridge and verify the model. The measured pressures were on the same order of magnitude (1–10 kPa) as estimated using the model for gap distances of 25 μm and 100 μm.

scholarly journals Novel Structure and Thermal Design and Analysis for CubeSats in Formation Flying

Aerospace ◽  
2021 ◽  
Vol 8 (6) ◽  
pp. 150
Author(s):  
Yeon-Kyu Park ◽  
Geuk-Nam Kim ◽  
Sang-Young Park
Keyword(s):  
Analytical Model ◽  
Formation Flying ◽  
Thermal Environment ◽  
Thermal Analyses ◽  
Thermal Design ◽  
Analytical Models ◽  
Test Results ◽  
Solar Panels ◽  
Novel Structure ◽  
Micro Propulsion

The CANYVAL-C (CubeSat Astronomy by NASA and Yonsei using a virtual telescope alignment for coronagraph) is a space science demonstration mission that involves taking several images of the solar corona with two CubeSats—1U CubeSat (Timon) and 2U CubeSat (Pumbaa)—in formation flying. In this study, we developed and evaluated structural and thermal designs of the CubeSats Timon and Pumbaa through finite element analyses, considering the nonlinearity effects of the nylon wire of the deployable solar panels installed in Pumbaa. On-orbit thermal analyses were performed with an accurate analytical model for a visible camera on Timon and a micro propulsion system on Pumbaa, which has a narrow operating temperature range. Finally, the analytical models were correlated for enhancing the reliability of the numerical analysis. The test results indicated that the CubeSats are structurally safe with respect to the launch environment and can activate each component under the space thermal environment. The natural frequency of the nylon wire for the deployable solar panels was found to increase significantly as the wire was tightened strongly. The conditions of the thermal vacuum and cycling testing were implemented in the thermal analytical model, which reduced the differences between the analysis and testing.

The effects of geometric offsets on the dynamic responses of a Scott—Russell amplifying mechanism with flexible hinges

2009 ◽  
Vol 223 (10) ◽  
pp. 2413-2423 ◽  
Author(s):  
C-M Chen ◽  
R-F Fung
Keyword(s):  
Numerical Simulations ◽  
Analytical Model ◽  
Dynamic Responses ◽  
Analytical Models ◽  
Dynamic Equations ◽  
Magnification Factor ◽  
Flexure Hinges ◽  
Magnification Factors ◽  
Straight Line ◽  
Deviation Factor

The dynamic equations of a micro-positioning Scott—Russell (SR) mechanism associated with two flexible hinges and an offset are developed to calculate output responses. Both rigid and flexible hinges are considered to explore the results. The main features in the kinematics of the SR mechanism are its displacement amplification and straight-line motion, which are widely needed in practical industries. The manufacturing inaccuracy of the SR mechanism definitely causes geometric offsets of flexure hinges, and affects displacement amplification and straight-line output motion. Analytical models based on kinematics and Hamilton's principle are derived to explore the variation of linearity ratio, magnification factor, and deviation factor due to various offsets and link lengths. From numerical simulations for the SR mechanism with various offsets of flexible hinges in the conditions of different link lengths, it is found that offsets of flexure hinges obviously affect the amplifying factor and linearity ratio, and appear to dominate the changes of magnification factors. Moreover, an analytical model is also used to predict magnification factors due to various offsets. Finally, some conclusions concerning the effects of offset on the performance of the SR mechanism are drawn.

Modeling of residual stresses by correlating surface topography in machining of AISI 52100 steel

2021 ◽  
pp. 1-26
Author(s):  
Chao Liu ◽  
Yan He ◽  
Yufeng Li ◽  
Yulin Wang ◽  
Shilong Wang ◽  
...  
Keyword(s):  
Residual Stress ◽  
Residual Stresses ◽  
Cutting Force ◽  
Surface Topography ◽  
Analytical Model ◽  
Analytical Models ◽  
Workpiece Surface ◽  
Dynamic Cutting Force ◽  
Intermittent Cutting ◽  
Effect Of Surface

Abstract The residual stresses could affect the ability of components to bear loading conditions and also the performance. The researchers considered workpiece surface as a plane and ignored the effect of surface topography induced by the intermittent cutting process when modeling residual stresses. The aim of this research develops an analytical model to predict workpiece residual stresses during intermittent machining by correlating the effect of surface topography. The relative motions of tool and workpiece are analyzed for modeling thermal-mechanical and surface topography. The influence of dynamic cutting force and thermal on different positions of surface topography is also considered in analytical model. Then the residual stresses model with the surface topography effect can be developed in intermittent cutting. The analytical models of dynamic cutting force, surface topography and residual stresses are verified by the experiments. The variation trend of evaluated values of the residual stress of workpiece is basically consistent with that of measured values. The compressive residual stress of workpiece surface in highest point of the surface topography are higher than that in the lowest point.

scholarly journals Approximate Analytical Models of Shock-Wave Structure at Steady Mach Reflection

Fluids ◽  
2021 ◽  
Vol 6 (9) ◽  
pp. 305
Author(s):  
Mikhail V. Chernyshov ◽  
Karina E. Savelova ◽  
Anna S. Kapralova
Keyword(s):  
Experimental Data ◽  
Shock Wave ◽  
Comparative Analysis ◽  
Analytical Model ◽  
Mach Reflection ◽  
Supersonic Jet ◽  
Wave Structure ◽  
Analytical Models ◽  
Analytical Prediction ◽  
Shock Wave Structure

In this study, we obtain the comparative analysis of methods of quick approximate analytical prediction of Mach shock height in planar steady supersonic flows (for example, in supersonic jet flow and in narrowing channel between two wedges), that are developed since the 1980s and being actively modernized now. A new analytical model based on flow averaging downstream curved Mach shock is proposed, which seems more accurate than preceding models, comparing with numerical and experimental data.

Determining Parametric Effects for Droplet Evaporation on Nanoporous Superhydrophillic Surfaces Using Machine Learning Techniques

2021 ◽  
Author(s):  
Emma R. McClure ◽  
Van P. Carey
Keyword(s):  
Machine Learning ◽  
Cooling System ◽  
Spray Cooling ◽  
Droplet Evaporation ◽  
Contact Angles ◽  
Machine Learning Techniques ◽  
Metallic Surfaces ◽  
Droplet Spreading ◽  
Droplet Vaporization ◽  
Speed Accuracy

Abstract Experimental results demonstrate that droplet vaporization on metal surfaces can be significantly enhanced with the application of a nanoporous, superhydrophilic surface coating. A thin layer of ZnO nanopillars can be easily seeded and grown on most metallic surfaces to achieve nanoscale pores between pillars, and ultra-low apparent contact angles. These surface coatings have the potential to improve spray cooling processes, and can be easily scaled up to larger and more complex heat exchangers. In order to characterize the potential improvement to a spray cooling system it is important to understand the dependence on system parameters, and to have a clear model of droplet vaporization on such surfaces. There are a number of surface and impact parameters that will affect the droplet spreading and subsequent vaporization on the surface. The surface contact angle, wicking speed and impact velocity all interact to affect the maximum spread of the droplet and the speed at which the droplet reaches this state. Along with variations in droplet volume and wall superheat, the model for droplet vaporization becomes more complex and nonlinear. Instead of exploring a single parameter at a time, machine learning tools can be utilized to determine the dependence of droplet evaporation time on these parameters simultaneously. In this study a genetic algorithm and a neural network were used to develop a droplet evaporation model for these superhydrophilic surfaces. Each algorithm demonstrated clear advantages depending on whether speed, accuracy, or an explicit mathematical model was prioritized.

Updating of Non-Conservative Systems Using Inverse Methods

1997 ◽  
Author(s):  
Ladislav Starek ◽  
Milos Musil ◽  
Daniel J. Inman
Keyword(s):  
Analytical Model ◽  
Degrees Of Freedom ◽  
Ad Hoc ◽  
Natural Frequencies ◽  
Eigenvalue Problems ◽  
Model Updating ◽  
Analytical Models ◽  
Mode Shapes ◽  
Element Analysis ◽  
Modal Data

Abstract Several incompatibilities exist between analytical models and experimentally obtained data for many systems. In particular finite element analysis (FEA) modeling often produces analytical modal data that does not agree with measured modal data from experimental modal analysis (EMA). These two methods account for the majority of activity in vibration modeling used in industry. The existence of these discrepancies has spanned the discipline of model updating as summarized in the review articles by Inman (1990), Imregun (1991), and Friswell (1995). In this situation the analytical model is characterized by a large number of degrees of freedom (and hence modes), ad hoc damping mechanisms and real eigenvectors (mode shapes). The FEM model produces a mass, damping and stiffness matrix which is numerically solved for modal data consisting of natural frequencies, mode shapes and damping ratios. Common practice is to compare this analytically generated modal data with natural frequencies, mode shapes and damping ratios obtained from EMA. The EMA data is characterized by a small number of modes, incomplete and complex mode shapes and non proportional damping. It is very common in practice for this experimentally obtained modal data to be in minor disagreement with the analytically derived modal data. The point of view taken is that the analytical model is in error and must be refined or corrected based on experimented data. The approach proposed here is to use the results of inverse eigenvalue problems to develop methods for model updating for damped systems. The inverse problem has been addressed by Lancaster and Maroulas (1987), Starek and Inman (1992,1993,1994,1997) and is summarized for undamped systems in the text by Gladwell (1986). There are many sophisticated model updating methods available. The purpose of this paper is to introduce using inverse eigenvalues calculated as a possible approach to solving the model updating problem. The approach is new and as such many of the practical and important issues of noise, incomplete data, etc. are not yet resolved. Hence, the method introduced here is only useful for low order lumped parameter models of the type used for machines rather than structures. In particular, it will be assumed that the entries and geometry of the lumped components is also known.

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