Diffuse-interface modelling of droplet impact

2007 ◽  
Vol 581 ◽  
pp. 97-127 ◽  
Author(s):  
V. V. KHATAVKAR ◽  
P. D. ANDERSON ◽  
P. C. DUINEVELD ◽  
H. E. H. MEIJER
Keyword(s):  
Solid Surface ◽  
Droplet Diameter ◽  
Spectral Element ◽  
Contact Angles ◽  
Diffuse Interface ◽  
Diffuse Interface Model ◽  
Impact Behaviour ◽  
A Value ◽  
Micron Size ◽  
The Impact

The impact of micron-size drops on a smooth, flat, chemically homogeneous solid surface is studied using a diffuse-interface model (DIM). The model is based on the Cahn–Hilliard theory that couples thermodynamics with hydrodynamics, and is extended to include non-90° contact angles. The (axisymmetric) equations are numerically solved using a combination of finite- and spectral-element methods. The influence of various process and material parameters such as impact velocity, droplet diameter, viscosity, surface tension and wettability on the impact behaviour of drops is investigated. Relevant dimensionless parameters are defined and, depending on the values of the Reynolds number, the Weber number and the contact angle, which for the cases considered here range from 1.3 to 130, 0.43 to 150 and 45° to 135°, respectively, the model predicts the spreading of a droplet with or without recoil or even rebound of the droplet, totally or partially, from the solid surface. The wettability significantly affects the impact behaviour and this is particularly demonstrated with an impact at Re = 130 and We = 1.5, where for θ < 60° the droplet oscillates a few times before attaining equilibrium while for θ ≥ 60° partial rebound of the droplet occurs, i.e. the droplet breaks into two unequal sized drops. The size of the part that remains in contact with the solid surface progressively decreases with increasing θ until at a value θ ≈ 120° a transition to total rebound happens. When the droplet rebounds totally, it has a top-heavy shape.

Capillary spreading of a droplet in the partially wetting regime using a diffuse-interface model

2007 ◽  
Vol 572 ◽  
pp. 367-387 ◽  
Author(s):  
V. V. KHATAVKAR ◽  
P. D. ANDERSON ◽  
H. E. H. MEIJER
Keyword(s):  
Liquid Droplet ◽  
Spectral Element ◽  
Contact Angles ◽  
Diffuse Interface ◽  
Equilibrium Contact Angle ◽  
Interface Model ◽  
Governing Equations ◽  
Ambient Fluid ◽  
Diffuse Interface Model ◽  
Capillary Spreading

The spreading of a liquid droplet on a smooth solid surface in the partially wetting regime is studied using a diffuse-interface model based on the Cahn--Hilliard theory. The model is extended to include non-90$^{\circ}$ contact angles. The diffuse-interface model considers the ambient fluid displaced by the droplet while spreading as a liquid. The governing equations of the model for the axisymmetric case are solved numerically using a finite-spectral-element method. The viscosity of the ambient fluid is found to affect the time scale of spreading, but the general spreading behaviour remains unchanged. The wettability expressed in terms of the equilibrium contact angle is seen to influence the spreading kinetics from the early stages of spreading. The results show agreement with the experimental data reported in the literature.

scholarly journals Modeling of droplet impact on a heated solid surface with a diffuse interface model

2020 ◽  
Vol 123 ◽  
pp. 103173 ◽  
Author(s):  
E.J. Gelissen ◽  
C.W.M. van der Geld ◽  
M.W. Baltussen ◽  
J.G.M. Kuerten
Keyword(s):  
Solid Surface ◽  
Droplet Impact ◽  
Diffuse Interface ◽  
Interface Model ◽  
Diffuse Interface Model

Computational Simulation of the Impact and Freezing of Micron-Size Water Droplets on Super-Hydrophobic Surfaces

2013 ◽  
Author(s):  
Mehdi Raessi ◽  
Miranda Thiele ◽  
Behrooz Amirzadeh
Keyword(s):  
Surface Temperature ◽  
Freezing Point ◽  
Computational Study ◽  
Computational Simulation ◽  
Contact Angles ◽  
Water Droplets ◽  
Hydrophobic Surfaces ◽  
Droplet Spreading ◽  
Micron Size ◽  
The Impact

We present a computational study on the dynamics and freezing of micron-size water droplets impinging onto super-hydrophobic surfaces, the temperatures of which are below the freezing point of water. Icing poses a great challenge for many industries. It is well known that increasing hydrophobicity can make a surface ice-phobic. Experiments show that millimeter size water drops landing on super-hydrophobic surfaces bounce off even when the surface temperature is well below the freezing point. However, it has been reported that the ice-phobicity feature of such surfaces can vanish due to frost formation on the surface, or when small micro-droplets begin to freeze and stick to the surface. Using an in-house, 3D, GPU-accelerated computational tool, we investigated the impact dynamics and freezing of a 40 μm water droplet impinging at 1.4 m/s onto two different super-hydrophobic surfaces chosen from [1]. The advancing and receding contact angles are 165° and 133°, respectively, on one surface, and 157° and 118°, respectively, on the other. The surface and initial droplet temperatures were varied from −25 to 25°C and from 0 to 25°C, respectively. On each surface a “transition” surface temperature was found, at which the drop behavior transitions from bouncing off the surface to sticking. The time between drop landing and bounce-off as well as the contact diameter between the stuck drop and the surface both increase with decreasing the surface temperature. The simulations also show that at some surface temperatures a thin ice layer forms during droplet spreading and then remelts as the droplet recoils.

Bubble Formation at Impingement of a Liquid Droplet on a Solid Surface

2000 ◽  
Author(s):  
Hitoshi Fujimoto ◽  
Tomoyuki Ogino ◽  
Osamu Takahashi ◽  
Hirohiko Takuda ◽  
Natsuo Hatta
Keyword(s):  
Solid Surface ◽  
Liquid Droplet ◽  
Droplet Diameter ◽  
Bubble Formation ◽  
Liquid Droplets ◽  
Vapor Bubbles ◽  
Experimental Conditions ◽  
Video Cameras ◽  
The Moment ◽  
The Impact

Abstract The collision of liquid droplets with a solid has been studied experimentally. The time evolution of the liquid/solid contact area as well as the shape of droplets has been observed by means of a flash-photographic method using two video cameras. It has been found that some air between the solid surface and the incoming droplet is entrapped at the moment of impact. In the case where the solid temperature is high (= 450 °C), numerous vapor bubbles appear at the liquid/solid interface after the collision. The bubble formation due to the entrapment of air has been examined for various experimental conditions. Water, and ethanol are used as test liquid. The droplet diameter is 2.4 mm for water and 1.9 mm for ethanol. The impact velocity varies from 0.8 to 3.1 m/s. The entrapment of air has been observed for both liquids under all conditions in the present study.

scholarly journals Experimental study on two consecutive droplets impacting onto an inclined solid surface

2021 ◽  
Vol 37 ◽  
pp. 432-445
Author(s):  
Chun-Kuei Chen ◽  
Sheng-Qi Chen ◽  
Wei-Mon Yan ◽  
Wen-Ken Li ◽  
Ta-Hui Lin
Keyword(s):  
Solid Surface ◽  
Contact Angles ◽  
Maximum Height ◽  
Droplet Spreading ◽  
Droplet Impingement ◽  
Impact Phenomena ◽  
The Moment ◽  
The Impact ◽  
Inclined Surface ◽  
Surface Angle

Abstract The present study is concerned with the experimental impingement of two consecutive droplets on an inclined solid surface. Attention is mainly paid to the effects of impingement timing with various oblique angles (Φ) of the surface on the impact phenomena, which mainly affect the maximum droplet spreading diameter. The investigation considers four impingement scenarios differentiated by impingement timing, namely Case 1: single-droplet impingement; Case 2 of Δt1: the moment when the leading droplet starts spreading along the oblique surface; Case 3 of Δt2: the moment when the leading droplet reaches its maximum spreading; and Case 4 of Δt3: the moment when the leading droplet starts retracting. It is observed that deformation behavior of two successive droplets impacting on the inclined surface experiences a complex asymmetric morphology evolution due to the enhancement of gravity effect and various conditions of the impingement timing. The merged droplet becomes slender with increasing oblique surface angle in the final steady shape, causing the decrease in the value of front and back contact angles. The impingement timing has a significant influence on the change of the maximum height of the merged droplet. The coalesced droplet spreads to the maximum dimensionless width diameter at Δt = Δt2 and the oblique angle of Φ = 45°, but reaches the maximum dimensionless height for Δt = Δt2 at Φ = 30°. The front contact angles converge to a fixed value eventually for all conditions of impingement timing, and the values become lower with the increasing surface inclination.

scholarly journals A diffuse-interface model for electrowetting drops in a Hele-Shaw cell

2007 ◽  
Vol 590 ◽  
pp. 411-435 ◽  
Author(s):  
H.-W. LU ◽  
K. GLASNER ◽  
A. L. BERTOZZI ◽  
C.-J. KIM
Keyword(s):  
Contact Angles ◽  
Diffuse Interface ◽  
Interface Model ◽  
Interface Thickness ◽  
Order Model ◽  
Diffuse Interface Model ◽  
Reduced Order ◽  
Confined Spaces ◽  
And Topology ◽  
Topology Changes

Electrowetting has recently been explored as a mechanism for moving small amounts of fluids in confined spaces. We propose a diffuse-interface model for drop motion, due to electrowetting, in a Hele-Shaw geometry. In the limit of small interface thickness, asymptotic analysis shows that the model is equivalent to Hele-Shaw flow with a voltage-modified Young–Laplace boundary condition on the free surface. We show that details of the contact angle significantly affect the time scale of motion in the model. We measure receding and advancing contact angles in the experiments and derive their influence through a reduced-order model. These measurements suggest a range of time scales in the Hele-Shaw model which include those observed in the experiment. The shape dynamics and topology changes in the model agree well with the experiment, down to the length scale of the diffuse-interface thickness.

Diffuse-interface Model-based Simulation Study of Droplet Motion on Textured Solid Surface

2016 ◽  
Vol 2016.29 (0) ◽  
pp. 4_298
Author(s):  
Naoki TAKADA ◽  
Kazuma KURIHARA ◽  
Ryohei HOKARI ◽  
Sohei MATSUMOTO ◽  
Junichi MATSUMOTO
Keyword(s):  
Solid Surface ◽  
Simulation Study ◽  
Diffuse Interface ◽  
Interface Model ◽  
Diffuse Interface Model ◽  
Droplet Motion ◽  
Model Based

Diffuse-interface modelling of thermocapillary flow instabilities in a Hele-Shaw cell

2001 ◽  
Vol 434 ◽  
pp. 153-166 ◽  
Author(s):  
M. VERSCHUEREN ◽  
F. N. VAN DE VOSSE ◽  
H. E. H. MEIJER
Keyword(s):  
Marangoni Convection ◽  
Spectral Element ◽  
Flow Instabilities ◽  
Diffuse Interface ◽  
Interface Model ◽  
Governing Equations ◽  
Diffuse Interface Model ◽  
Element Discretization ◽  
Fixed Interface ◽  
Hele Shaw Cell

In this paper we present the results of a diffuse-interface model for thermocapillary or Marangoni flow in a Hele-Shaw cell. We use a Galerkin-type spectral element discretization, based on Gauss–Lobatto quadrature, for numerical implementation of the governing equations resulting from the diffuse-interface model. The results are compared to classical results for a linear and circular fixed interface. It is found that the diffuse-interface solution converges to the classical solution in the sharp-interface limit. The results are sufficiently accurate if the interfacial thickness is only small compared to the size of the thermocapillary boundary layer, even if the interfacial thickness used is much larger than the real interfacial thickness. We also consider freely movable interfaces with a temperature gradient perpendicular to the interface. It will be shown that this situation can lead to a destabilizing Marangoni convection.

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