Effect of Dynamic Contact Angle on Single/Successive Droplet Impingement

2007 ◽  
Author(s):  
S. Sangplung ◽  
J. A. Liburdy
Keyword(s):  
Surface Tension ◽  
Contact Angle ◽  
Solid Surface ◽  
Contact Line ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Droplet Impingement ◽  
Spreading Velocity ◽  
Fluid Properties ◽  
The Impact

Successive droplet impingement onto a solid surface is numerically investigated using a CFD multiphase flow model (VOF method). The main focus of this study is to better understand the hydrodynamics of the non-splash impingement process, particularly the effect of a dynamic contact angle and fluid properties along with the interaction between successive droplets while they are impinging onto a solid surface. The pre-impact droplet conditions are prescribed based on a spherical droplet diameter, velocity, and inter-droplet spacing. The molecular kinetic theory is used to model the dynamic contact angle as a function of a contact line velocity. The numerical scheme is validated against experiment results. In the impact spreading and receding processes, results are analyzed to determine the nondimensional deformation characteristics of both single and successive droplet impingements with the variation of fluid properties such as surface tension and dynamic viscosity. These characteristics include spreading ratio, spreading velocity, and a dynamic contact angle. The inclusion of a dynamic contact angle is shown to have a major effect on droplet spreading. In successive droplet impingement, the second drop causes a surge of spreading velocity and contact angle with an associate complex recirculating flow near the contact line after it initially impacts the preceding droplet when it is in an advancing condition. This interaction is less dramatic when the first drop is receding or stationary. The surface tension has the most effect on the maximum spreading radius in both single and successive droplet impingements. In contrast to this, the viscosity directly affects the damping of the spreading-receding process.

Moving contact lines in liquid/liquid/solid systems

1997 ◽  
Vol 334 ◽  
pp. 211-249 ◽  
Author(s):  
YULII D. SHIKHMURZAEV
Keyword(s):  
Mathematical Model ◽  
Surface Tension ◽  
Contact Angle ◽  
Flow Field ◽  
Contact Line ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Three Phase

A general mathematical model which describes the motion of an interface between immiscible viscous fluids along a smooth homogeneous solid surface is examined in the case of small capillary and Reynolds numbers. The model stems from a conclusion that the Young equation, σ1 cos θ = σ2 − σ3, which expresses the balance of tangential projection of the forces acting on the three-phase contact line in terms of the surface tensions σi and the contact angle θ, together with the well-established experimental fact that the dynamic contact angle deviates from the static one, imply that the surface tensions of contacting interfaces in the immediate vicinity of the contact line deviate from their equilibrium values when the contact line is moving. The same conclusion also follows from the experimentally observed kinematics of the flow, which indicates that liquid particles belonging to interfaces traverse the three-phase interaction zone (i.e. the ‘contact line’) in a finite time and become elements of another interface – hence their surface properties have to relax to new equilibrium values giving rise to the surface tension gradients in the neighbourhood of the moving contact line. The kinematic picture of the flow also suggests that the contact-line motion is only a particular case of a more general phenomenon – the process of interface formation or disappearance – and the corresponding mathematical model should be derived from first principles for this general process and then applied to wetting as well as to other relevant flows. In the present paper, the simplest theory which uses this approach is formulated and applied to the moving contact-line problem. The model describes the true kinematics of the flow so that it allows for the ‘splitting’ of the free surface at the contact line, the appearance of the surface tension gradients near the contact line and their influence upon the contact angle and the flow field. An analytical expression for the dependence of the dynamic contact angle on the contact-line speed and parameters characterizing properties of contacting media is derived and examined. The role of a ‘thin’ microscopic residual film formed by adsorbed molecules of the receding fluid is considered. The flow field in the vicinity of the contact line is analysed. The results are compared with experimental data obtained for different fluid/liquid/solid systems.

The interaction of a moving fluid/fluid interface with a flat plate

1995 ◽  
Vol 296 ◽  
pp. 325-351 ◽  
Author(s):  
J. Billingham ◽  
A. C. King
Keyword(s):  
Surface Tension ◽  
Contact Angle ◽  
Flat Plate ◽  
Contact Line ◽  
Large Time ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Phase Contact ◽  
Three Phase ◽  
Time Problem

A well-known technique for metering a multiphase flow is to use small probes that utilize some measurement principle to detect the presence of different phases surrounding their tips. In almost all cases of relevance to the oil industry, the flow around such local probes is inviscid and driven by surface tension, with negligible gravitational effects. In order to study the features of the flow around a local probe when it meets a droplet, we analyse a model problem: the interaction of an infinite, initially straight, interface between two inviscid fluids, advected in an initially uniform flow towards a semi-infinite thin flat plate oriented at 90° to the interface. This has enabled us to gain some insight into the factors that control the motion of a contact line over a solid surface, for a range of physical parameter values.The potential flows in the two fluids are coupled nonlinearly at the interface, where surface tension is balanced by a pressure difference. In addition, a dynamic contact angle boundary condition is imposed at the three-phase contact line, which moves along the plate. In order to determine how the interface deforms in such a flow, we consider the small- and large-time asymptotic limits of the solution. The small-time and linearized large-time problems are solved analytically, using Mellin transforms, whilst the general large-time problem is solved numerically, using a boundary integral method.The form of the dynamic contact angle as a function of contact line velocity is the most important factor in determining how an interface deforms as it meets and moves over the plate. Depending on this, the three-phase contact line may, at one extreme, hang up on the leading edge of the plate or, at the other extreme, move rapidly along the surface of the plate. At large times, the solution asymptotes to an interface configuration where the contact line moves at the far-field velocity.

scholarly journals Numerical Investigation of Different Dynamic Contact Angle Models for a Droplet Impacting a Surface in OpenFOAM

2019 ◽  
Vol 3 (1) ◽  
pp. 9-17
Author(s):  
Ndivhuwo Musehane ◽  
Rhameez Herbst
Keyword(s):  
Surface Tension ◽  
Contact Angle ◽  
Contact Line ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Navier Stokes ◽  
Spreading Process ◽  
Moving Contact Line ◽  
Continuity Equations ◽  
Moving Contact

Computational Fluid Dynamics (CFD) is used to study the spreading process of a water droplet with a radius of 0.00275mm impacting a wax surface at a velocity of 1.18ms−1 . This type of flow is considered to be Multiphase, incompressible, laminar, surface tension dominated and is governed by the Navier stokes and continuity equations. To accurately model the spreading process 3 different contact angle models are investigated, two of which take into account the moving contact line. The governing equations are solved using the open source C++ library OpenFOAM, which uses a Finite Volume Method (FVM) of discretization and a Volume Of Fluid (VOF) interface capturing method. The VOF method is known to produce unphysical velocities when high pressure gradients exist between the two phases, thus a numerical improvement is implemented to reduce the magnitudes of the unphysical velocities. The improvement reduces the magnitudes of the unphysical velocities and as shown in literature their magnitudes increase with an increase in surface tension dominance. The improvement is implemented together with different contact angle models and results obtained show that contact angle models that take into account the moving contact line gives a good correlation of the spreading diameter obtained numerically with the one obtained experimentally.

Description of Dynamic Contact Angle on a Rough Solid Surface

2003 ◽  
Author(s):  
X. F. Peng ◽  
X. D. Wang ◽  
D. J. Lee
Keyword(s):  
Contact Angle ◽  
Solid Surface ◽  
Contact Line ◽  
Mechanical Performance ◽  
Solid Wall ◽  
Dynamic Contact Angle ◽  
Intrinsic Property ◽  
Dynamic Contact ◽  
Characteristic Parameter ◽  
Precursor Film

An investigation was conducted to understand the contact line movement and associated contact angle phenomena. Contact line was supposed to move on a thin precursor film caused by molecular interaction between solid and liquid and asperity of solid surface. It is expected that contact line has a velocity and is subject to viscous stress on the film or geometrically on the solid surface. With the introduction of a characteristic parameter, λ′, the movement of contact line and contact angle phenomena were very well described in both physics and mathematics. The viscous shearing stress exerted by liquid on solid surface was derived, and the behavior of dynamic contact angle was recognized on rough solid surfaces. The analyses indicate that characteristic parameter, λ′, is dependent upon solid wall intrinsic property and mechanical performance, not liquid property. The comparison of theoretical predictions with available experimental data in open literature showed a quite good agreement with each other.

scholarly journals Moving contact lines and dynamic contact angles: a ‘litmus test’ for mathematical models, accomplishments and new challenges

2020 ◽  
Vol 229 (10) ◽  
pp. 1945-1977 ◽  
Author(s):  
Yulii D. Shikhmurzaev
Keyword(s):  
Contact Angle ◽  
Mathematical Models ◽  
Contact Line ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Dynamic Wetting ◽  
Line Speed ◽  
Moving Contact ◽  
New Challenges ◽  
Litmus Test

Abstract After a brief overview of the ‘moving contact-line problem’ as it emerged and evolved as a research topic, a ‘litmus test’ allowing one to assess adequacy of the mathematical models proposed as solutions to the problem is described. Its essence is in comparing the contact angle, an element inherent in every model, with what follows from a qualitative analysis of some simple flows. It is shown that, contrary to a widely held view, the dynamic contact angle is not a function of the contact-line speed as for different spontaneous spreading flows one has different paths in the contact angle-versus-speed plane. In particular, the dynamic contact angle can decrease as the contact-line speed increases. This completely undermines the search for the ‘right’ velocity-dependence of the dynamic contact angle, actual or apparent, as a direction of research. With a reference to an earlier publication, it is shown that, to date, the only mathematical model passing the ‘litmus test’ is the model of dynamic wetting as an interface formation process. The model, which was originated back in 1993, inscribes dynamic wetting into the general physical context as a particular case in a wide class of flows, which also includes coalescence, capillary breakup, free-surface cusping and some other flows, all sharing the same underlying physics. New challenges in the field of dynamic wetting are discussed.

Simulation of Spreading Dynamics of a EWOD Droplet With Dynamic Contact Angle and Contact Angle Hysteresis

2009 ◽  
Author(s):  
Fangjun Hong ◽  
Ping Cheng ◽  
Zhen Sun ◽  
Huiying Wu
Keyword(s):  
Contact Angle ◽  
Contact Line ◽  
Low Voltage ◽  
Contact Angle Hysteresis ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Dielectric Surface ◽  
Contact Radius ◽  
Droplet Spreading ◽  
Spreading Dynamics

In this paper, the electrowetting dynamics of a droplet on a dielectric surface was investigated numerically by a mathematical model including dynamic contact angle and contact angle hysteresis. The fluid flow is described by laminar N-S equation, the free surface of the droplet is modeled by the Volume of Fluid (VOF) method, and the electrowetting force is incorporated by exerting an electrical force on the cells at the contact line. The Kilster’s model that can deal with both receding and advancing contact angle is adopted. Numerical results indicate that there is overshooting and oscillation of contact radius in droplet spreading process before it ceases the movement when the excitation voltage is high; while the overshooting is not observed for low voltage. The explanation for the contact line overshooting and some special characteristics of variation of contact radius with time were also conducted.

Implications of Contact Line Dynamics on Taylor Bubble Flow Morphology

2010 ◽  
Author(s):  
Alexandru Herescu ◽  
Jeffrey S. Allen
Keyword(s):  
Contact Angle ◽  
Contact Line ◽  
Hydraulic Jump ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Film Deposition ◽  
Hydrophobic Coating ◽  
Glass Capillaries ◽  
Flow Morphology ◽  
Deposited Film

Film deposition experiments are performed in circular glass capillaries of 500 μm diameter. Two surface wettabilities are considered, contact angle of 30° for water on glass and of 105° when a hydrophobic coating is applied. It was observed that the liquid film deposited as the meniscus translates with a velocity U presents a ridge that also moves in the direction of the flow. The ridge is bounded by a contact line moving at a velocity UCL as well as a front of velocity UF, and it translates over the deposited stagnant film. The behavior of the ridge presents striking dissimilarities when the wettability is changed. Both UCL and UF are approximately twice as large for the non-wetting case at the same capillary number Ca. The Taylor bubbles forming due to the growth of the ridge are also differentiated by wettability, being much shorter in the non-wetting case. The dynamics of the contact line is studied experimentally and a criterion is proposed to explain the occurrence of a shock at the advancing front of the ridge. The hydraulic jump cannot be explained by the Froude condition of shock formation in shallow waters, or by an inertial dewetting of the deposited film. For a dynamic contact angle of θd = 6° and according to the proposed criterion, a hydraulic jump forms at the front of the ridge when a critical velocity is reached.

scholarly journals Experimental investigation on the effect of accelerating motion of contact line on the dynamic contact angle

2014 ◽  
Vol 80 (809) ◽  
pp. FE0004-FE0004 ◽  
Author(s):  
Takahiro ITO ◽  
Shoji HIRUTA ◽  
Ryota SHIMURA ◽  
Kenji KATOH ◽  
Tatsuro WAKIMOTO ◽  
...  
Keyword(s):  
Contact Angle ◽  
Experimental Investigation ◽  
Contact Line ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Accelerating Motion

Spreading-Droplet Simulation With Surface Tension Model Using Inter-Particle Force in Particle Method

2013 ◽  
Author(s):  
Eiji Ishii ◽  
Taisuke Sugii
Keyword(s):  
Surface Tension ◽  
Contact Angle ◽  
Dynamic Contact Angle ◽  
Particle Method ◽  
Dynamic Contact ◽  
Contact Angles ◽  
Particle Methods ◽  
Static Contact ◽  
Particle Force ◽  
Surface Tension Model

Predicting the spreading behavior of droplets on a wall is important for designing micro/nano devices used for reagent dispensation in micro-electro-mechanical systems, printing processes of ink-jet printers, and condensation of droplets on a wall during spray forming in atomizers. Particle methods are useful for simulating the behavior of many droplets generated by micro/nano devices in practical computational time; the motion of each droplet is simulated using a group of particles, and no particles are assigned in the gas region if interactions between the droplets and gas are weak. Furthermore, liquid-gas interfaces obtained from the particle method remain sharp by using the Lagrangian description. However, conventional surface tension models used in the particle methods are used for predicting the static contact angle at a three-phase interface, not for predicting the dynamic contact angle. The dynamic contact angle defines the shape of a spreading droplet on a wall. We previously developed a surface tension model using inter-particle force in the particle method; the static contact angle of droplets on the wall was verified at various contact angles, and the heights of droplets agreed well with those obtained theoretically. In this study, we applied our surface tension model to the simulation of a spreading droplet on a wall. The simulated dynamic contact angles for some Weber numbers were compared with those measured by Šikalo et al, and they agreed well. Our surface tension model was useful for simulating droplet motion under static and dynamic conditions.

Surface Tension and Dynamic Contact Angle of Water in Thin Quartz Capillaries

2000 ◽  
Vol 222 (1) ◽  
pp. 51-54 ◽  
Author(s):  
V.D. Sobolev ◽  
N.V. Churaev ◽  
M.G. Velarde ◽  
Z.M. Zorin
Keyword(s):  
Surface Tension ◽  
Contact Angle ◽  
Dynamic Contact Angle ◽  
Dynamic Contact
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