The dynamic contact angle I. Dependence of the receding contact angle on velocity in the surfactant-containing three-phase system

1987 ◽  
Vol 265 (12) ◽  
pp. 1075-1084 ◽  
Author(s):  
W. Hopf ◽  
Th. Geidel
Keyword(s):  
Contact Angle ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Phase System ◽  
Three Phase ◽  
Receding Contact ◽  
Receding Contact Angle

Motion of drops on inclined surfaces in the inertial regime

2013 ◽  
Vol 726 ◽  
pp. 26-61 ◽  
Author(s):  
Baburaj A. Puthenveettil ◽  
Vijaya K. Senthilkumar ◽  
E. J. Hopfinger
Keyword(s):  
Contact Angle ◽  
Slip Length ◽  
Water Drop ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Drop Diameter ◽  
Angle Variation ◽  
Hydrodynamic Description ◽  
Receding Contact ◽  
Receding Contact Angle

AbstractWe present experimental results on high-Reynolds-number motion of partially non-wetting liquid drops on inclined plane surfaces using: (i) water on fluoro-alkyl silane (FAS)-coated glass; and (ii) mercury on glass. The former is a high-hysteresis ($3{5}^{\circ } $) surface while the latter is a low-hysteresis one (${6}^{\circ } $). The water drop experiments have been conducted for capillary numbers $0. 0003\lt Ca\lt 0. 0075$ and for Reynolds numbers based on drop diameter $137\lt Re\lt 3142$. The ranges for mercury on glass experiments are $0. 0002\lt Ca\lt 0. 0023$ and $3037\lt Re\lt 20\hspace{0.167em} 069$. It is shown that when $Re\gg 1{0}^{3} $ for water and $Re\gg 10$ for mercury, a boundary layer flow model accounts for the observed velocities. A general expression for the dimensionless velocity of the drop, covering the whole $Re$ range, is derived, which scales with the modified Bond number ($B{o}_{m} $). This expression shows that at low $Re$, $Ca\sim B{o}_{m} $ and at large $Re$, $Ca \sqrt{Re} \sim B{o}_{m} $. The dynamic contact angle (${\theta }_{d} $) variation scales, at least to first-order, with $Ca$; the contact angle variation in water, corrected for the hysteresis, collapses onto the low-$Re$ data of LeGrand, Daerr & Limat (J. Fluid Mech., vol. 541, 2005, pp. 293–315). The receding contact angle variation of mercury has a slope very different from that in water, but the variation is practically linear with $Ca$. We compare our dynamic contact angle data to several models available in the literature. Most models can describe the data of LeGrand et al. (2005) for high-viscosity silicon oil, but often need unexpected values of parameters to describe our water and mercury data. In particular, a purely hydrodynamic description requires unphysically small values of slip length, while the molecular-kinetic model shows asymmetry between the wetting and dewetting, which is quite strong for mercury. The model by Shikhmurzaev (Intl J. Multiphase Flow, vol. 19, 1993, pp. 589–610) is able to group the data for the three fluids around a single curve, thereby restoring a certain symmetry, by using two adjustable parameters that have reasonable values. At larger velocities, the mercury drops undergo a change at the rear from an oval to a corner shape when viewed from above; the corner transition occurs at a finite receding contact angle. Water drops do not show such a clear transition from oval to corner shape. Instead, a direct transition from an oval shape to a rivulet appears to occur.

The Effects of Asymmetric Micro Ratchets on Dynamic Contact Angle and Pool Boiling Performance

2012 ◽  
Author(s):  
Lance Austin Brumfield ◽  
Sunggook Park
Keyword(s):  
Contact Angle ◽  
High Speed ◽  
Pool Boiling ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Contact Angles ◽  
Equilibrium Contact Angle ◽  
Droplet Impingement ◽  
Receding Contact ◽  
Receding Contact Angle

The dynamic advancing and receding contact angles of 5μl water droplets were experimentally measured via the droplet impingement technique on a polished brass surface, one brass symmetric micro ratchet, and five brass asymmetric micro ratchet samples of varying dimensions. Droplets were released from varying heights (Weber number) and the impacts studied via high speed camera. Equilibrium advancing and receding contact angles were measured by placing a water droplet on the surfaces and tilting it. Contact angle values were then compared to an existing pool boiling model which incorporates the dynamic receding contact angle, surface roughness ratio, and equilibrium contact angle.

scholarly journals Study of Fluids Motion in a Microchannel under Heat Source

2020 ◽  
Vol 2 (SI2) ◽  
pp. First
Author(s):  
Long Thanh Le
Keyword(s):  
Contact Angle ◽  
Heat Source ◽  
Water Droplet ◽  
Stokes Equations ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Immiscible Fluids ◽  
Navier Stokes ◽  
Two Phase ◽  
Receding Contact Angle

In this study, the numerical computation is used to investigate the transient thermocapillary migration of a water droplet in a Microchannel. For tracking the evolution of the free interface between two immiscible fluids, we employed the finite element method with the two-phase level set technique to solve the Navier-Stokes equations coupled with the energy equation. Both the upper wall and the bottom wall of the microchannel are set to be an ambient temperature. The heat source is placed at the left side of a water droplet. When the heat source is turned on, a pair of asymmetric thermocapillary convection vortices is formed inside the droplet and the thermocapillary on the receding side is smaller than that on the advancing side. The temperature gradient inside the droplet increases quickly at the initial times and then decreases versus time. Therefore, the actuation velocity of the water droplet first increases significantly, and then decreases continuously. The dynamic contact angle is strongly affected by the oil flow motion and the net thermocapillary momentum inside the droplet. The advancing contact angle is always larger than the receding contact angle during actuation 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.

Visualization of Dynamic Contact Angle

2013 ◽  
Author(s):  
Brandon S. Field
Keyword(s):  
Contact Angle ◽  
Contact Line ◽  
High Speed ◽  
Solid Phase ◽  
Capillary Rise ◽  
Dynamic Contact Angle ◽  
Fluid Phase ◽  
Dynamic Contact ◽  
Force Balance ◽  
Receding Contact

Capillary rise of air-water-solid systems have been recorded with high-speed video. Glass and metal have been used as the solid phase, and the dynamic shape of the meniscus and contact angle have been characterized. The advancing and receding contact angle is of interest in computational simulations of boiling flow, and the present visualizations attempt to quantify the dynamic aspects of contact line motion. The centroid of the capillary meniscus has been tracked in order to determine the force at the contact line based on a force balance of the elevated fluid phase. The solid phase is raised and lowered in the fluid at different rates to observe advancing and receding contact lines.

scholarly journals Relaxation of a dewetting contact line. Part 2. Experiments

2008 ◽  
Vol 604 ◽  
pp. 55-75 ◽  
Author(s):  
GILES DELON ◽  
MARC FERMIGIER ◽  
JACCO H. SNOEIJER ◽  
BRUNO ANDREOTTI
Keyword(s):  
Contact Angle ◽  
Large Scale ◽  
Contact Angle Hysteresis ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Dip Coating ◽  
Hydrodynamic Theory ◽  
Open Problems ◽  
Receding Contact ◽  
Large Scale Flow

The dynamics of receding contact lines is investigated experimentally through controlled perturbations of a meniscus in a dip-coating experiment. We first describe stationary menisci and their breakdown at the coating transition. Above this transition where liquid is deposited, it is found that the dynamics of the interface can be interpreted as a quasi-steady succession of stationary states. This provides the first experimental access to the entire bifurcation diagram of dynamical wetting, confirming the hydrodynamic theory developed in Part 1. In contrast to quasi-static theories based on a dynamic contact angle, we demonstrate that the transition strongly depends on the large-scale flow geometry. We then establish the dispersion relation for large wavenumbers, for which we find a decay rate σ proportional to wavenumber |q|. The speed dependence of σ is described well by hydrodynamic theory, in particular the absence of diverging time scales at the critical point. Finally, we highlight some open problems related to contact angle hysteresis that lead beyond the current description.

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