On the contact-line pinning in cavity formation during solid–liquid impact

2015 ◽  
Vol 783 ◽  
pp. 504-525 ◽  
Author(s):  
H. Ding ◽  
B.-Q. Chen ◽  
H.-R. Liu ◽  
C.-Y. Zhang ◽  
P. Gao ◽  
...  
Keyword(s):  
Contact Line ◽  
Quantitative Description ◽  
Liquid Pool ◽  
Force Balance ◽  
Diffuse Interface ◽  
Cavity Formation ◽  
Object A ◽  
Moving Contact ◽  
Contact Line Pinning ◽  
The Impact

We investigate the cavity formation during the impact of spheres and cylinders into a liquid pool by using a combination of experiments, simulations and theoretical analysis, with particular interest in contact-line pinning and its relation with the subsequent cavity evolution. The flows are simulated by a Navier–Stokes diffuse-interface solver that allows for moving contact lines. On the basis of agreement on experimentally measured quantities such as the position of the pinned contact line and the interface shape, we investigate flow details that are not accessible experimentally, identify the interface regions in the cavity formation and examine the geometric effects of impact objects. We connect wettability, inertia, geometry of the impact object, interface bending and contact-line position with the contact-line pinning by analysing the force balance at a pinned meniscus, and the result compares favourably with those from simulations and experiments. In addition to adjusting the interface bending, the object geometry also has a significant effect on the magnitude of low pressure in the liquid and the occurrence of flow separation. As a result, it is easier for an object with sharp edges to generate a cavity than a smooth object. A theoretical model based on the Rayleigh–Besant equation is developed to provide a quantitative description of the radial expansion of the cavity after the pinning of the contact line. The accuracy of the solution is greatly affected by the geometrical information on the interface connected to the pinned meniscus, showing the dependence of the global cavity dynamics on the local flows around the pinned contact line. Vertical ripple propagation on the cavity wall is found to follow the dispersion relation for the perturbation evolution on a hollow jet.

Cavity formation by the impact of Leidenfrost spheres

2012 ◽  
Vol 699 ◽  
pp. 465-488 ◽  
Author(s):  
J. O. Marston ◽  
I. U. Vakarelski ◽  
S. T. Thoroddsen
Keyword(s):  
Free Surface ◽  
Contact Line ◽  
Liquid Pool ◽  
Physical Contact ◽  
Cavity Formation ◽  
Cavity Structure ◽  
Leidenfrost Effect ◽  
Contact Line Pinning ◽  
The Impact ◽  
Initial Entry

AbstractWe report observations of cavity formation and subsequent collapse when a heated sphere impacts onto a liquid pool. When the sphere temperature is much greater than the boiling point of the liquid, we observe an inverted Leidenfrost effect where the sphere is encompassed by a vapour layer that prevents physical contact with the liquid. This creates the ultimate non-wetting scenario during sphere penetration through a free surface, producing very smooth cavity walls. In some cases during initial entry, however, the liquid contacts the sphere at the equator, leading to the formation of a dual cavity structure. For cold sphere impacts, where a contact line is observed, we reveal details of the contact line pinning, which initially forms a sawtooth pattern. We also observe surface waves on the cavity interface for cold spheres. We compare our experimental results to previous studies of cavity dynamics and, in particular, the influence of hydrophobicity on the entry of the sphere.

scholarly journals Moving contact line on chemically patterned surfaces

2008 ◽  
Vol 605 ◽  
pp. 59-78 ◽  
Author(s):  
XIAO-PING WANG ◽  
TIEZHENG QIAN ◽  
PING SHENG
Keyword(s):  
Contact Line ◽  
Critical Value ◽  
Diffuse Interface ◽  
Patterned Surfaces ◽  
Fluid Interface ◽  
Two Phase ◽  
Stick Slip ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Wetting Fluid

We simulate the moving contact line in two-dimensional chemically patterned channels using a diffuse-interface model with the generalized Navier boundary condition. The motion of the fluid–fluid interface in confined immiscible two-phase flows is modulated by the chemical pattern on the top and bottom surfaces, leading to a stick–slip behaviour of the contact line. The extra dissipation induced by this oscillatory contact-line motion is significant and increases rapidly with the wettability contrast of the pattern. A critical value of the wettability contrast is identified above which the effect of diffusion becomes important, leading to the interesting behaviour of fluid–fluid interface breaking, with the transport of the non-wetting fluid being assisted and mediated by rapid diffusion through the wetting fluid. Near the critical value, the time-averaged extra dissipation scales as U, the displacement velocity. By decreasing the period of the pattern, we show the solid surface to be characterized by an effective contact angle whose value depends on the material characteristics and composition of the patterned surfaces.

Entrapping an impacting particle at a liquid–gas interface

2018 ◽  
Vol 841 ◽  
pp. 1073-1084 ◽  
Author(s):  
Han Chen ◽  
Hao-Ran Liu ◽  
Xi-Yun Lu ◽  
Hang Ding
Keyword(s):  
Immersed Boundary Method ◽  
Density Ratio ◽  
Liquid Pool ◽  
Diffuse Interface ◽  
Critical Conditions ◽  
Immersed Boundary ◽  
Structure Interaction ◽  
Scaling Models ◽  
The Impact

We numerically investigate the mechanism leading to the entrapment of spheres at the gas–liquid interface after impact. Upon impact onto a liquid pool, a hydrophobic sphere is seen to follow one of the three regimes identified in the experiment (Lee & Kim, Langmuir, vol. 24, 2008, pp. 142–145): sinking, bouncing or being entrapped at the interface. It is important to understand the role of wettability in this process of flow–structure interaction with dynamic wetting, and in particular, to what extent the wettability can determine whether the sphere is entrapped at the interface. For this purpose, a diffuse-interface immersed boundary method is adopted in the numerical simulations. We expand the parameter space considered previously, provide the phase diagrams and identify the key phenomena in the impact dynamics. Then, we propose the scaling models to interpret the critical conditions for the occurrence of sphere entrapment, accounting for the wettability of the sphere. The models are shown to provide a good correlation among the impact inertia of the drop, the surface tension, the wettability and the density ratio of the sphere to the liquid.

Sliding, pinch-off and detachment of a droplet on a wall in shear flow

2010 ◽  
Vol 644 ◽  
pp. 217-244 ◽  
Author(s):  
HANG DING ◽  
MOHAMMAD N. H. GILANI ◽  
PETER D. M. SPELT
Keyword(s):  
Shear Flow ◽  
Contact Line ◽  
Contact Angle Hysteresis ◽  
Stress Singularity ◽  
Local Maximum ◽  
Diffuse Interface ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Effective Slip Length ◽  
Maximum Angle

We investigate here what happens beyond the onset of motion of a droplet on a wall by the action of an imposed shear flow, accounting for inertial effects and contact-angle hysteresis. A diffuse-interface method is used for this purpose, which alleviates the shear stress singularity at a moving contact line, resulting in an effective slip length. Various flow regimes are investigated, including steadily moving drops, and partial or entire droplet entrainment. In the regime of quasi-steadily moving drops, the drop speed is found to be linear in the imposed shear rate, but to exhibit an apparent discontinuity at the onset of motion. The results also include the relation between a local maximum angle between the interface and the wall and the instantaneous value of the contact-line speed. The critical conditions for the onset of entrainment are determined for pinned as well as for moving drops. The corresponding critical capillary numbers are found to be in a rather narrow range, even for quite substantial values of a Reynolds number. The approach to breakup is then investigated in detail, including the growth of a ligament on a drop, and the reduction of the radius of a pinching neck. A model based on an energy argument is proposed to explain the results for the rate of elongation of ligaments. The paper concludes with an investigation of detachment of a hydrophobic droplet from the solid wall.

Sharp-interface limit of the Cahn–Hilliard model for moving contact lines

2010 ◽  
Vol 645 ◽  
pp. 279-294 ◽  
Author(s):  
PENGTAO YUE ◽  
CHUNFENG ZHOU ◽  
JAMES J. FENG
Keyword(s):  
Contact Line ◽  
Diffusion Length ◽  
Slip Length ◽  
Sharp Interface ◽  
Diffuse Interface ◽  
Contact Lines ◽  
Sharp Interface Limit ◽  
Interface Models ◽  
Moving Contact ◽  
Moving Contact Lines

Diffuse-interface models may be used to compute moving contact lines because the Cahn–Hilliard diffusion regularizes the singularity at the contact line. This paper investigates the basic questions underlying this approach. Through scaling arguments and numerical computations, we demonstrate that the Cahn–Hilliard model approaches a sharp-interface limit when the interfacial thickness is reduced below a threshold while other parameters are fixed. In this limit, the contact line has a diffusion length that is related to the slip length in sharp-interface models. Based on the numerical results, we propose a criterion for attaining the sharp-interface limit in computing moving contact lines.

Numerical Simulation for Moving Contact Line with Continuous Finite Element Schemes

2015 ◽  
Vol 18 (1) ◽  
pp. 180-202 ◽  
Author(s):  
Yongyue Jiang ◽  
Ping Lin ◽  
Zhenlin Guo ◽  
Shuangling Dong
Keyword(s):  
Finite Element ◽  
Contact Line ◽  
Immiscible Fluids ◽  
Diffuse Interface ◽  
Discrete Energy ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Pressure Variable ◽  
Model Equations ◽  
The Stability

AbstractIn this paper, we compute a phase field (diffuse interface) model of Cahn-Hilliard type for moving contact line problems governing the motion of isothermal multiphase incompressible fluids. The generalized Navier boundary condition proposed by Qian et al. [1] is adopted here. We discretize model equations using a continuous finite element method in space and a modified midpoint scheme in time. We apply a penalty formulation to the continuity equation which may increase the stability in the pressure variable. Two kinds of immiscible fluids in a pipe and droplet displacement with a moving contact line under the effect of pressure driven shear flow are studied using a relatively coarse grid. We also derive the discrete energy law for the droplet displacement case, which is slightly different due to the boundary conditions. The accuracy and stability of the scheme are validated by examples, results and estimate order.

scholarly journals Diffuse Interface Methods for Multiple Phase Materials: An Energetic Variational Approach

2015 ◽  
Vol 8 (2) ◽  
pp. 220-236 ◽  
Author(s):  
J. Brannick ◽  
C. Liu ◽  
T. Qian ◽  
H. Sun
Keyword(s):  
Contact Line ◽  
Variational Approach ◽  
Virtual Work ◽  
Dissipation Function ◽  
Force Balance ◽  
Diffuse Interface ◽  
Least Action Principle ◽  
Least Action ◽  
Interfacial Energies ◽  
The Least Action Principle

AbstractIn this paper, we introduce a diffuse interface model for describing the dynamics of mixtures involving multiple (two or more) phases. The coupled hydrodynamical system is derived through an energetic variational approach. The total energy of the system includes the kinetic energy and the mixing (interfacial) energies. The least action principle (or the principle of virtual work) is applied to derive the conservative part of the dynamics, with a focus on the reversible part of the stress tensor arising from the mixing energies. The dissipative part of the dynamics is then introduced through a dissipation function in the energy law, in line with Onsager's principle of maximum dissipation. The final system, formed by a set of coupled time-dependent partial differential equations, reflects a balance among various conservative and dissipative forces and governs the evolution of velocity and phase fields. To demonstrate the applicability of the proposed model, a few two-dimensional simulations have been carried out, including (1) the force balance at the three-phase contact line in equilibrium, (2) a rising bubble penetrating a fluid-fluid interface, and (3) a solid particle falling in a binary fluid. The effects of slip at solid surface have been examined in connection with contact line motion and a pinch-off phenomenon.

scholarly journals Moving contact line dynamics: from diffuse to sharp interfaces

2015 ◽  
Vol 788 ◽  
pp. 209-227 ◽  
Author(s):  
H. Kusumaatmaja ◽  
E. J. Hemingway ◽  
S. M. Fielding
Keyword(s):  
Excellent Agreement ◽  
Contact Line ◽  
Scaling Laws ◽  
Slip Length ◽  
Dynamic Contact Angle ◽  
Sharp Interface ◽  
Diffuse Interface ◽  
Fluid Viscosity ◽  
Moving Contact Line ◽  
Moving Contact

We reconcile two scaling laws that have been proposed in the literature for the slip length associated with a moving contact line in diffuse interface models, by demonstrating each to apply in a different regime of the ratio of the microscopic interfacial width $l$ and the macroscopic diffusive length $l_{D}=(M{\it\eta})^{1/2}$, where ${\it\eta}$ is the fluid viscosity and $M$ the mobility governing intermolecular diffusion. For small $l_{D}/l$ we find a diffuse interface regime in which the slip length scales as ${\it\xi}\sim (l_{D}l)^{1/2}$. For larger $l_{D}/l>1$ we find a sharp interface regime in which the slip length depends only on the diffusive length, ${\it\xi}\sim l_{D}\sim (M{\it\eta})^{1/2}$, and therefore only on the macroscopic variables ${\it\eta}$ and $M$, independent of the microscopic interfacial width $l$. We also give evidence that modifying the microscopic interfacial terms in the model’s free energy functional appears to affect the value of the slip length only in the diffuse interface regime, consistent with the slip length depending only on macroscopic variables in the sharp interface regime. Finally, we demonstrate the dependence of the dynamic contact angle on the capillary number to be in excellent agreement with the theoretical prediction of Cox (J. Fluid Mech., vol. 168, 1986, p. 169), provided we allow the slip length to be rescaled by a dimensionless prefactor. This prefactor appears to converge to unity in the sharp interface limit, but is smaller in the diffuse interface limit. The excellent agreement of results obtained using three independent numerical methods, across several decades of the relevant dimensionless variables, demonstrates our findings to be free of numerical artefacts.

Sign in / Sign up

Export Citation Format

Share Document