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.

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.

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 On multiscale moving contact line theory

2015 ◽  
Vol 471 (2179) ◽  
pp. 20150224 ◽  
Author(s):  
Shaofan Li ◽  
Houfu Fan
Keyword(s):  
Contact Line ◽  
Liquid Droplet ◽  
Stress Singularity ◽  
Adhesive Contact ◽  
Solid Substrate ◽  
Coarse Grained ◽  
Adhesive Interaction ◽  
Droplet Spreading ◽  
Moving Contact Line ◽  
Moving Contact

In this paper, a multiscale moving contact line (MMCL) theory is presented and employed to simulate liquid droplet spreading and capillary motion. The proposed MMCL theory combines a coarse-grained adhesive contact model with a fluid interface membrane theory, so that it can couple molecular scale adhesive interaction and surface tension with hydrodynamics of microscale flow. By doing so, the intermolecular force, the van der Waals or double layer force, separates and levitates the liquid droplet from the supporting solid substrate, which avoids the shear stress singularity caused by the no-slip condition in conventional hydrodynamics theory of moving contact line. Thus, the MMCL allows the difference of the surface energies and surface stresses to drive droplet spreading naturally. To validate the proposed MMCL theory, we have employed it to simulate droplet spreading over various elastic substrates. The numerical simulation results obtained by using MMCL are in good agreement with the molecular dynamics results reported in the literature.

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.

Moving contact line

2001 ◽  
Vol 11 (PR6) ◽  
pp. Pr6-199-Pr6-212 ◽  
Author(s):  
Y. Pomeau
Keyword(s):  
Contact Line ◽  
Moving Contact Line ◽  
Moving Contact
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