Results It was found that variations in wettability disturb the flow of adjacent liquid (Fig. 3). Our results suggest that for a given liquid the normal.

Slides:



Advertisements
Similar presentations
Gravitational Wave Astronomy Dr. Giles Hammond Institute for Gravitational Research SUPA, University of Glasgow Universität Jena, August 2010.
Advertisements

Impact of Microdrops on Solids James Sprittles & Yulii Shikhmurzaev Failure of conventional models All existing models are based on the contact angle being.
Lecture 2 Properties of Fluids Units and Dimensions.
Convection.
ON WIDTH VARIATIONS IN RIVER MEANDERS Luca Solari 1 & Giovanni Seminara 2 1 Department of Civil Engineering, University of Firenze 2 Department of Environmental.
Self-propelled motion of a fluid droplet under chemical reaction Shunsuke Yabunaka 1, Takao Ohta 1, Natsuhiko Yoshinaga 2 1)Department of physics, Kyoto.
Design Constraints for Liquid-Protected Divertors S. Shin, S. I. Abdel-Khalik, M. Yoda and ARIES Team G. W. Woodruff School of Mechanical Engineering Atlanta,
MAE 5130: VISCOUS FLOWS Introduction to Boundary Layers
Boundary Layer Flow Describes the transport phenomena near the surface for the case of fluid flowing past a solid object.
Dr. Kirti Chandra Sahu Department of Chemical Engineering IIT Hyderabad.
Drops on patterned surfaces Halim Kusumaatmaja Alexandre Dupuis Julia Yeomans.
Chapter 2: Properties of Fluids
Hydrodynamic Slip Boundary Condition for the Moving Contact Line in collaboration with Xiao-Ping Wang (Mathematics Dept, HKUST) Ping Sheng (Physics Dept,
Equations of Continuity
1 MECH 221 FLUID MECHANICS (Fall 06/07) Tutorial 6 FLUID KINETMATICS.
Dynamics of liquid drops in precision deposition on solid surfaces J.E Sprittles Y.D. Shikhmurzaev Particulate Engineering Seminar May 2009.
Molecular hydrodynamics of the moving contact line in collaboration with Ping Sheng (Physics Dept, HKUST) Xiao-Ping Wang (Mathematics Dept, HKUST) Tiezheng.
Drop Impact and Spreading on Surfaces of Variable Wettability J.E Sprittles Y.D. Shikhmurzaev Bonn 2007.
Preliminary Assessment of Porous Gas-Cooled and Thin- Liquid-Protected Divertors S. I. Abdel-Khalik, S. Shin, and M. Yoda ARIES Meeting, UCSD (March 2004)
Momentum flux across the sea surface
An Introduction to Stress and Strain
2-1 Problem Solving 1. Physics  2. Approach methods
A variational approach to the moving contact line hydrodynamics
Direct numerical simulations of droplet emulsions in sliding bi-periodic frames using the level-set method See Jo Wook Ryol Hwang*
James Sprittles ECS 2007 Viscous Flow Over a Chemically Patterned Surface J.E. Sprittles Y.D. Shikhmurzaev.
Paradoxes in Capillary Flows James Sprittles Yulii Shikhmurzaev.
Temperature Gradient Limits for Liquid-Protected Divertors S. I. Abdel-Khalik, S. Shin, and M. Yoda ARIES Meeting (June 2004) G. W. Woodruff School of.
Hydrodynamic Slip Boundary Condition for the Moving Contact Line in collaboration with Xiao-Ping Wang (Mathematics Dept, HKUST) Ping Sheng (Physics Dept,
Slip to No-slip in Viscous Fluid Flows
Fluid mechanics 3.1 – key points
Some Aspects of Drops Impacting on Solid Surfaces J.E Sprittles Y.D. Shikhmurzaev EFMC7 Manchester 2008.
Simulation and Animation
Flow and Thermal Considerations
Convection Prepared by: Nimesh Gajjar. CONVECTIVE HEAT TRANSFER Convection heat transfer involves fluid motion heat conduction The fluid motion enhances.
Shell Momentum Balances
James Sprittles BAMC 2007 Viscous Flow Over a Chemically Patterned Surface J.E Sprittles Y.D. Shikhmurzaev.
A Hybrid Particle-Mesh Method for Viscous, Incompressible, Multiphase Flows Jie LIU, Seiichi KOSHIZUKA Yoshiaki OKA The University of Tokyo,
PTT 204/3 APPLIED FLUID MECHANICS SEM 2 (2012/2013)
Microfluidic Free-Surface Flows: Simulation and Application J.E Sprittles Y.D. Shikhmurzaev Indian Institute of Technology, Mumbai November 5 th 2011 The.
Boundary Layer Laminar Flow Re ‹ 2000 Turbulent Flow Re › 4000.
The Onsager Principle and Hydrodynamic Boundary Conditions Ping Sheng Department of Physics and William Mong Institute of Nano Science and Technology The.
CHAPTER 1 INTRODUCTION.  At the end of this chapter, you should be able to: 1. Understand the basic concepts of fluid mechanics and recognize the various.
Mass Transfer Coefficient
Chapter 03: Macroscopic interface dynamics Xiangyu Hu Technical University of Munich Part A: physical and mathematical modeling of interface.
Measurements in Fluid Mechanics 058:180:001 (ME:5180:0001) Time & Location: 2:30P - 3:20P MWF 218 MLH Office Hours: 4:00P – 5:00P MWF 223B-5 HL Instructor:
Physical Fluid Dynamics by D. J. Tritton What is Fluid Dynamics? Fluid dynamics is the study of the aforementioned phenomenon. The purpose.
1 Chapter 6 Flow Analysis Using Differential Methods ( Differential Analysis of Fluid Flow)
Ch 4 Fluids in Motion.
Compressible Frictional Flow Past Wings P M V Subbarao Professor Mechanical Engineering Department I I T Delhi A Small and Significant Region of Curse.
Fluid Mechanics SEMESTER II, 2010/2011
An Ultimate Combination of Physical Intuition with Experiments… P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Boundary Layer.
Two-phase hydrodynamic model for air entrainment at moving contact line Tak Shing Chan and Jacco Snoeijer Physics of Fluids Group Faculty of Science and.
1 CONSTITUTIVE RELATION FOR NEWTONIAN FLUID The Cauchy equation for momentum balance of a continuous, deformable medium combined with the condition of.
CP502 Advanced Fluid Mechanics
Heat Transfer Su Yongkang School of Mechanical Engineering # 1 HEAT TRANSFER CHAPTER 6 Introduction to convection.
CONVECTION : An Activity at Solid Boundary P M V Subbarao Associate Professor Mechanical Engineering Department IIT Delhi Identify and Compute Gradients.
05:53 Fluid Mechanics Basic Concepts.
Chapter 1: Basic Concepts
J.E. Sprittles (University of Oxford, U.K.) Y.D. Shikhmurzaev(University of Birmingham, U.K.) International Society of Coating Science & Technology Symposium,
An Unified Analysis of Macro & Micro Flow Systems… P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Slip to No-slip in Viscous Fluid.
Chapter 6: Introduction to Convection
Hamdache Abderrazaq 1*, Belkacem Mohamed 1, Hannoun Nourredine 2
Part IV: Detailed Flow Structure Chap. 7: Microscopic Balances
Hydrodynamics of slowly miscible liquids
Numerical Modeling of Fluid Droplet Spreading and Contact Angle Hysteresis Nikolai V. Priezjev, Mechanical Engineering, Michigan State University, MI
Two-dimensional Lattice Boltzmann Simulation of Liquid Water Transport
Today’s Lecture Objectives:
Introduction to Fluid Mechanics
CN2122 / CN2122E Fluid Mechanics
Chapter 9 Analysis of a Differential Fluid Element in Laminar Flow
Presentation transcript:

Results It was found that variations in wettability disturb the flow of adjacent liquid (Fig. 3). Our results suggest that for a given liquid the normal flux per unit time J, is related to the wettability of the solids by This may be considered as a measure of the effect that a patterned surface has on an adjacent flow. For the case when solid 1 is more hydrophobic, there is a flux into the interface. Introduction In microfluidics an increasing surface area to volume ratio of liquids means that surface effects are of greater significance. The correct description of the physics at solid-liquid interfaces then becomes imperative to the success of any attempt to model this class of flows. How do variations in the wettability of a substrate affect the flow of an adjacent liquid? A no-slip condition predicts no effect. Molecular dynamics simulations suggest that this is not the case (Priezjev et al 05, Qian et al 05), see Fig. 1. Acknowledgments The author acknowledges the financial support of Kodak and the EPSRC. Problem Formulation Consider the steady flow of an incompressible, viscous, Newtonian fluid over a stationary flat solid surface, driven by a shear in the far field. The bulk flow is described by the Navier-Stokes equations. The boundary conditions to be applied at the solid- liquid interface are provided by the interface formation model. For a given liquid, a solid’s wettability is defined by the equilibrium contact angle θ, which a liquid-gas free surface would form with that solid. Solid 1 (2) is characterised by a contact angle θ 1 (θ 2 ) The resulting set of equations are solved numerically using the finite element method. Conclusions When fluid particles forming the interface are driven by the outer flow from a hydrophilic region into a hydrophobic one, the surface interacts with the bulk in order to attain its new equilibrium state. Notably this creates a normal component to the flow. This effect is qualitatively in agreement with molecular dynamics simulations and is here realised in a continuum framework. Viscous flow over a chemically patterned surface J.E. Sprittles and Y.D. Shikhmurzaev School of Mathematics, University of Birmingham, Edgbaston, B15 2TT Literature cited N.V. Priezjev, A.A. Darhuber and S.M. Troian. Slip behaviour in liquid films on surfaces of patterned wettability: Comparison between continuum and molecular dynamics simulations. Phys. Rev. E 71:041608, 2005 T. Qian, X. Wang and P. Sheng. Hydrodynamic boundary condition at chemically patterned surfaces: A continuum deduction from molecular dynamics. Phys. Rev. E, 72:022501, 2005 Y.D. Shikhmurzaev. The moving contact line on a smooth solid surface. Int. J. Multiphase Flow, 19:589, Y. D. Shikhmurzaev. Macroscopic rupture of free liquid films. C.R. Mecanique, 333:205, For further information Please contact Fig. 1. Snapshot of a molecular dynamics simulation showing flow driven by a shear over a patterned surface. Red indicates a hydrophobic regions while blue represents hydrophilic regions. Interface formation model The no-slip boundary condition is generalised to allow for situations in which the classical fluid mechanics approach breaks down (e.g. Shikhmurzaev 93 and Shikhmurzaev 05). The interface is treated as a system in its own right, interacting with the bulk via mass, energy and momentum fluxes. In the continuum approximation the interaction across a layer of finite width (of the order of nanometres), caused by an asymmetry of intermolecular forces at the interface, is described by a set of equations to be applied at the surface. The state of the interface is described by properties such as surface tension, surface density and surface velocity. The concept of wettability naturally fits into the model without any ad-hoc alterations. Specifically the equilibrium surface density is higher for a more hydrophilic solid-liquid interface. Fig. 3. Streamlines of the flow. Notice the non-zero normal velocity on the liquid facing side of each solid-liquid interface. Fig. 4. Tangential velocity on the surface Fig. 5. Normal velocity on the surface. Curve 1: θ 1 = 10 o θ 2 = 60 o Curve 2: θ 1 = 60 o θ 2 = 110 o Curve 3: θ 1 = 10 o θ 2 = 110 o Aim Examine the case of a plane-parallel shear flow that encounters a change in solid substrate (Fig. 2). Here we consider the case where solid 1 is more hydrophilic. This is carried out in a continuum framework using the interface formation model. Fig. 2. Sketch of the problem Note variations in density near the surface indicate a normal component of the flow. There is a flux out of the interface due to the surface density being above its equilibrium value. Slip on the surface is caused by shear stress and Marangoni effects. How is the magnitude of the effect dependent on the solids chosen? Figs. 4 and 5 show the velocity components for three different combinations of solids where, in each case, the first solid is more hydrophilic.