Spri ringer. INTERFACIAL TRANSPORT PHENOMENA 2 nd Edition. John C. Slattery Department ofaerospace Engineering Texas A&M University

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1 INTERFACIAL TRANSPORT PHENOMENA 2 nd Edition John C. Slattery Department ofaerospace Engineering Texas A&M University Leonard Sagis Department of Agrotechnology & Food Science Wageningen University Eun-Suok Oh LG Chem, Research Park South Korea Spri ringer

2 Contents 1 Kinematics and Conservation of Mass Motion Body Stretch and Rotation [19, p. 17] Motion of Multiphase Bodies What are Phase Interfaces? Three-Dimensional Interfacial Region Dividing surface Dividing Surface as a Model for a Three-Dimensional Interfacial Region Motion of Dividing Surface Stretch and Rotation within Dividing Surfaces More about Surface Velocity Rate of Deformation Moving Common Lines: Qualitative Description Moving Common Lines: Emission of Material Surfaces [16] Moving Common Lines: Velocity is Multivalued on a Rigid Solid Moving Common Lines: Quantitative Description Mass Conservation of Mass Surface Mass Density Surface Transport Theorem Transport Theorem for Body Containing Dividing Surface Jump Mass Balance Location of Dividing Surface Transport Theorem for Body Containing Intersecting Dividing Surfaces Mass Balance at a Common Line 79

3 vi Contents Comment on Velocity Distribution in Neighborhood of Moving Common Line on Rigid Solid More Comments on Velocity Distribution in Neighborhood of Moving Common Line on Rigid Solid Frame Changes of Frame Frame Indifferent Sealars, Vectors, and Tensors Equivalent Motions Principle of Frame Indifference Foundations for Momentum Transfer Force What are Forces? Momentum and Moment of Momentum Balances Body Forces and Contact Forces Momentum Balance at Dividing Surfaces Surface Stress Tensor Jump Momentum Balance T (ff) is Symmetrie Tangential Tensor Surface Velocity, Surface Stress, and Surface Body Forcel Momentum Balance at Common Line Momentum Balance at Common Line on Relatively Rigid Solid Factors Influencing Measured Contact Angles Relationships for Measured Contact Angles More Comments Concerning Moving Common Lines and Contact Angles on Rigid Solids and Their Relation to the Disjoining Pressure Correcting Material Behavior for Intermolecular Forces from Adjacent Phases [20] The Correction One Unbounded Dividing Surface: View (iv) One Thin Lens or Fracture: View (iv) One Thin Film: View (v) A Discontinuous Thin Film: View (v) One Unbounded Common Line: View (iv) Applications of the Differential Balances to Momentum Transfer Philosophy Structure of Problem Approximations Only Interfacial Tension Classes of Problems Spinning Drop Interfacial Tensiometer [21] 164

4 Contents vii Meniscal Breakoff Interfacial Tensiometer Pendant Drop Sessile Drop Applications of Our Extension of Continuum Mechanics to the Nanoscale Supercritical Adsorption [22] Static Contact Angle [20] A Review of Coalescence (with J. D. Chen) Coalescence [23-25] Moving Common Line and Receding Contact Angle Nanoscale Fracture [26] Foundations for Simultaneous Momentum, Energy, and Mass Transfer Viewpoint Viewpoint in Considering Multicomponent Materials Body, Motion, and Material Coordinates of Species A Motion of Multicomponent Dividing Surface More about Surface Velocity of Species A Mass Balance Species Mass Balance Concentrations, Velocities, and Mass Fluxes Location of Multicomponent Dividing Surface Further Comments on Viewpoint Further Comments on Viewpoint of Multicomponent Materials Mass Conservation of Mass Force Momentum and Moment of Momentum Balances Jump Momentum Balance T( ff ) is Symmetrie, Tangential Tensor Energy Rate of Energy Transmission Energy Balance Radiant and Contact Energy Transmission Jump Energy Balance Entropy Entropy Inequality Radiant and Contact Entropy Transmission Jump Entropy Inequality Behavior as Restricted by Entropy Inequality Behavior of Multicomponent Materials Bulk Behavior: Implications of Entropy Inequality 304

5 Vlll Contents Surface Behavior: Implications of Jump Entropy Inequality Surface Behavior: Adsorption Isotherms and Equations of State Alternative Forms for the Energy Balances and the Entropy Inequalities Behavior as Restricted by Frame Indifference Other Principles to be Considered Alternative Independent Variables in Constitutive Equations Bulk Behavior: Constitutive Equations for Stress Tensor, Energy Flux Vector and Mass Flux Vector Surface Behavior: Constitutive Equations for Surface Stress Tensor Boussinesq Surface Fluid Simple Surface Material Surface Isotropy Group Isotropie Simple Surface Materials Simple Surface Solid Simple Surface Fluid Fading Memory and Special Cases of Simple Surface Fluid Simple Surface Fluid Crystals Surface Behavior: Constitutive Equations for Surface Energy Flux Vector Surface Behavior: Constitutive Equations for Surface Mass Flux Vector Intrinsically Stable Equilibrium [27] Stable Equilibrium Constraints on Isolated Systems Implications of ( ) for Intrinsically Stable Equilibrium Implications of ( ) for Intrinsically Stable Equilibrium Thermodynamics of Single-Component, Elastic, Crystalline Surface Solids [28] Thermodynamics of Surface Crystals Constraints on Isolated Systems Implications of Equilibrium Stress-Deformation Behavior of Single-Walled Carbon Nanotubes Applications of the Differential Balances to Momentum, Energy and Mass Transfer Philosophy 429

6 Contents ix Structure of Problems Involving Momentum Transfer Structure of Problems Involving Energy Transfer Structure of Problems Involving Mass Transfer Problems Involving Momentum Transfer Boussinesq Surface Fluid in a Knife-edge Surface Viscometer Generalized Boussinesq Surface Fluid in a Deep Channel Surface Viscometer Simple Surface Fluid in Curvilineal Surface Flows [29] Simple Surface Fluid in a Deep Channel Surface Viscometer [29] Simple Surface Fluid in an Oscillating Deep Channel Surface Viscometer [29] Limiting Cases when Effects of Interfacial Viscosities Dominate Displacement in a Capillary [30] Several Interfacial Viscometers Suitable for Measuring Gener alized Boussinesq Surface Fluid Behavior [31] Stochastic Interfacial Disturbances Created by Thermal Noise and the Importance of the Interfacial Viscosities [32] Capillary Rise [30, 33] Common Line Motion in Systems with Simple Surface Fluid Material Behavior: Implications of the Entropy Inequality [34, 35] More on Common Line Motion in Systems with Simple Surface Fluid Material Behavior: Implications in Polymer Extrusion [36] Limiting Cases of Energy Transfer Motion of a Drop or Bubble [37; with D. Li] Limiting Cases of Mass Transfer Motion of a Drop or Bubble [38; with D. Li] Longitudinal and Transverse Waves [32] 587 A Differential Geometry 611 A.l Physical Space 611 A.l.l Euclidean Space 611 A.1.2 Notation in (E 2, V 3 ) 613 A.1.3 Surface in (E 3,V 3 ) 617 A.2 Vector Fields 617 A.2.1 Natural Basis 617 A.2.2 Surface Gradient of Scalar Field 624 A.2.3 Dual Basis 625 A.2.4 Covariant and Contravariant Components 625 A.2.5 Physical Components 626

7 x Contents A.2.6 Tangential and Normal Components 627 A.3 Second-Order Tensor Fields 629 A.3.1 Tangential Transformations and Surface Tensors 629 A.3.2 Projection Tensor 631 A.3.3 Tangential Cross Tensor 633 A.3.4 Transpose 636 A.3.5 Inverse 637 A.3.6 Orthogonal Tangential Transformation 639 A.3.7 Surface Determinant of Tangential Transformation 641 A.3.8 Polar Decomposition 643 A.4 Third-Order Tensor Fields 646 A.4.1 Surface Tensors 646 A.5 Surface Gradient 647 A.5.1 Spatial Vector Field 647 A.5.2 Vector Field is Explicit Function of Position in Space A.5.3 Vector Field is Explicit Function of Position on Surface 649 A.5.4 Second-Order Tensor Field 660 A.5.5 Tensor Field is Explicit Function of Position in Space A.5.6 Tensor Field is Explicit Function of Position on Surface 662 A.6 Integration 666 A.6.1 Line Integration 666 A.6.2 Surface Integration 668 A.6.3 Surface Divergence Theorem 669 B Summary of Useful Equations 673 B.l Useful Equations for Single Component Systems 673 B.l.l Bulk Phases 673 B.l.2 Dividing Surfaces 675 B.l.3 Common Lines 693 B.2 Useful Equations for Multicomponent Systems with Simultaneous Momentum, Energy, and Mass Transfer 694 B.2.1 Concentrations, Velocities, and Fluxes 694 B.2.2 Jump Mass, Jump Energy, and Jump Entropy Balance. 700 B.2.3 Specific Forms 704 C Applications of integral averaging to momentum, energy, and mass transfer 735 Ol Integral balances 735 C.l.l Integral overall mass balance 736 C.1.2 The Integral Mass Balance for Species A 738 C.1.3 Integral momentum balance 739 C.1.4 Integral mechanical energy balance 742 C.1.5 The Integral Energy Balance 749 C.1.6 The Integral Entropy Inequality 753

8 Contents xi Notation 757 References 773 Author Index 809 Index 821