INTERMEDIATE FLUID DYNAMICS
CONTENTS A PREVIEW A A BRIEF HISTORICAL PERSPECTIVE OF TRANSPORT PHENOMENA IN CHEMICAL ENGINEERING B THE NATURE OF THE SUBJECT C A BRIEF DESCRIPTION OF THE CONTENTS OF THIS BOOK NOTES AND REFERENCES BASIC PRINCIPLES A THE CONTINUUM APPROXIMATION FOUNDATIONS CONSEQUENCES B CONSERVATION OF MASS – THE CONTINUITY EQUATION C NEWTON’S LAWS OF MECHANICS D CONSERVATION OF ENERGY AND THE ENTROPY INEQUALITY E CONSTITUTIVE EQUATIONS F FLUID STATICS – THE STRESS TENSOR FOR A STATIONARY FLUID G THE CONSTITUTIVE EQUATION FOR THE HEAT FLUX VECTOR – FOURIER’S LAW H CONSTITUTIVE EQUATIONS FOR A FLOWING FLUID – THE NEWTONIAN FLUID I THE EQUATIONS OF MOTION FOR A NEWTONIAN FLUID – THE NAVIER–STOKES EQUATION J COMPLEX FLUIDS – ORIGINS OF NON-NEWTONIAN BEHAVIOR K CONSTITUTIVE EQUATIONS FOR NON-NEWTONIAN FLUIDS L BOUNDARY CONDITIONS AT SOLID WALLS AND FLUID INTERFACES THE KINEMATIC CONDITION THERMAL BOUNDARY CONDITIONS THE DYNAMIC BOUNDARY CONDITION M FURTHER CONSIDERATIONS OF THE BOUNDARY CONDITIONS AT THE INTERFACE BETWEEN TWO PURE FLUIDS – THE STRESS CONDITIONS GENERALIZATION OF THE KINEMATIC BOUNDARY CONDITION FOR AN INTERFACE THE STRESS CONDITIONS THE NORMAL-STRESS BALANCE AND CAPILLARY FLOWS THE TANGENTIAL-STRESS BALANCE AND THERMOCAPILLARY FLOWS CONTENTS N THE ROLE OF SURFACTANTS IN THE BOUNDARY CONDITIONS AT A FLUID INTERFACE NOTES AND REFERENCE PROBLEMS UNIDIRECTIONAL AND ONE-DIMENSIONAL FLOW AND HEAT TRANSFER PROBLEMS A SIMPLI?CATION OF THE NAVIER–STOKES EQUATIONS FOR UNIDIRECTIONAL FLOWS B STEADY UNIDIRECTIONAL FLOWS – NONDIMENSIONALIZATION AND CHARACTERISTIC SCALES C CIRCULAR COUETTE FLOW – A ONE-DIMENSIONAL ANALOG TO UNIDIRECTIONAL FLOWS D START-UP FLOW IN A CIRCULAR TUBE – SOLUTION BY SEPARATION OF VARIABLES E THE RAYLEIGH PROBLEM – SOLUTION BY SIMILARITY TRANSFORMATION F START-UP OF SIMPLE SHEAR FLOW G SOLIDI?CATION AT A PLANAR INTERFACE H HEAT TRANSFER IN UNIDIRECTIONAL FLOWS STEADY-STATE HEAT TRANSFER IN FULLY DEVELOPED FLOW THROUGH A HEATED (OR COOLED) SECTION OF A CIRCULAR TUBE TAYLOR DIFFUSION IN A CIRCULAR TUBE I PULSATILE FLOW IN A CIRCULAR TUBE NOTES AN INTRODUCTION TO ASYMPTOTIC APPROXIMATIONS A PULSATILE FLOW IN A CIRCULAR TUBE REVISITED – ASYMPTOTIC SOLUTIONS FOR HIGH AND LOW FREQUENCIES B ASYMPTOTIC EXPANSIONS – GENERAL CONSIDERATIONS C THE EFFECT OF VISCOUS DISSIPATION ON A SIMPLE SHEAR FLOW D THE MOTION OF A FLUID THROUGH A SLIGHTLY CURVED TUBE – THE DEAN PROBLEM E FLOW IN A WAVY-WALL CHANNEL – “DOMAIN PERTURBATION METHOD” FLOW PARALLEL TO THE CORRUGATION GROOVES FLOW PERPENDICULAR TO THE CORRUGATION GROOVES F DIFFUSION IN A SPHERE WITH FAST REACTION – “SINGULAR PERTURBATION THEORY” G BUBBLE DYNAMICS IN A QUIESCENT FLUID THE RAYLEIGH–PLESSET EQUATION EQUILIBRIUM SOLUTIONS AND THEIR STABILITY BUBBLE OSCILLATIONS DUE TO PERIODIC PRESSURE OSCILLATIONS – RESONANCE AND “MULTIPLE-TIME-SCALE ANALYSIS” STABILITY TO NONSPHERICAL DISTURBANCES THE THIN-GAP APPROXIMATION – LUBRICATION PROBLEMS A THE ECCENTRIC CYLINDER PROBLEM THE NARROW-GAP LIMIT – GOVERNING EQUATIONS AND SOLUTIONS LUBRICATION FORCES B DERIVATION OF THE BASIC EQUATIONS OF LUBRICATION THEORY C APPLICATIONS OF LUBRICATION THEORY THE SLIDER-BLOCK PROBLEM THE MOTION OF A SPHERE TOWARD A SOLID, PLANE BOUNDARY D THE AIR HOCKEY TABLE C LIFT ON THE DISK THE THIN-GAP APPROXIMATION – FILMS WITH A FREE SURFACE A DERIVATION OF THE GOVERNING EQUATIONS THE BASIC EQUATIONS AND BOUNDARY CONDITIONS SIMPLI?CATION OF THE INTERFACE BOUNDARY CONDITIONS FOR A THIN FILM DERIVATION OF THE DYNAMICAL EQUATION FOR THE SHAPE FUNCTION, H(XS, T) B SELF-SIMILAR SOLUTIONS OF NONLINEAR DIFFUSION EQUATIONS C FILMS WITH A FREE SURFACE – SPREADING FILMS ON A HORIZONTAL SURFACE GRAVITATIONAL SPREADING CAPILLARY SPREADING D THE DYNAMICS OF A THIN FILM IN THE PRESENCE OF VAN DER WAALS FORCES LINEAR STABILITY SIMILARITY SOLUTIONS FOR FILM RUPTURE E SHALLOW-CAVITY FLOWS THE HORIZONTAL, ENCLOSED SHALLOW CAVITY THE HORIZONTAL SHALLOW CAVITY WITH A FREE SURFACE A SOLUTION BY MEANS OF THE CLASSICAL THIN-?LM ANALYSIS B SOLUTION BY MEANS OF THE METHOD OF DOMAIN PERTURBATIONS C THE END REGIONS THERMOCAPILLARY FLOW IN A THIN CAVITY A THIN-?LM SOLUTION PROCEDURE B SOLUTION BY DOMAIN PERTURBATION FOR ? = CREEPING FLOW – TWO-DIMENSIONAL AND AXISYMMETRIC PROBLEMS A NONDIMENSIONALIZATION AND THE CREEPING-FLOW EQUATIONS B SOME GENERAL CONSEQUENCES OF LINEARITY AND THE CREEPING-FLOW EQUATIONS THE DRAG ON BODIES THAT ARE MIRROR IMAGES IN THE DIRECTION OF MOTION THE LIFT ON A SPHERE THAT IS ROTATING IN A SIMPLE SHEAR FLOW LATERAL MIGRATION OF A SPHERE IN POISEUILLE FLOW RESISTANCE MATRICES FOR THE FORCE AND TORQUE ON A BODY IN CREEPING FLOW CONTENTS C REPRESENTATION OF TWO-DIMENSIONAL AND AXISYMMETRIC FLOWS IN TERMS OF THE STREAMFUNCTION D TWO-DIMENSIONAL CREEPING FLOWS: SOLUTIONS BY MEANS OF EIGENFUNCTION EXPANSIONS (SEPARATION OF VARIABLES) GENERAL EIGENFUNCTION EXPANSIONS IN CARTESIAN AND CYLINDRICAL COORDINATES APPLICATION TO TWO-DIMENSIONAL FLOW NEAR CORNERS E AXISYMMETRIC CREEPING FLOWS: SOLUTION BY MEANS OF EIGENFUNCTION EXPANSIONS IN SPHERICAL COORDINATES (SEPARATION OF VARIABLES) GENERAL EIGENFUNCTION EXPANSION APPLICATION TO UNIFORM STREAMING FLOW PAST AN ARBITRARY AXISYMMETRIC BODY F UNIFORM STREAMING FLOW PAST A SOLID SPHERE – STOKES’ LAW G A RIGID SPHERE IN AXISYMMETRIC, EXTENSIONAL FLOW THE FLOW FIELD DILUTE SUSPENSION RHEOLOGY – THE EINSTEIN VISCOSITY FORMULA H TRANSLATION OF A DROP THROUGH A QUIESCENT FLUID AT LOW RE I MARANGONI EFFECTS ON THE MOTION OF BUBBLES AND DROPS J SURFACTANT EFFECTS ON THE BUOYANCY-DRIVEN MOTION OF A DROP GOVERNING EQUATIONS AND BOUNDARY CONDITIONS FOR A TRANSLATING DROP WITH SURFACTANT ADSORBED AT THE INTERFACE THE SPHERICAL-CAP LIMIT THE LIMIT OF FAST ADSORPTION KINETICS CREEPING FLOW – THREE-DIMENSIONAL PROBLEMS A SOLUTIONS BY MEANS OF SUPERPOSITION OF VECTOR HARMONIC FUNCTIONS PRELIMINARY CONCEPTS A VECTOR “EQUALITY” – PSEUDO-VECTORS B REPRESENTATION THEOREM FOR SOLUTION OF THE CREEPING-?OW EQUATIONS C VECTOR HARMONIC FUNCTIONS THE ROTATING SPHERE IN A QUIESCENT FLUID UNIFORM FLOW PAST A SPHERE B A SPHERE IN A GENERAL LINEAR FLOW C DEFORMATION OF A DROP IN A GENERAL LINEAR FLOW D FUNDAMENTAL SOLUTIONS OF THE CREEPING-FLOW EQUATIONS THE “STOKESLET”: A FUNDAMENTAL SOLUTION FOR THE CREEPING-FLOW EQUATIONS AN INTEGRAL REPRESENTATION FOR SOLUTIONS OF THE CREEPING-FLOW EQUATIONS DUE TO LADYZHENSKAYA E SOLUTIONS FOR SOLID BODIES BY MEANS OF INTERNAL DISTRIBUTIONS OF SINGULARITIES FUNDAMENTAL SOLUTIONS FOR A FORCE DIPOLE AND OTHER HIGHER-ORDER SINGULARITIES TRANSLATION OF A SPHERE IN A QUIESCENT FLUID (STOKES’ SOLUTION) SPHERE IN LINEAR FLOWS: AXISYMMETRIC EXTENSIONAL FLOW AND SIMPLE SHEAR UNIFORM FLOW PAST A PROLATE SPHEROID APPROXIMATE SOLUTIONS OF THE CREEPING-FLOW EQUATIONS BY MEANS OF SLENDER-BODY THEORY F THE BOUNDARY INTEGRAL METHOD A RIGID BODY IN AN UNBOUNDED DOMAIN PROBLEMS INVOLVING A FLUID INTERFACE PROBLEMS IN A BOUNDED DOMAIN G FURTHER TOPICS IN CREEPING-FLOW THEORY THE RECIPROCAL THEOREM FAXEN’S LAW FOR A BODY IN AN UNBOUNDED FLUID INERTIAL AND NON-NEWTONIAN CORRECTIONS TO THE FORCE ON A BODY HYDRODYNAMIC INTERACTIONS BETWEEN WIDELY SEPARATED PARTICLES – THE METHOD OF RE?ECTIONS CONVECTION EFFECTS IN LOW-REYNOLDS-NUMBER FLOWS A FORCED CONVECTION HEAT TRANSFER – INTRODUCTION GENERAL CONSIDERATIONS SCALING AND THE DIMENSIONLESS PARAMETERS FOR CONVECTIVE HEAT TRANSFER THE ANALOGY WITH SINGLE-SOLUTE MASS TRANSFER B HEAT TRANSFER BY CONDUCTION (PE ?0) C HEAT TRANSFER FROM A SOLID SPHERE IN A UNIFORM STREAMING FLOW AT SMALL, BUT NONZERO, PECLET NUMBERS INTRODUCTION – WHITEHEAD’S PARADOX EXPANSION IN THE INNER REGION EXPANSION IN THE OUTER REGION A SECOND APPROXIMATION IN THE INNER REGION HIGHER-ORDER APPROXIMATIONS SPECI?ED HEAT FLUX D UNIFORM FLOW PAST A SOLID SPHERE AT SMALL, BUT NONZERO, REYNOLDS NUMBER E HEAT TRANSFER FROM A BODY OF ARBITRARY SHAPE IN A UNIFORM STREAMING FLOW AT SMALL, BUT NONZERO, PECLET NUMBERS F HEAT TRANSFER FROM A SPHERE IN SIMPLE SHEAR FLOW AT LOW PECLET NUMBERS G STRONG CONVECTION EFFECTS IN HEAT AND MASS TRANSFER AT LOW REYNOLDS NUMBER – AN INTRODUCTION GOVERNING EQUATIONS AND RESCALING IN THE THERMAL BOUNDARY-LAYER REGION SOLUTION OF THE THERMAL BOUNDARY-LAYER EQUATION I THERMAL BOUNDARY-LAYER THEORY FOR SOLID BODIES OF NONSPHERICAL SHAPE IN UNIFORM STREAMING FLOW TWO-DIMENSIONAL BODIES AXISYMMETRIC BODIES PROBLEMS WITH CLOSED STREAMLINES (OR STREAM SURFACES) J BOUNDARY-LAYER ANALYSIS OF HEAT TRANSFER FROM A SOLID SPHERE IN GENERALIZED SHEAR FLOWS AT LOW REYNOLDS NUMBER CONTENTS K HEAT (OR MASS) TRANSFER ACROSS A FLUID INTERFACE FOR LARGE PECLET NUMBERS GENERAL PRINCIPLES MASS TRANSFER FROM A RISING BUBBLE OR DROP IN A QUIESCENT FLUID L HEAT TRANSFER AT HIGH PECLET NUMBER ACROSS REGIONS OF CLOSED-STREAMLINE FLOW HEAT TRANSFER FROM A ROTATING CYLINDER IN SIMPLE SHEAR FLOW LAMINAR BOUNDARY-LAYER THEORY A POTENTIAL-FLOW THEORY B THE BOUNDARY-LAYER EQUATIONS C STREAMING FLOW PAST A HORIZONTAL FLAT PLATE – THE BLASIUS SOLUTION D STREAMING FLOW PAST A SEMI-IN?NITE WEDGE – THE FALKNER–SKAN SOLUTIONS E STREAMING FLOW PAST CYLINDRICAL BODIES – BOUNDARY-LAYER SEPARATION F STREAMING FLOW PAST AXISYMMETRIC BODIES – A GENERALIZAITON OF THE BLASIUS SERIES G THE BOUNDARY-LAYER ON A SPHERICAL BUBBLE HEAT AND MASS TRANSFER AT LARGE REYNOLDS NUMBER A GOVERNING EQUATIONS (RE ?1, PE ?1, WITH ARBITRARY PR OR SC NUMBERS) B EXACT (SIMILARITY) SOLUTIONS FOR PR (OR SC) ?O(1) E USE OF THE ASYMPTOTIC RESULTS AT INTERMEDIATE PE (OR SC) F APPROXIMATE RESULTS FOR SURFACE TEMPERATURE WITH SPECI?ED HEAT FLUX OR MIXED BOUNDARY CONDITIONS G LAMINAR BOUNDARY-LAYER MASS TRANSFER FOR FINITE INTERFACIAL VELOCITIES HYDRODYNAMIC STABILITY A CAPILLARY INSTABILITY OF A LIQUID THREAD THE INVISCID LIMIT VISCOUS EFFECTS ON CAPILLARY INSTABILITY FINAL REMARKS B RAYLEIGH–TAYLOR INSTABILITY (THE STABILITY OF A PAIR OF IMMISCIBLE FLUIDS THAT ARE SEPARATED BY A HORIZONTAL INTERFACE) THE INVISCID FLUID LIMIT THE EFFECTS OF VISCOSITY ON THE STABILITY OF A PAIR OF SUPERPOSED FLUIDS DISCUSSION CONTENTS C SAFFMAN–TAYLOR INSTABILITY AT A LIQUID INTERFACE DARCY’S LAW THE TAYLOR–SAFFMAN INSTABILITY CRITERIA D TAYLOR–COUETTE INSTABILITY A SUF?CIENT CONDITION FOR STABILITY OF AN INVISCID FLUID VISCOUS EFFECTS E NONISOTHERMAL AND COMPOSITIONALLY NONUNIFORM SYSTEMS F NATURAL CONVECTION IN A HORIZONTAL FLUID LAYER HEATED FROM BELOW – THE RAYLEIGH–BENARD PROBLEM THE DISTURBANCE EQUATIONS AND BOUNDARY CONDITIONS STABILITY FOR TWO FREE SURFACES THE PRINCIPLE OF EXCHANGE OF STABILITIES STABILITY FOR TWO NO-SLIP, RIGID BOUNDARIES G DOUBLE-DIFFUSIVE CONVECTION H MARANGONI INSTABILITY I INSTABILITY OF TWO-DIMENSIONAL UNIDIRECTIONAL SHEAR FLOWS INVISCID FLUIDS A THE RAYLEIGH STABILITY EQUATION B THE IN?ECTION-POINT THEOREM VISCOUS FLUIDS A THE ORR–SOMMERFELD EQUATION B A SUF?CIENT CONDITION FOR STABILITY