1,3.3 RHEOLOGICAL PROPERTIES OF FLUIDS,1. Rheology(流变学) 2. Newtonian and non-newtonian fluids (牛顿性流体与非牛顿性流体) Time-independent flow (与时间无关的粘性流动） 3. Time-dependent flow (与时间有关的粘性流动） 4. Viscoelastic fluids. （粘弹性流体）,2,3. Time-dependent flow,Thixotropic（触变性） liquids break down under continued shear and on mixing give lower shear stress for a given shear rate; that is, their apparent viscosity decreases with time.,3,Rheopectic（流凝性） substances behave in the reverse manner, and the shear stress increases with time, as does the apparent viscosity. The original structures and apparent viscosities are usually recovered on standing.,The rheological characteristics of fluids are summarized in Table 3.1.,4,4. Viscoelastic fluids粘弹性流体,Viscoelastic fluids show both viscous and elastic properties. They exhibit elastic recovery from deformations that occur during flow, but usually only part of the deformation is recovered upon removal of the stress. Examples of viscoelastic fluids are flour dough, napalm（凝固汽油）, and certain polymer melts(聚合物熔体).,5,In this course, only Newtonian fluid will be discussed.,6,3.4 VISCOSITY黏度,1. Concept of viscosity 2. Viscosity and momentum flux 3. Viscosities of gases and liquids 4. Kinematic viscosity.,7,1. Concept of viscosity,In a newtonian fluid, the shear stress is proportional to the shear rate, and the proportionality constant is called the viscosity,(3.3),8,-Newtons law of viscosity 牛顿粘性定律 The equation is only valid for newtonian fluid in laminar flow,or,9,10,Unit of viscosity: SI system: kilograms per meter-second or pascal-second 1 (Pa.s) = 1 (kg/m.s),cgs system: grams per centimeter-second, and this unit is called the poise (P) 泊 1（g/cm.s) = 1 P,11,millipascal-seconds(mPas) or centipoises(cP)厘泊 ( 1 mPas=1 cP = 0.01 P ),fps system: pounds per foot-second or pounds per foot-hour. (lb/ft s) or (lb/ft h),Conversion factors among the different systems are given in Table 3.2.,12,2. Viscosity and momentum flux,Equation (3.3) states that the momentum flux normal to the direction of fluid flow is proportional to the velocity gradient, with the viscosity as the proportionality factor.,(3.3),13,v : momentum flux (kg m/s)/m2 s rate of momentum transfer per unit area u : momentum per unit volume,(kg m/s)/m3 d(u)/dy : momentum concentration gradient / : momentum diffusivity, m2/s.,Or,14,momentum flux = (momentum diffusivity) x (momentum concentration gradient),15,3. Viscosities of gases and liquids,viscosity = f (temperature, molecular structure, pressure),16,Effect of temperature:,Gas viscosities increase with temperature,Liquid viscosities decrease with temperature,(3.5),Effect of pressure:,17,Effect of molecular weight:,For gas viscosities, there is no simple correlation with molecular weight.,The liquid viscosities usually increase with molecular weight,18,Viscosity of a mixture,Gas mixture:,yi : molar fraction of i component in the mixture i : viscosity of pure i component at the same temperature. Mi : molecular weight of i component.,19,Liquid mixture: For unassociated liquid mixture,xi : molar fraction of i component in the mixture,20,Magnitude of viscosity,Liquid : 0.1 cP- liquids near their boiling point 106 P - polymer melts.,the viscosity of water: 1.79 cP at 0 0.28 cP at 100 ,21,Gas: viscosities at room temperature are generally between 0.005 and 0.02 cP.,At 20 the viscosity is 0.018 cP for air, 0.014 cP for carbon dioxide, 0.007 cP for benzene vapor, 0.009 cP for hydrogen.,22,Source of viscosity: Appendix 8: viscosities for gases Appendix 9: viscosities for liquids Perrys Chemical Engineering Handbook,23,4. Kinematic viscosity 运动粘度,kinematic viscosity (dynamic viscosity) ,24,Units of kinematic viscosity (dynamic viscosity),SI: m2/s, cgs system: stoke (St)(沲)， cSt(厘沲） 1 St = 1 cm2/s 1 St = 100 cSt fps unit: ft2/s,Conversion factors are,25,For liquids, kinematic viscosities vary with temperature over a somewhat narrower range than absolute viscosities. For gases, the kinematic viscosity increases more rapidly with temperature than does the absolute viscosity.,26,3.5 TURBULENCE,1. Reynolds experiment (discussed earlier) 2. Reynolds number and transition from laminar to turbulent flow (discussed earlier) 3. Reynolds number for non-newtonian fluids 4. Nature of turbulence 5. Deviating velocities in turbulent flow,27, 6. Statistical nature of turbulence 7. Intensity and scale of turbulence 8. Isotropic turbulence 9. Reynolds stresses 10. Eddy viscosity,28, 3. Reynolds number for non-newtonian fluids,(3.9),The onset of turbulence occurs at Reynolds numbers above 2,100 with pseudoplastic fluids, for which n 1.,29,4. Nature of turbulence,Turbulent flow consists of a mass of eddies of various sizes coexisting in the flowing stream.,disappear,viscous dissipation,30,when the smallest eddies are obliterated by viscous action, mechanical energy is finally converted to heat. Energy conversion by viscous action is called viscous dissipation.,