【正文】 Parallel Plates (a) Shear (b) Elongation Capillary 3 2 1 0 1 2 3 4 510 10 10 10 10 10 10 10 10? ? ?ConeandPlate Concentric Cylinder Concentrated Regime Dilute Regime 1 (s )?For Melts amp。 0xzy yxv y v v?? ? ?FIG. . Streamlines for elongational flow (b=0) 22xyzvxvyvz????????(a) Shear (b) Shearfree Shear rate Elongation rate ? The Stress Tensor x y z 0000x x y xy x y yzzpppp????? ???? ???????? ? ? ????000000xxyyzzpppp??????? ? ??????? ? ? ????Shear Flow Elongational Flow yxx x y yy y z z???????S he a r S t res s :F i rst Normal S t res s D i f f eren c e :S ec on d Normal S t res s D i f f eren c e : z z x x???T e n s ile S t res s :*See 167。 24 Material Functions in Elongational Flows Topics in Each Section ? Two standard kinds of flows, shear and shearfree, are used to characterize polymeric liquids . Rheometry FIG. . Steady simple shear flow xvy??。 22 Basic Vector/Tensor Manipulations ? Vector Operations ? Tensor Operations ?167。 21 Rheometry ? Shear and Shearfree Flows ? Flow Geometries amp。 PrenticeHall, Englewood cliffs, NJ (1964), p. 120.] ?Dimensionless groups in NonNewtonian fluid mechanics the Deborah number (De) ?: the characteristic time of the fluid, tflow: the characteristic time of the flow system the Weissenberg number (We) ?: the characteristic strain rate in the flow ?Dimensionless groups in Newtonian fluid mechanics the Reynolds number (Re) L: the characteristic length。 a solution of g of polymethylmethacrylate (Mn = 106 g/mol) in 100 cm3 of dimethylphthalate (P) shows an increase by a factor in diameter as it flows downward out of the tube. [Reproduced from A. S. Lodge, Elastic Liquids, Academic Press, New York (1964), p. 242.] [Retrieved from the video of NonNewtonian Fluid Mechanics (University of Wales Institute of NonNewtonian Fluid Mechanics, 2022)] ? Tubeless Siphon When the siphon tube is lifted out of the fluid, the Newtonian liquid (N) stops flowing。 (b) the polymer flows out faster than the Newtonian fluid. [Reproduced from R. B. Bird, R. C. Armstrong and O. Hassager, Dynamics of Polymeric Liquids. Vol I: Fluid Mechanics, 2nd edition, WileyInterscience (1987), p. 61.] [Retrieved from the video of NonNewtonian Fluid Mechanics (University of Wales Institute of NonNewtonian Fluid Mechanics, 2022)] Normal Stress Difference and Elasticity ? RodClimbing Fixed cylinder with rotating rod. (N) The Newtonian liquid, glycerin, shows a vortex。 Shear Thinning/Thickening Dilatants (Shear thickening) Newtonian Fluids Pseudoplastics (Shear thinning) Dilatants (Shear thickening) Newtonian Fluids Pseudoplastics (Shear thinning) ?0 pleatau (a) Shear stress vs shear rate and (b) log viscosity vs log shear rate for Dilatants, Newtonian fluids and Pseudoplastics. For very high shear rates the pseudoplastic material reaches a second Newtonian pleatau. [Reproduced from G. M. Kavanagh and S. B. RossMurphy, “Rheological characterisation of polymer gels”, Prog. Polym. Sci., 23, 533 (1998).] Shear Thinning/Thickening (cont.) Tube flow and “shear thinning”. In each part, the Newtonina behavior is shown on the left (N)。 the behavior of a polymer on the right (P). (a) A tiny sphere falls at the same rate through each。 (P) the polymer solution, polyacrylamide in glycerin, climbs the rod. [Reproduced from R. B. Bird, R. C. Armstrong and O. Hassager, Dynamics of Polymeric Liquids. Vol I: Fluid Mechanics, 2nd edition, WileyInterscience (1987), p. 63.] [Retrieved from the video of NonNewtonian Fluid Mechanics (University of Wales Institute of NonNewtonian Fluid Mechanics, 2022)] Normal Stress Difference and Elasticity (cont.) ? Extrudate Swell (also called “die swell”) Behavior of fluid issuing from orifices. A stream of Newtonian fluid (N, silicone fluid) shows no diameter increase upon emergence from the capillary tube。 the macromolecular fluid (P) continues to be siphoned. [Reproduced from R. B. Bird, R. C. Armstrong and O. Hassager, Dynamics of Polymeric Liquids. Vol I: Fluid Mechanics, 2nd edition, Wiley Interscience (1987), p. 74.] [Retrieved from the video of NonNewtonian Fluid Mechanics (University of Wales Institute of NonNewtonian Fluid Mechanics, 2022)] Normal Stress Difference and Elasticity (cont.) ? Elastic Recoil An aluminum soap solution, made of aluminum dilaurate in decalin and mcresol, is (a) poured from a beaker and (b) cut in midstream. In (c), note that the liquid above the cut springs back to the breaker and only the fluid below the cut falls to the container. [Reproduced from A. S. Lodge, Elastic Liquids, Academic Press, New York (1964), p. 238.] Normal Stress Difference and Elasticity (cont.) A solution of 2% carboxymethylcellulose (CMC 70H) in water is made to flow under a pressure gradient that is turned off just before frame 5. [Reprodeced from A. G. Fredrickson, Principles and Applications of Rheology, 169。 V, ? and ? are the velocity, the density and the viscosity of fluid f lo w/De t?????We?? /Re LV? The Deborah/Weissenberg Number The Deborah/Weissenberg Number (cont.) Streak photograph showing the streamlines for the flow downward through an axisymmetric sudden contraction with contraction ratio to 1 as a function of De. (a) De = 0 for a Newtonian glucose syrup. (be) De = , 1, 3 and 8 respectively for a % polyacrylamide glucose solution. [Reproduced from D. B. Boger and H. Nguyen, Polym. Eng. Sci., 18, 1038 (1978).] Typical viscosity curve of a polyolefin PP homopolymer, melt flow rate (230 ?C/ Kg) of 8 g/10 min a