【正文】 rzrzwRQ ??g?? ? dw0233 ?? ? )3ddQ(R1ww3w Q?? ???g?)3d l nd l n(4)3dd(4wawaawaw ???? ?gg?gg?gg ??????For nonNewtonian flow profile Rabinowitsch Correction n = d (log ?) d (log g) . Corrected shear flow (polymer melts) If n = , = * gc . 4 Q ? R3 Apparent shear rate (Newtonian material) ga = . polyethylene to polypropylene to PVC to polyamide to . ga . 4 Q ? R3 3n + 1 4n gc = . Optional, but try to keep consistency! Wall Slip correction Wall Slip ? A fundamental assumption in most rheology is velocity at the metal wall = 0 ? Slip is well known to occur in PVC, HDPE and metallocene catalysed polymers ? Difficult to measure can be approximated using capillary rheometry ? Slip is affected by fillers and lubricants Evidence of wall slip U n f i l l e d H D PE a t 2 0 0 176。 short dies) Giving us: Shear stress (at a range or rates) Extensional stress (at a range or rates) Capillary rheometry Long die: shear Short die: extension 3 Shear viscosity ? 完全發(fā)展區(qū)剪切應(yīng)力的計算 ? 管壁處 22 rPrL ??? ???L2Pr???LPR2???3 Shear viscosity ? 不可壓縮性流體剪切速率的計算 )zv( r00rz ???? ?g?? ?2rzp11rv0rz0r????????? )rR(zp41v 220r??? ?zp8Rr d r)rR(zp21drvr2Q04220R0rR0 ????????? ???????30Nw R4Q???g ? ???L 2R 3 Shear viscosity Given quantity: piston speed ? wall shear rate Measured quantity: pressure drop ? wall shear stress Entrance pressure drop Shear pressure drop v Measured pressure drop = + P L BARREL PL Pl Pw ENTRANCE LENGTH FULLY DEVELOPED FLOW REGION 0 Z 0 L ? small ram extruder Measuring Principle Pressure drop through a capillary/slit die N o n Ne w to n ia n flu id rh e o lo g ic a l equ a tio n o f sta te :( p o w e r la w ) ? = K ( a )n ? = K . a n 1n = ? lo g ? / ? lo g aNewtonian fluid shear rate , = 4Q / ? r3 shear stress, ? = ?Pr / 2L shear viscosity, ? = ? / Shear Flow Analysis w he r e : K = co nsiste ncy i nd e x ( P n ) n = po w e r l aw ( n o n N e w t o ni an) i nd e x Q = v o l um e tr ic f l o w r ate m 3 / m i n r = capi l l ar y r adi us ( m ) L = ca pi l l ar y l e ng th ( m ) . ? P = p r e s s ur e d r o p ( P a )g . g . (g) . g . g . Calculation of Entrance Pressure Drops 1. Historical BagleyMethod according to DIN 11443 10 20 30 40 L/D Pges (L/D=0) = Entrance Pressure Drop ? ? ? ? 176。 176。 C 。一旦超越該臨界值，就會發(fā)生從層流到湍流，從平整到波動，從管壁無滑移到有滑移的轉(zhuǎn)變，破壞了事先假定的穩(wěn)定流動條件。熔體在管壁發(fā)生滑移與此類現(xiàn)象密切相關(guān)。 ? 從現(xiàn)象上分，擠出破裂行為可歸為兩類： ? 一類稱 LDPE（低密度聚乙烯）型。熔體破裂的特征是先呈現(xiàn)粗糙表面，而后隨著剪切速率的提高逐步出現(xiàn)有規(guī)則畸變，如竹節(jié)狀、螺旋型畸變等。隨著剪切速率的提高，流變曲線出現(xiàn)大幅度壓力振蕩或剪切速率突變，曲線不連續(xù)，有時使流變測量不能進行 ? 造成熔體破裂現(xiàn)象的機理十分復(fù)雜，肯定地說，它與熔體的非線性粘彈性、與分子鏈在剪切流場中的取向和解取向（構(gòu)象變化及分子鏈松弛的滯后性）、纏結(jié)和解纏結(jié)及外部工藝條件諸因素有關(guān)。當(dāng)剪切速率較低時，流動是穩(wěn)定的，死角處的渦流也是穩(wěn)定的，對擠出物不產(chǎn)生影響。這是兩種形變歷史和攜帶能量完全不同的流體，可以預(yù)見，它們擠出時的彈性松弛行為也完全不同，由此造成口模出口處擠出物的無規(guī)畸變。又因為應(yīng)力集中使熔體貯能大大增加，當(dāng)能量累積到超過熔體與模壁之間的摩擦力所能承受的極限時，將造成熔體沿模壁滑移，熔體突然增速（柱塞上壓力下降），同時釋放出能量。此時應(yīng)力集中效應(yīng)將轉(zhuǎn)到口模入口區(qū)。 ? 1． 3． 1 口模形狀、尺寸的影響 ? 口模的入口角對 LDPE型熔體的擠出破裂行為影響很大。 ? 對于 LDPE型熔體，已知造成熔體破裂現(xiàn)象的根源在于入口區(qū)的流線擾動。擠出速度越小，材料發(fā)生的彈性形變小，且形變得以松弛的時間較長，因此熔體內(nèi)的壓力波動幅度較小。 ? 從材料角度看，平均分子量大的物料，最大松弛時間較長，容易發(fā)生熔體破裂。這一是因為某些軟化劑的增塑作用；二是填料本身無熵彈性，填入后使能夠發(fā)生破裂的熔體比例減少。C Cogswell: Entrance Pressure Drop ? Extensional Viscosity Shear viscosity curve 1 10 100 1000 1 10 100 1000 10000 100000 Corrected shear rate [1/s] Shear viscosity [Pas] sample 1 sample 2 Extensional viscosity curve 10 100 1 10 100 1000 10000 Extensional rate [1/s] Extensional viscosity [kPas] ? Differences only in extension (Structure sensitivity) Benefits of Capillary Rheometry Comparison of Data from Capillary amp。 dies: 50100,000 s1 1mm 216。 C 。 additive investigation Material specification Troubleshooting 11. PVT / Density test 11. PVT / density test 11. PVT / density test results LDPE at 200176。 RH10D RH2100/2200 Measurement Example: DesktopRH2022 RH2022 (Investigation of dental posites to find optimum geometry for pumping and surface effects) Conclusion The plete flow behaviour under processing conditions Rosand Double Capillary System with Orifice Die: ? direct measurement of the entrance pressure drop no extrapolation needed ? calculation of extensional viscosity according Cogswell method ? flow curve up to very high shear end extensional rates (107 s1) ? ability to detect wall slip by Mooney‘s method ? correlation with structural changes during processing ? additional Options for detection of elastic behaviour (DieSwell) Rheological Data for Computational Modelling Aim: describe how mercial modelling software uses rheological data Modelling software (CFD) ? Simulation of melt flow ? Extrusion and injection moulding ? Uses finite element methods divides flow up into very small pieces ? Continuum mechanics ? Principles of conservation of mass, momentum, energy etc Modelling software (CFD) ? Velocity profiles ? Temperature profiles ? Pressure drops ? Stress, shear and extension r