【正文】 / 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。 Principle: ? Measurement of the Full Pressure Drop at constant Shear rate and different L / D ratio ? Linear extrapolation to L / D = 0 E. B. Bagley, J. Appl. Physics 28 (1957), 624 DDnL PDLDL PDL PPDLP f u l lf u l len tf u l l ??????????? ///Calculation of Entrance Pressure Drops 2. Practical Difficulties with Historical Bagley Method 10 20 30 40 L/D negative Entrance Pressure Drop ! ? ? ? ? ? Problems: ? linear extrapolation can lead to physically impossible results ? Extrapolation shows very large standard deviation Calculation of Entrance Pressure Drops 3. Reasons for the Errors in Extrapolation Reasons: ? at small L/D values nonlinearities occur for all samples ? at the moment there is no theoretical approach ? at high L/Dvalues nonlinearities due to wall slip, pressibility ... (theoretical prediction) 2 4 6 8 10 12 L/D Nonlinearities at small L / D Historical Bagley True curve ? ? ? ? ? ? ? ? ? Kelly, Coates, Dobbie, Fleming, Plastics, Rubber and Composites Processing and Applications1996, , , 313. Datas not true to scale. Calculation of Entrance Pressure Drops 4. Solution: Double capillary system 5 10 15 20 L/D Innovation: ? Measurement no Extrapolation needed! ? Simultaneous measurement of full pressure drop along capillary die and entrance pressure drop on orifice die ? Pshear = Pfull Po ? ? Orifice die ( pin hole with neglectable L/Dratio ) Capillary die with L/D=16 The Rosand Double Capillary System with orifice die Measure the die entrance pressure drop directly L 2R v pentrance pshear Pfull Pfull= Pshear + Pentrance v pentrance left: Capillary die right: Orifice die Rabinowitsch Correction ??? rzRr ?rzd1Rdr ?? ?? g??drdv zdrdrdvrdrdrdvrdrvr2Q zR0 2zR0 202zR0 ??? ?????? ???? Rz rvrzrzwRQ ??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。 D a t a f ro m R o s a n d O L R8010012014016018020022050 70 90 110 130 150 170 190 210 230 250Sh e a r St ra i n R a t e (/ s )Shear Stress (kPa) 8 x 0 . 5 m m1 2 x 0 . 7 5 m m1 6 x 1 m mL i n e o f c o n s t a n tSh e a r St re s sWall Slip Correction No Wall Slip gapp 1/R ? Result: Dependency of wall slip velocity on shear stress (true shear rate) slip shear full Q Q Q ? ? R v 4 slip true app ? g ? g . . 2 slip 3 true 3 app R v 4 R 4 R ? ? ? ? ? g ? ? ? g . . Mooney, M., J. Rheology 2, 210 (1931) Wall Slip Measurement ?Slip ponent of flowrate, Q = ? R2 v [Vs] mm/s [?w] kPa PE Vs = (?w/100) ?w 90 kPa ? PVC Vs = (?w/100) ?Some typical slip velocities ?Many materials only slip above a critical stress, typically MPa Extensional Flow Analysis 4 Extensional Flow Analysis 4 Extensional Flow Analysis 4 Extensional Flow Analysis 4 Extensional Flow Analysis ? 拉伸黏度是在實(shí)際紡絲過程即非穩(wěn)態(tài)拉伸流中的黏度。許多情況下，流場邊界條件存在一個(gè)臨界值。研究這類熔體流動不穩(wěn)定性及壁滑現(xiàn)象是從“否定”意義上討論高分子的流變性質(zhì)，具有重要意義。高分子流動不穩(wěn)定性主要表現(xiàn)為擠出過程中的熔體破裂現(xiàn)象、拉伸過程（纖維紡絲和薄膜拉伸成型）中的拉伸共振現(xiàn)象及輥筒加工過程中的物料斷裂現(xiàn)象等。可以肯定地說，這些現(xiàn)象與高分子液體的非線性粘彈行為，尤其是彈性行為有關(guān)，是高分子液體彈性湍流的表現(xiàn)。 ? 表現(xiàn)為：最初表面粗糙，而后隨剪切速率（或切應(yīng)力）的增大，分別出現(xiàn)波浪型、鯊魚皮型、竹節(jié)型、螺旋型畸變，直至無規(guī)破裂。破裂特征是先呈現(xiàn)粗糙表面，當(dāng)擠出超過臨界剪切速率發(fā)生熔體破裂時(shí)，呈現(xiàn)無規(guī)破裂狀。 ? 一類稱 HDPE（高密度聚乙烯）型。很高時(shí)，出現(xiàn)無規(guī)破裂。 ? 這種分類不夠嚴(yán)格，有些材料的熔體破裂行為不具有這種典型性 ? 流變曲線的差別： ? 屬于 LDPE型的熔體，其流變曲線上可明確標(biāo)出臨界剪切速率或臨界剪切力 位置，曲線在臨界剪切速率之前為光滑曲線，之后出現(xiàn)波動，但基本為一連續(xù)曲線 ? 屬于 HDPE型的熔體，其流變曲線在達(dá)到臨界剪切速率后變得復(fù)雜。 ? 從形變能的觀點(diǎn)看，高分子液體的彈性是有限的，其彈性貯能本領(lǐng)也是有限的。 Elongational viscosity influence Convergence into a flat entry die LDPE HDPE Also important in any convergent or divergent part of a process ? Tordella的流動雙折射實(shí)驗(yàn) ? 對 LDPE型熔體，其應(yīng)力主要集中在口模入口區(qū)，且入口區(qū)的流線呈典型的喇叭型收縮，在口模死角處存在環(huán)流或渦流。但當(dāng)剪切速率 后，入口區(qū)出現(xiàn)強(qiáng)烈的拉伸流，其造成的拉伸形變超過熔體所能承受的彈性形變極限，強(qiáng)烈的應(yīng)力集中效應(yīng)使主流道內(nèi)的流線斷裂，使死角區(qū)的環(huán)流或渦流乘機(jī)進(jìn)入主流道而混入口模。這樣交替輪換，主流道和