,, Taylor [ 9, 10] Taylor Einstein,,,, ( 1, L B, ), Lamb Stokes, Taylor,, D, ( = d/ ) (= d / m ) ( = m g ), d m, g, d, ( ) ( ), crit < crit, Tay

Size: px

Start display at page:

Download ",, Taylor [ 9, 10] Taylor Einstein,,,, ( 1, L B, ), Lamb Stokes, Taylor,, D, ( = d/ ) (= d / m ) ( = m g ), d m, g, d, ( ) ( ), crit < crit, Tay"

瑾颉昌
5 years ago
Views:

1 28 3 Vol128 No ADVANCES IN MECHAN ICS Aug125, , , ( ) ( ),, ; ( ),,,,,,, 1 ( Polymer Blend),,,,, [15, ],,,,, ( -,,, ),,,, [68, ],, :, : , :

2 ,, Taylor [ 9, 10] Taylor Einstein,,,, ( 1, L B, ), Lamb Stokes, Taylor,, D, ( = d/ ) (= d / m ) ( = m g ), d m, g, d, ( ) ( ), crit < crit, Taylor D Ε D crit ( D crit = 015 ) 1 Taylor : () (), D D = L - B L + B D = 5 4, = , = / 4, (0) (1) = / 2, (µ 1), 212 Cox [ 11] Taylor, Cox Taylor,, D = (2) (19 / 40)

3 2 µ 1,= O (1) = O (1) = tg (3),µ 1, Cox Taylor Taylor Cox, 2 D [ 12, 13] 213 Choi & Schowalter Choi & Schowalter, Cox,, : (1) ν 1,= O (1) D = (5+ 2) 4 (+ 1) g (4) = 1 ( ) (2+ 3) y 5 (19+ 16) (+ 1) 4 (+ 1) (2+ 3) g a(5) (2) ν 1,µ 1 5 (19+ 16) 1 5 (5+ 2) D = 1 + g (6) 4 (+ 1) (19 / 40) (+ 1) = = tg (7) 40 (3) = O (1),µ 1 a ] D = g = tg (9) 40 g g0, Choi & Schowalter Taylor Cox 3 4 Choi & Schowalter Cox Torza [13 ], Choi & Schowalter 404 (8)

4 , Cox, (= 316) 3 D (= 0108 ) 4 D (= 316) Cox Choi & Schowalter D, Taylor,, ( ),, Taylor, Cox Choi &Showalter [ 11,14,15] 214 ( Small Deformation Theory) Taylor,, Cox [11 ], Barth s - Biesel & Acrivos [14 ] Rallison [15 ] Taylor, Rallison, r = a{ 1 + r 3 F : (1/ r) + 2 [ - 6/ 5 F : F + r 5 H : (1/ r) ] + O ( 2 ) } (10) r, F H Bentley & 405

5 Leal [16 ], > 0105 D (5), 5 D (= 01118) 215 (Large Deformation Theory) [ 1721] < 0101, Taylor, Buckmaster [17,18 ] Acrivos & Lo [19 ] Acrivos & Lo ( u x = Gx, u r = - 1/ 2 G r, u= 0),, x, r = G L R ( x), G L R ( x) = 1 2 1/ 2 / G L 2 r5 (1 - x 2 ) (11) 6 1/ 6, 1/ 6 = 1 5 1/ 2 1/ (12) = L 1/ 3 / a (11) 6, = / 6 = 01296,, 1/ 6 = Hinch & 406 crit

6 Acrivos [20 ] crit, crit 1/ 6 = 01290,, Bentley & Leal [16 ] crit 1/ 6 = 01290/ 1/ 2 ( ) crit 216 Rayleigh & Tomotika [ 2227] Taylor,,, Rayleigh Tomotika, q q = (, ) / 2 m R 0 (13), (, ), R 0 (7) 7 A R 0 R = ( R A 2 / 2) 1/ 2 m ( m, ), 0101 ΦΦ 10 ( m, ) = exp [ log (log ) (log ) (log ) 4 ] A t (14) A = A 0 exp [ qt ] (15) A 0 = (21 k B T) / (8 3/ 2 ) 1/ 2, k B, T A = R g 0181 R 0, t b = (1/ q) ln[0181 R 0 / A 0 ] t 3 b t b g /= 2[ln (0181 R 0 / A 0 ) ]/ ( m, ) t 3 b crit,> crit, [2426 t > t b ] t b, t 3 b / crit, t 3 b = ( (16) / crit ) (17) Taylor Tomotika,,, / crit < 011, ; 011 < / crit < 1, ; 1 < / < 4, ; / > 4, crit [27 ] crit 407

7 ,,,,, 217 Vanoene [ 28], Vanoene [28 ], Vanoene, Cox,,,, Vanoene,, 12 = 12 + ( d/ 12) [ ( ) d - ( ) c ] (18) 0 12, ( ) i ( i = d) ( i = c) ( ) d > ( ) c 12 > 0 12,,, ( ) d < ( ) c 12 < 0 12, Vanoene Elmendorp &Maalcke [29 ] (8) Vanoene, v 12, Elmendorp Maalcke [29 ] Levitt [30 ] Vanoene v 12 Vanoene 218 Chin & Han [ 31] 8 1, 2 3, 4 Vanoene 5, 6 Cox Chin & Han ( Perturbation Technique) r = (19+ 16) P (cos ) (19+ 16) (+ 1) 2 P 4 (cos ) + + eg E 126 (+ 1) 0 2 [ Z 1 P 2 (cos ) + Z 2 P 4 (cos ) ] (19) P n ( cos ) n Legendre, Z 1 Z 2, e, g E 408

8 , 0 9 (19) D, < 011, D, > 011, D Chin & Han 9 [3235 ] 219 Elmendorp [29 ], [32 ],, g d = 2 ( a2 i - b 2 i) 8 T c ( b 2 icos 2 + a 2 isin 2 ) 2 17( a 4 i + b 4 i) - 2a 2 ib 2 i + 4( a 4 i - b 4 i) [cos(6 ) - 5cos(2 ) ] - ( a 2 i - b 2 i) 2 cos(8 ) (20) T c = 4(+ 1) [ g c (+ 2) ], g c,, a i b i, (19) g d = b g c (21) b, g c, b : (20), ( ), ( R [811,14,15, ), ], (= 1), (= 1),, d g in, c g c = d g in = 1 + b (22) c g c (22), ( ν 1 ), 12, 409

9 ;, 12,, ( µ 1 ), 12,, 12,, [30 ] 2110 ( Couette), ( x ) ( y ) ( xoy ), x y, z,, z y, Levitt Macosko [30 ], (Couette), xoz Levitt Macosko z :,, z, < 1, < 2, ( 22 ) ( 33 ) (10), d - P d R 2 R 3 = - P m + 11 m (23) 22 d - P d R 1 g = - P m + 22 m (24) R 3 33 d - P d = - P m + 33 m (25) R 1 R 2 z, : = ( 22 d - R crit 2 d 33) - ( 22 m - 33) m = N 2 d - N 2 m (26) N 2 = 4 N 1 / 7,, N 1 = 2 G, G, R crit 2 = 4 7 ( G m - G d ) (27) (27) 11, ( R 3 max / R 0, R 0 ) 410

10 11 v/ R crit 2 Levitt Macosko,,,,, ;,,,,,,,, :,,, 013 < < 115,, Ε 318,,, 3 (1) (7), Taylor Rayleigh & Tomotika, Tay2 lor,, Taylor,, : (1) :,, ; (2) :,,, ; [36 (3) : ], 015 %, 411

11 015 %, ; (4) :,,,,,,,, [5 ], 1 J A, L H,, :, C D, :, Z, C G,, :, :, , 5 : Rumscheidt F D, Mason S G Particle motions in sheared suspensions, xii : deformation and burst of fluid drops in shear and hyperbilic flow J Colloid Sci, 1961, 16 : Han C D Multi - Phase Flow in Polymer Processing New York : Academic Press, Utracki L A, Shi Z H Development of polymer blend morphology during compounding in a twin - screw extruder Part I : droplet dispersion and coalescence a review Polym Eng Sci, 1992, 32 (24) : Taylor G I The viscosity of a fluid containing small drops of another fluid Proc Ror Soc, 1932, A138 : Taylor G I The formation emulsions in definable fields of flow Proc Ror Soc, 1934, A146 : Cox R G The Deformation of a drop in a general time - dependent fluid flow J Fluid Mech, 1969, 37 (3) : Choi S J, Schowalter W R Rheological properties of nondilute suspensions of deformable particles Phys Fluids, 1975, 18 : Torza S, Cox R G, Mason S G Particle motions in sheared suspensions : transient and steady deformation and burst of liquid drops J Colloid Interf ace Sci, 1972, 38 : Barths s - Biesel D, Acrivos A Deformation and burst of a liquid droplet freely suspended in linear shear field J Fluid Mech, 1973, 61 : Rallison J M A Note on the time - depandent deformation of a viscous drop which is almost sphecircal J Fluid Mech, 1980, 98 : Bentley B J, Leal L G An Experimental investigation of drop deformation and breakup in steady, two - dimension2 al linear flow J Fluid Mech, 1986, 167 : Buckmaster B J Pointed bubbles in slow viscous flow J Fluid Mech, 1972, 55 : Buckmaster B J The burst of pointed drops in slow viscous flow J A ppl Mech, 1973, 40 : Acrivos A, Lo T S Deformation and breakup of a single slender drop in an extensional flow J Fluid Mech, 1978, 86 : Hinch E J, Acrivos A Steady of long slender droplets in two - dimensional straining motion J Fluid Mech, 1979, 91 : Hinch E J, Acrivos A Long slender drops in a shear flow J Fluid Mech, 1980, 98 : Tomotika S On the instability of a cylindrical thread of a viscous liquid surrounded by another viscous fluid Proc R Soc, 1935, A150 : Tomotika S Breaking up of a drop of viscous liquid immersed in another viscous fluid which is extending at a uni2 form rate Proc RSoc, 1936, A153 : Grace H P Dispersion phenommna in high viscosity immiscible fluid systems and application of static mixers as dis2 persion devices in such systems Chem Eng Com m un, 1982, 14 : Elemans P H M, Janssen J M H, Meijer H E M The breaking thread method : the measurement of interfacial ten2 sion in poiymer systems J Rheol, 1990, 34 : Janssen J M H Dynamics of liquid - liquid mixing PhD Thesis The Netherlands : Eindhoven University of Tech2 nology, Huneault M A, Shi Z H, Utracki L A Development of polymer blend morphology during compounding in a twin - 412

12 screw extruder Part IV : a new computational model with coalescence Polym Eng Sci, 1995, 35 : Vanoene H Modes of dispersion of viscoelastic fluids in flow J Coll Interf Sci, 1972, 40 : Elmendorp J J, Maalcke R J A study on polymer blending microrheology : Part I Polym Eng Sci, 1985, 25 (16) : Levitt L, Macosko C W, Pearson S D Influence of normal stress difference onpolymer drop deformation Polym Eng Sci, 1996, 36 (12) : Chin H B, Han C D Studies on droplet Deformation and Breakup J Rheol, 1979, 23 : ,, :,,, :, , - :,,, :, Zhou Chixin, Zhang Hongbin Modeling microstructure development of polymer blends in flow field In : Akiyama S, Takemura K, Qi Z N eds Proceeding of Japan - China Seminer on Advances Engineering Plastic, Polymer Al2 loys and Composites Oct 89, 1996 Tokyo, Japan, , 36 Elmendorp J J, Van der Vegt A K A study on polymer microrheology : Part IV The influence of coalescence in blend morphology origination Polym Eng Sci, 1986, 26 : THEORETICAL MODELS OF D ROPL ET D EFORMATION FOR POLYMER BL END SYSTEMS IN FLOW FIELDS Zhang Hongbin Zhou Chixing Polymeric Materials Research Institute, Shanghai Jiao Tong University, Shanghai Abstract For two - phase polymer blending systems, the development of theoretical models on the deformation of Newtonian (or viscoelastical) droplet suspended in anot her Newtonian ( viscoelasti2 cal) medium is discussed The dominating factors which influence t he droplet deformation include composition, viscosity and elasticity ratios, dynamic interfacial tension, critical capillary number, and flow field type and its intensity For the systems in which both of the two phases are Newtonian liquids, the theoretical predictions are consistent with the experiments, whereas for the systems in which the two phases (or one of the two phases) are viscoelastical liquids, the deformation studies become very complicated due to the influence of elasticity, and the theoretical model should be im2 proved In order to establish a more pertinent t heoretical model of droplet deformation, it is essential to st udy t he interface layer, microscopic molecular deformation, interaction between droplet s and between droplet and continuous p hase media and it s effect on droplet deformation Keywords Newtonian liquid, viscoelatical liquid, polymer blend, deformation, theoretical model, flow field 413

11 : 1345,,. Feuillebois [6]. Richard Mochel [7]. Tabakova [8],.,..,. Hindmarsh [9],,,,,. Wang [10],, (80 µm),.,. Isao [11]. Ismail Salinas [12],. Kaw

11 : 1345,,. Feuillebois [6]. Richard Mochel [7]. Tabakova [8],.,..,. Hindmarsh [9],,,,,. Wang [10],, (80 µm),.,. Isao [11]. Ismail Salinas [12],. Kaw 1344 E 2006, 36(11): 1344~1354 * ** (, 100022).,.,.,.,....,,,,,,,.,.,.,,,.,. Hayashi [1] :., [2] [3~5],,.,,.,. : 2006-03-22; : 2006-06-17 * ( : 50376001) ( : G2005CB724201) **, E-mail: liuzhl@bjut.edu.cn