NONWOVENS: MELT- AND SOLUTION BLOWING. A.L. Yarin Department of Mechanical Eng. UIC, Chicago

Transcription

1 NONWOVENS: MELT- AND SOLUTION BLOWING A.L. Yarin Department of Mechanical Eng. UIC, Chicago

2 Acknowledgement The Nonwovens Cooperative Research Center (NCRC), USA Collaboration with: PhD student S. Sinha-Ray NC State: Prof. B. Pourdeyhimi

3 Outline 1. Meltblowing. Experimental: Solid flexible threadline in parallel high speed gas flow 3. Turbulence, bending perturbations, their propagation and flapping 4. Theoretical: Solid flexible threadline in parallel high speed gas flow 5. Comparison between theory and experiment 6. Theoretical: Polymer viscoelastic liquid jets in parallel high speed gas flow 7. Fiber-size distribution 8. Fiber orientation distribution in laydown 9. Spatial mass distribution in laydown 10. Experiments with solution blowing and co-blowing of core-shell and hollow fibers

4 My book published in 1993 by Longman (U.K.) and Wiley&Sons (New York) encompasses all relevant equations and a number of relevant solutions for free liquid jets moving in air

5 General quasi-one-dimensional equations of dynamics of free liquid jets moving in air 1. Continuity-Mass Balance- Equation f fw 0 t s All terms in Eq. (1) are of the order of a. Momentum Balance Equation fv fwv 1 PQ fg + t s s All terms in Eq. () except the shearing force Q are of the order of a ; Q is of the order of a 4 q total

6 General quasi-one-dimensional equations of dynamics of free liquid jets moving in air 3. The Moment-of-Momentum Balance- Equation K t Uj U j j U j j WK j V 1M 1 Q- kj g+ m s s j W k All terms in Eq. (3) are of the order of a 4 Equations (1)-(3) are supplemented with the geometric, kinematic, and material relations. The material relations for P and M follow from the rheological constitutive equation projected on the quasi-1d kinematics

7 Main results for highly viscous and viscoelastic jets rapidly moving in air: flame throwers The linear stability analysis: small 3D perturbations grow with the rate: 4 3 au a0 a0 a0 where the dimensionless wavenumber a / The bending instability sets in when: 0 U U / a * 0 0 a 0

8 Main results for highly viscous and viscoelastic jets rapidly moving in air: flame throwers The bending perturbations grow much faster than the capillary perturbations for highly viscous liquids when: a U 0 a 0 1 Linear spectrum:

9 Nonlinear-numerical-results for D bending Newtonian jet

10 Nonlinear-numerical-results for D bending Newtonian jet Viscoelastic jet

11 Meltblowing Experimental: threadline blowing setup to probe turbulence S. Sinha-Ray, A.L. Yarin, B. Pourdeyhimi. J. Appl. Phys. 108, (010)

12 Air velocity at the nozzle exit Chocking at pressure ratio of 47.91

13 Experimental: threadline configurations at different time moments ARROWS DENOTE THE FLAPPING LENGTH

14 Threadline envelope: nd method to define flapping length

15 Measured threadline oscillations

16 FFT: Spectrum of the threadline oscillations

17 Fourier reconstruction of the threadline oscillations with high frequency truncation above 167 Hz

18 Autocorrelation function: chaotic nature of threadline oscillations

19 Turbulence, bending perturbations, their propagation and flapping 3 Large eddy frequency : U / L 10 Hz 0 1/ Taylor microscale : 1.3Re x d cm 5 6 Microscale frequency : U / Hz 0 Threadline oscillation frequency :10 10 Hz Multiple impacts of large eddies : ' 1/ A [ v t] ' ' ' ' ' v u v uv 1 ( u/ y) ' v turbulent eddy viscosity! t

20 Turbulence, bending perturbations, their propagation and flapping Therefore, 1/ A ( t) t In axisymmetric turbulent gas jets : 0.015U d const t 0 0 Time t is restricted by bending perturbation propagation over the threadline : t L/ P/(S ) threadline Threadline tension : P q L, which is imposed by air drag : U a 0 0 q 0.65a U 0 g 0 g 0.81

21 Turbulence, bending perturbations, their propagation and flapping For U 30 m / s, d 0.05 cm in air : t cm / s, t s 1 Therefore, t 39Hz a remarkable agreement with the data! 1/ A ( t) 0.94 cm a reasonable t agreement with the data!

22 Turbulence, bending perturbations, their propagation and flapping The shape of the threadline envelope in the case of distributed impacts of turbulent pulsations without distributed lift force is predicted as : 1/ /4 Ud d dl 0 A(x) 0.16 L (1 x) g g i.e. A(x) 1 (1 x) 1/4 1/4

23 Turbulence vs. distributed aerodynamic lift force

24 Distributed drag, lift and random forces

25 Straight unperturbed sewing threadline in high speed air flow The unperturbed momentum balance dp q 0, P xx a 0 dx The longitudinal aerodynamic drag force 0.81 U a 0 0 q 0.65a U 0 g 0 g Integrating the momentum balance, we obtain q(lx) xx a 0

26 Perturbed threadline in high speed air flow The lateral bending force q U a n g 0 0 x The linearized lateral momentum balance Vn a kpq 0 n t The lateral velocity and thread curvature read V, k n t x

27 Perturbed threadline in high speed air flow Then, the thread configuration is governed by U (x) g 0 xx 0 (1) t x If q L /( a ) U, then Eq.(1) is xx 0 0 g 0 hyperbolic at 0 x x, and elliptic at x x L. * * The transition cross section is found from q(lx) U x g 0 * a 0 The threadline is clamped and perturbed at x 0 H exp(it), / x 0 x0 0 x0

28 Perturbed threadline in high speed air flow Solution in the hyperbolic part is (x, t) exp(it) cos[ I(x)] where 0 1/ ql U / g 0 a a 0 0 I(x) 1/ q q(lx) U / g 0 a 0 Solution in the elliptic part is cosh J(x) cos I(x ) * (x, t) exp(it) 0 isinh J(x) sin I(x ) * where J(x) a q x 0 q a 0 ql/( a) U 0 g 0 1/

29 Flapping of solid flexible threadline

30 Theory vs. experiments for threadline

31 Theory vs. experiments for threadline

32 Polymeric liquid jet in high speed air flow The quasi one dimensional continuity and momentum balance equations for a straight jet dfv 0, f a a V a 0 V 0 dx dfv d f xx dx where dx q 0.81 (U V )a g g g g q 0.65 a (U V ) and the stress is foundfrom xx xx yy

33 Polymeric liquid jet in high speed air flow The upper convected Maxwell model of viscoelasticity d dv dv xx d dv dv yy which are solved numerically simultaneously xx V xx dx dx dx yy V yy dx dx dx with the transformed momentum balance. The following dimensonless groups are used L V a V R,, Re, De a L 0 g g R g E, M De ReM

34 Polymeric liquid jet in high speed air flow The dimensionless equations for a straight polymeric jet solved numerically dv E( )/(DeV ) q xx yy dx 1E( 3)/V xx yy d 1 dv dv xx xx xx dx V dx dx De dyy 1 dv dv yy yy dx V dx dx De The boundary conditions are x 0: V 1,, 0 xx xx 0 yy

35 Unperturbed polymer jet in melt blowing: velocity and radius distributions

36 Unperturbed polymer jet in melt blowing: longitudinal deviatoric stress distribution

37 Unperturbed polymer jet in melt blowing: lateral deviatoric stress distribution

38 Unperturbed polymer jet in melt blowing: K(x) distribution

39 Bending perturbations of polymeric liquid jet in high speed air flow The linearized lateral momentum balance reads (dimensional) : (U V ) g g xx V V 0 t xt x and normalized : V V R(U V ) E 0 g xx t xt x All coefficients depend only on the unperturbed solution!!!

40 Bending perturbations of polymeric liquid jet in high speed air flow Solution in the hyperbolic part : exp[ ii (x)] (x, t) exp(i t) where exp[ ii (x)] x I(x) 1 0 V (x) E (x) R[U (x) V (x)] xx g x I(x) dx dx 0 V (x) E (x) R[U (x) V (x)] xx g di / dx di / dx 1 x 0

41 Bending perturbations of polymeric liquid jet in high speed air flow Solution in the elliptic part : H0 (x,t) exp{i [t J (x)]} 1 1 exp[ ii (x )]exp[ J (x)] 1 * exp[ ii (x )]exp[ J (x)] * where V(x) J(x) dx V (x) R[U (x) V (x)] E (x) x 1 x * g xx x R[U (x) V (x)] E (x) g xx x * V g xx J(x) 0 U(x) U(0) g g x.4d 0 dx (x) R[U (x) V (x)] E (x) The velocity distribution in turbulent gas jet is.4d

42 Bending perturbations of polymeric liquid jet in melt blowing

43 Meltblowing: Nonlinear theory Nonlinear model for predicting large perturbations on polymeric viscoelastic jets. Isothermal polymer and gas jets-d bending of 1 jet Basic vectorial equations Scalar projections of the momentum balance equation in D Numerical results Non-isothermal polymer and gas jets-d bending of 1 jet Basic vectorial equations Scalar projections of the momentum balance equation in D Numerical results 3D results: single and multiple jets A.L. Yarin, S. Sinha-Ray, B. Pourdeyhimi. J. Appl. Phys. 108, (010).

44 Nonlinear Model for Isothermal Polymer and Gas Jets

45 Basic equations: Momentless theory f fw 0 t s Continuity Equation fv fwv 1 P fg + t s s q total Momentum Equation Taking s to be a Lagrangian parameter of liquid elements in the jet, W=0, which gives a a The integral of the continuity equation

46 Relation of the coordinate system associated with the jet axis and the laboratory coordinate system in D cases R=i(s, t) j(s, t) Stretching ratio 1/,s,s Curvature of the jet axis k,ss s,ss,s 3/,s,s Gas jet n 1 /,s,s 1/ Polymer jet n / 1 /,s,s,s,s 1/

47 Scalar projections of the momentum balance equation in D V q 1 Vn 1 P Vn kv g t s f s f total, V q n 1 Vn Pk V kv gn t s f f total,n q nq q total total,n total, / sign / 1 /,s,ss,s,ss,s,s,s,s,s gugn f a 5/,s,s,s,s 0.81 a Ug V agug V 0.65 g

48 The rheological constitutive viscoelastic model. The mean flow field in the turbulent gas jet Rheological Constitutive Equation :Upper Convected Maxwell Model 1 1 t t t The mean flow field in the turbulent gas jet U (, ) U (, ) g g0 4.8 / 1 (, ), (, ) 1 /8 4.8 / / L/a 0, where a 0 is the nozzle radius and L is the distance between the nozzle and deposition screen

49 Time, coordinates and functions t s,h, Dimensionless groups Rendered dimensionless by the scales L/U g0 L k L -1 U g0 /L U g0 U g0, U g,v,v n a a 0 q total, g U g0 a 0 t Re J LU g g0 U g0 Fr gl a U Rea De U L 1/ 0 g0 g0 g

50 Dimensionless equations for numerical implementation 1 total, J t Re s Fr f q,s /,s sign,s /,s,s,s n 1 (, ) J (, ) J t Re s Fr a 1 / 1/ De,and is found from : t De where (1) () (3) and 0.81 a qtotal, a (, ) V 0.65 Re a (, ) V

51 Nature of the equations 1 total, J t Re s Fr f q,s /,s sign,s /,s,s,s n 1 (, ) J (, ) J t Re s Fr a 1 / (1) () Both the equations are basically wave equations. While (1) is for the elastic sound (compression/stretching) wave propagation, () is nothing but bending wave propagation.

52 Boundary Conditions: 1) ss origin Boundary and initial conditions 0, exp(it) ss origin 0 where 1/ 1/ 1/ / Re / 0 0 L U g0 ),s s 1, free end,s s 0 free end The initial condition for the longitudinal stress in the polymer jet: birth 1/ De / t t 0 0

53 Numerical results for D: the isothermal case Velocity flow field in gas jet Snapshots of configurations of polymer jet axis

54 Numerical results in D: the isothermal case (continued)

55 Self-entanglement: Can lead to roping and fly The evolution points at possible self-intersection in meltblowing, even in the case of a single jet considered here SEM image of solution blown PAN fiber mat obtained from single jet showing existence of roping

56 Nonlinear Model for Non-isothermal Polymer and Gas Jets

57 Thermal variation of the rheological parameters U 1 1 T 0 U 1 1 0exp, 0 exp R T T0 T R T T0 where T 0 is the melt and gas jet temperature at the origin, µ 0 and θ 0 are the corresponding values of the viscosity and relaxation time, U is the activation energy of viscous flow and R is the absolute gas constant.

58 T t The additional and changed dimensionless equations; D, non-isothermal case JC Nu T T Re Pr a g 0 g Thermal Balance Equation T T t Re Pr De T De T(, ) T Nu JC g 1 Texp UA 1 a g Prt 1/ 1 Tg / 1 /8 g g Pr where 0 go T/De /, 0 U U 1/3 1/3 De 0, UA, Nu Re L RT a Prg 0 t Rheological Constitutive Equation Mean Temperature Field in the Gas Jet

59 Numerical results for the D nonisothermal case The mean temperature field in the gas jet Snapshots of the axis configurations of polymer jet for the nonisothermal case

60 Numerical results for the D nonisothermal case Snapshots of the axis configurations of the polymer jet in the isothermal case Snapshots of the axis configurations of the polymer jet for the nonisothermal case

61 Numerical results (continued) Following material elements in the polymer jet in the isothermal case Following material elements in the polymer jet in the nonisothermal case

62 The initial section of the jet-no bending

63 3D isothermal results: single jet Three snapshots of the polymer jet axis in the isothermal three-dimensional blowing at the dimensional time moments t=15, 30 and 45

64 9 jets meltblown onto a moving screen-the beginning of deposition

65 9 jets meltblown onto a moving screen-a later moment

66 6 jets meltblown onto a moving screen

67 6 jets meltblown onto a moving screen

68 6 jets meltblown onto a moving screen: a higher screen velocity

69 6 jets meltblown onto a moving screen: a higher screen velocity

70 6 jets meltblown onto a moving screen: comparison with experiment

71 6 jets meltblown onto a moving screen: comparison with experiment

72 6 jets meltblown onto a moving screen

73 6 jets meltblown onto a moving screen

74 Experimental: solution blowing and coblowing setups

75 Solution-blown polymer jet: Vigorous bending and flapping

76 Solution-blown and co-blown nanofibers and nanotubes Monolithic PAN nanofibers

77 Solution-blown and co-blown nanofibers and nanotubes Optical image of PMMA-PAN core-shell co-blown fibers PMMA-PAN carbonized: Hollow carbon nanotubes

78 Solution-blown monolithic nanofibers

79 Solution-blown core-shell nanofibers

80 Close Relatives Sea snakes, electrospun and meltblown jets, and flame thrower napalm jets extract energy from the surrounding medium via bending