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Aero-breakup of elastic liquids as a competition of aerodynamics and elasticity

Aero-breakup of elastic liquids as a competition of aerodynamics and elasticity. Constitutive dimensionless numbers:. Elasticity number E =  g v 2 / G. Deborah number De =( g / l )  v / d. Breakup Criterion: f ( E, De )= ?. Formation of high strain rates in the liquids.

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Aero-breakup of elastic liquids as a competition of aerodynamics and elasticity

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  1. Aero-breakup of elastic liquids as a competition of aerodynamics and elasticity Constitutive dimensionless numbers: • Elasticity number E=gv2/G • Deborah number De=(g/l)v/d Breakup Criterion: f(E, De)=?

  2. Formation of high strain rates in the liquids • Water gun accelerates liquid up to velocity of few hundreds meters per second • Liquid jet impacts a small disk- or cone-like target, forming liquid sheet

  3. Formation of high strain rates in the liquids 1 cm ____ Jet: v0=18 m/s ro=1 mm • In the liquid sheet the liquid element is subjected to extension =r/ro~100 during few milliseconds • Elongational strain rate is of order of v0/r0~104 s-1 2r(t)

  4. Creation of high strain rates in the liquids 1 cm ____ Jet: v0=18 m/s ro=1 mm • In the liquid sheet the liquid element is subjected to extension =r/ro~100 during few milliseconds • Elongational strain rate is of order of v0/r0~104 s-1 r(t)

  5. Dynamics of the liquid sheet for elastic liquids • Equation of motion: d2r/dt2=-/r • Elastic liquid:=G(r/r0)2 • Rim trajectory: d2r/dt2=-Gr/r02 • Initial conditions: t=0, r=0, dr/dt=v0: • Solution: r=v0(G/r02)-1/2sin((G/r02)1/2t) 2r(t)

  6. Best fitting for PEO M=4m, c=10k ppm

  7. Best fitting for PEO M=4m, c=40k ppm

  8. Best fitting for PEO M=4m, c=100k ppm

  9. Elastic modulus as function of concentration at high strain rate

  10. The bell shapes in the vacuum shall be used for estimation of the liquid relaxation time 3.8 %PSBMA-in-TBP d0=2 mm

  11. The bell shapes in the vacuum shall be used for estimation of the liquid relaxation time PEO M=4m c=10k ppm d0=2 mm Used to match PSBMA

  12. The effect of air resistance PEO M=4m c=10k ppm d0=2 mm

  13. Conclusions • Modeling of the aero-breakup of the viscoelastic liquids requires knowledge of the liquid rheological parameters • Liquid rheological parameters strongly depend on strain rate of the liquid • Liquid sheets and liquid bells can be used as sources of high strain rate • Rheological parameters can be estimated by means of best fitting analysis of data of high speed video-monitoring of sheet and bell liquid flows

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