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Secondary atomization

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Abstract

When a drop is subjected to a surrounding dispersed phase that is moving at an initial relative velocity, aerodynamic forces will cause it to deform and fragment. This is referred to as secondary atomization. In this paper, the abundant literature on secondary atomization experimental methods, breakup morphology, breakup times, fragment size and velocity distributions, and modeling efforts is reviewed and discussed. Focus is placed on experimental and numerical results which clarify the physical processes that lead to breakup. From this, a consistent theory is presented which explains the observed behavior. It is concluded that viscous shear plays little role in the breakup of liquid drops in a gaseous environment. Correlations are given which will be useful to the designer, and a number of areas are highlighted where more work is needed.

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Abbreviations

a :

drop acceleration (m/s2)

c :

velocity of sound (m/s)

D 10 :

drop or fragment arithmetic mean diameter (m)

D 30 :

drop or fragment volume mean diameter (m)

D 32 :

drop or fragment Sauter mean diameter (m)

D 43 :

drop or fragment de Brouckere mean diameter (m)

d 0 :

drop initial spherical diameter (m)

d core :

diameter of drop core at end of sheet-thinning breakup (m)

d cro :

drop cross-stream diameter (m)

d str :

drop stream-wise diameter (m)

F D :

aerodynamic drag force (kg m/s2)

F surf :

net surface force (kg m/s2)

F μ :

shear force (kg m/s2)

f 0(D):

fragment number PDF (1/m)

f 3(D):

fragment volume PDF (1/m)

K :

power-law fluid consistency index (kg/m s(2−n))

k :

wave number; 2π/λ (1/m)

MMD :

drop or fragment mass median diameter (m)

q :

net electrostatic charge (C)

q Ra :

Rayleigh charge limit (C)

t :

time (s)

U 0 :

initial relative velocity between drop and ambient fluid in main flow direction (m/s)

U core :

velocity of drop core relative to ambient fluid (m/s)

\( \bar{U}_{\text{f}} \) :

mean relative velocity of fragments in main flow direction (m/s)

V 0 :

initial relative velocity between drop and ambient fluid perpendicular to main flow direction (m/s)

\( \bar{V}_{\text{f}} \) :

mean relative velocity of fragments in cross-stream direction (m/s)

δ :

boundary layer thickness (m)

ε a :

electrical permittivity of ambient (C2/N m2)

λ :

wavelength (m)

λ (1) :

elastic fluid relaxation time (s)

μa :

ambient viscosity (kg/m s)

μ d :

drop viscosity (kg/m s)

μ eff :

power-law effective viscosity (kg/m s)

μ sol :

solvent shear viscosity (kg/m s)

ρ a :

ambient density (kg/m3)

ρ d :

drop density (kg/m3)

σ :

surface tension (kg/s2)

C D :

instantaneous coefficient of drag based on drop cross-stream diameter

\( \bar{C}_{\text{D}} \) :

average coefficient of drag based on initial spherical diameter

C D-sphere :

coefficient of drag of a solid sphere at a given Reynolds number

Eo cr :

Eötvös number at end of sheet-thinning breakup; \( {{a\left| {\rho_{\rm d} - \rho_{\rm a} } \right|d_{\text{core}}^{2} } \mathord{\left/ {\vphantom {{a\left| {\rho_{\rm d} - \rho_{\rm a} } \right|d_{\text{core}}^{2} } \sigma }} \right. \kern-\nulldelimiterspace} \sigma } \)

La :

Laplace number; La = Oh −2

Ma :

Mach number

N :

viscosity ratio; μ d/μ a

n :

power-law fluid flow behavior index

Oh :

Ohnesorge number; \( {{\mu_{\rm d} } \mathord{\left/ {\vphantom {{\mu_{\rm d} } {\sqrt {\rho_{\rm d} d_{0} \sigma } }}} \right. \kern-\nulldelimiterspace} {\sqrt {\rho_{\rm d} d_{0} \sigma } }} \)

Re :

gas-phase Reynolds number; \( {{\rho_{\rm a} U_{0} d_{0} } \mathord{\left/ {\vphantom {{\rho_{\rm a} U_{0} d_{0} } {\mu_{\rm a} }}} \right. \kern-\nulldelimiterspace} {\mu_{\rm a} }} \)

Re NN :

Reynolds number for a power-law fluid; ρU 2−n0 d n0 /K

T :

dimensionless time; \( tU_{0} \varepsilon^{{{{ - 1} \mathord{\left/ {\vphantom {{ - 1} 2}} \right. \kern-\nulldelimiterspace} 2}}} d_{0}^{ - 1} \)

T ini :

breakup initiation time

T tot :

total breakup time

We :

Weber number; \( {{\rho_{\rm a} U_{0}^{2} d_{0} } \mathord{\left/ {\vphantom {{\rho_{\rm a} U_{0}^{2} d_{0} } \sigma }} \right. \kern-\nulldelimiterspace} \sigma } \)

We c :

critical Weber number

We cOh→0 :

critical Weber number at low Ohnesorge number

We core :

Weber number of drop core at end of sheet-thinning breakup

We e− :

electrostatic Weber number; \( {{\rho_{\rm a} U_{0} d_{0}^{2} } \mathord{\left/ {\vphantom {{\rho_{\rm a} U_{0} d_{0}^{2} } {\left( {\sigma - {{q^{2} } \mathord{\left/ {\vphantom {{q^{2} } {8\pi^{2} \varepsilon_{\rm a} d_{0}^{3} }}} \right. \kern-\nulldelimiterspace} {8\pi^{2} \varepsilon_{\rm a} d_{0}^{3} }}} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {\sigma - {{q^{2} } \mathord{\left/ {\vphantom {{q^{2} } {8\pi^{2} \varepsilon_{\rm a} d_{0}^{3} }}} \right. \kern-\nulldelimiterspace} {8\pi^{2} \varepsilon_{\rm a} d_{0}^{3} }}} \right)}} \)

Wi :

Weissenberg number; \( {{\lambda^{(1)} U_{0} } \mathord{\left/ {\vphantom {{\lambda^{(1)} U_{0} } {d_{0} }}} \right. \kern-\nulldelimiterspace} {d_{0} }} \)

y :

non-dimensional displacement of drop equator; 1 − (d 0/d cro)2

ε :

density ratio; ρ d/ρ a

ω :

exponential growth factor

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Acknowledgments

The authors would like to thank Prof. Stephen Heister of Purdue University, Dr. Sachin Khosla of the CFD Research Corporation, Prof. Rolf Reitz of the University of Wisconsin, and Prof. David Schmidt of the University of Massachusetts-Amherst for their stimulating discussions and guidance during the preparation of this review.

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  1. Maurice J. Zucrow Laboratories, School of Mechanical Engineering, Purdue University, West Lafayette, IN, 47907-2014, USA

    D. R. Guildenbecher, C. López-Rivera & P. E. Sojka

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  1. D. R. Guildenbecher
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Correspondence to D. R. Guildenbecher.

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This material is based upon work supported under a National Science Foundation Graduate Research Fellowship.

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Guildenbecher, D.R., López-Rivera, C. & Sojka, P.E. Secondary atomization. Exp Fluids 46, 371–402 (2009). https://doi.org/10.1007/s00348-008-0593-2

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