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A new method to measure homogeneous nucleation rates in shock tubes

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Abstract

The centered expansion wave of a shock tube is utilized to expand and supersaturate a condensable vapor in small concentration in an inert carrier gas. The supersaturated state, located at the rear of the expansion wave, is preserved for a controlled period and then terminated by a recompressing shock wave. During the period of supersaturation, condensation nuclei are formed homogeneously. The nucleation rate is measured as a function of supersaturation by a Mie-light scattering technique. The method is tested using water and the results are compared with classical nucleation theory.

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Abbreviations

a :

speed of sound

d :

distance of observer from scattering particle

D :

distance between observation station and virtual origin in the expansion fan of the shock tube

Δ * :

increase of the free energy of the system for the formation of one droplet of critical size

I :

intensity of scattered light

I o :

average intensity of incident light illuminating droplet

J :

nucleation rate

k :

Boltzmann constant

K :

preexponential factor in J = K exp (− ΔG */kT)

M :

Mach number

n :

index of refraction

N :

number of droplets in scattering volume

p :

pressure

r :

radius of droplet

r * :

radius of nucleus of critical size

R :

universal gas constant

S :

saturation ratio, S=yp/p ∞ (T)

t :

time

T :

temperature or relative scattered intensity

r :

scattering volume

\(\bar V\) :

molar volume

gl:

distance upstream from virtual origin of expansion fan

y :

mole fraction of condensable vapor in carrier

γ:

gas ratio of specific heats

λ:

wavelength of laser

ϕ:

scattering angle

σ:

surface tension

1:

driven side of shock tube, initial state

2:

state behind initial shock

3:

state at tail of expansion wave

4:

driver side of shock tube, initial state

exp:

experimental

n:

nucleation at observation station

nc:

nucleation (corrected) along path of fluid element

s:

at saturation, i.e. where the adiabatic expansion attains saturation of the vapor

t:

mixing tank

w:

water

∞:

flat surface equilibrium

References

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Authors and Affiliations

  1. Applied Mechanics Mason Laboratory, Yale University, P.O. Box 2159 Yale Station, 06520, New Haven, CT, USA

    F. Peters

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  1. F. Peters
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Peters, F. A new method to measure homogeneous nucleation rates in shock tubes. Experiments in Fluids 1, 143–148 (1983). https://doi.org/10.1007/BF00272013

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  • DOI: https://doi.org/10.1007/BF00272013

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