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Effects of solid–gas coupling and pore and particle microstructures on the effective gaseous thermal conductivity in aerogels

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Abstract

An analytical model was developed to predict the pressure-dependent gaseous thermal conductivity in aerogels based on the spherical porous secondary particle aggregate structure. The model includes the effects of particle size, pore and particle microstructures, and solid–gas coupling including the quasi lattice vibrations for solid-like vibrating gas molecules in the gaps between adjacent secondary particles that are not included in previous models. The results show that the pressure-dependent effective gaseous thermal conductivities of RF and silica aerogels predicted by the present model agree well with experimental results. The solid–gas coupling significantly increases the effective gaseous thermal conductivity in the aerogels as the quasi lattice vibrating gas molecules in the gaps more effectively bridge adjacent particles. The effects of solid–gas coupling and pore and particle microstructures are significant for particle aggregate structures with mean pore and particle diameters in the range of 100 nm–10 μm while the Knudsen formula and the Zeng’s model have limited applicability in this size range. Micron and millimeter-scale pores that can occur in nanoporous silica aerogel samples due to the mechanical fragility of these nanostructures can be well represented by the present three pore size model.

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Abbreviations

a :

Equivalent solid cubic element length (m)

a 1 :

Crystal lattice constant (m)

A :

Parameter in Eqs. 22 and 33

A i :

Ring area of the ith hollow cylinder (m2)

B :

Parameter in Eq. 37

C 1, C 2, C 3, C 4, C 5, C 6, C 7 :

Parameters

c v :

Specific heat at constant volume (J kg−1 K−1)

d :

Diameter (m)

D :

Pore diameter (m)

k :

Thermal conductivity (W m−1 K−1)

k B :

Boltzmann’s constant (1.38 × 10−23 J K−1)

l :

Mean free path (m)

l contact :

Contact length between adjacent particles (m)

M :

Gas molecular weight (kg mol−1)

N :

Number of partitions

p :

Pressure (Pa)

Pr :

Prandtl number

R m :

Universal gas constant (8.314 J mol−1 K−1)

S :

Specific surface area (m2 kg−1)

T :

Temperature (K)

T m :

Melting point (K)

v :

Group velocity (m s−1)

x, y, z :

Coordinates (m)

α:

Energy accommodation coefficient

μ:

Dynamic viscosity (N s m−2)

γ:

Adiabatic coefficient

γ1 :

Gruneisen constant

Π:

Aerogel porosity

ρ:

Density (kg m−3)

φ:

Porosity or volume fraction

ϕ:

Volume fraction

0:

Free space or ambient conditions

a:

Aerogel

Ar:

Argon

b:

Bulk

ce:

Coupling effect

CM:

Continuum regime

exp:

Experiment

FM:

Free molecular regime

g:

Gas

He:

Helium

p:

Pore

part:

Aerogel particle

r:

Radiation

s:

Solid

total:

Total or effective

TR:

Transition regime

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Acknowledgments

The authors acknowledge financial support from NSFC (No. 21176133) and SRFDP (No. 20100002110045).

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Authors and Affiliations

  1. Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Tsinghua University, Beijing, 100084, China

    Jun-Jie Zhao, Yuan-Yuan Duan & Bu-Xuan Wang

  2. State Key Laboratory of Alternate Electrical Power Systems with Renewable Energy Sources, North China Electric Power University, Beijing, 102206, China

    Xiao-Dong Wang

  3. Beijing Key Laboratory of Multiphase Flow and Heat Transfer for Low Grade Energy, North China Electric Power University, Beijing, 102206, China

    Xiao-Dong Wang

Authors
  1. Jun-Jie Zhao
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  2. Yuan-Yuan Duan
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  3. Xiao-Dong Wang
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  4. Bu-Xuan Wang
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Correspondence to Yuan-Yuan Duan or Xiao-Dong Wang.

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Zhao, JJ., Duan, YY., Wang, XD. et al. Effects of solid–gas coupling and pore and particle microstructures on the effective gaseous thermal conductivity in aerogels. J Nanopart Res 14, 1024 (2012). https://doi.org/10.1007/s11051-012-1024-0

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