Open Access

Property value estimation for inhaled therapeutic binary gas mixtures: He, Xe, N2O, and N2 with O2

  • Ira Katz1, 2Email author,
  • Georges Caillibotte1,
  • Andrew R Martin1 and
  • Philippe Arpentinier3
Medical Gas Research20111:28

DOI: 10.1186/2045-9912-1-28

Received: 8 July 2011

Accepted: 6 December 2011

Published: 6 December 2011

Abstract

Background

The property values of therapeutic gas mixtures are important in designing devices, defining delivery parameters, and in understanding the therapeutic effects. In the medical related literature the vast majority of articles related to gas mixtures report property values only for the pure substances or estimates based on concentration weighted averages. However, if the molecular size or structures of the component gases are very different a more accurate estimate should be considered.

Findings

In this paper estimates based on kinetic theory are provided of density, viscosity, mean free path, thermal conductivity, specific heat at constant pressure, and diffusivity over a range of concentrations of He-O2, Xe-O2, N2O-O2 and N2-O2 mixtures at room (or normal) and body temperature, 20 and 37°C, respectively and at atmospheric pressure.

Conclusions

Property value estimations have been provided for therapeutic gas mixtures and compared to experimental values obtained from the literature where possible.

Introduction

Inhaled therapeutic gases in use today include helium (He) for respiratory treatments, and xenon (Xe) and nitrous oxide (N2O) for anesthesia. For clinical applications these gases are used in the form of mixtures with oxygen in a range of concentrations (typically starting from 20% oxygen (O2) concentration by volume, which is equivalent to a mole fraction of 0.20) so as to maintain adequate oxygenation. Other gases, such as nitric oxide (NO) for pulmonary vascular dilation, are used only in trace amounts.

The property values of therapeutic gas mixtures are important in designing devices, defining delivery parameters, and in understanding the therapeutic effects. Properties of interest include density, viscosity, mean free path, thermal conductivity, specific heat, and diffusivity. In the medical literature the vast majority of articles related to gas mixtures report property values only for the pure substances or estimates based on (volume or molar) concentration weighted averages [17]. However, if the molecular size or structures of the component gases are very different a more accurate estimate could be considered [810]. For this reason property values of helium and xenon mixtures should be considered for more accurate estimation.

Starting with kinetic theory for molecules treated as hard spheres as a basis, a rich literature has developed regarding the modeling of property values based on first principles and increasing complexity of the molecular interactions; in particular, the attraction and repulsion of molecules as first formulated by Chapman and Enskog [8, 9]. The empirically determined Lennard-Jones potential energy function has proved to be a good model for many applications. Extensive measurements of the viscosity of gases using oscillating-disk viscometry have primarily been published by Kestin and his colleagues [1116]. Other equilibrium and transport properties have been extrapolated from the viscosity measurements using the models described above [8, 9]. There also exists limited thermal conductivity data measured using a hot wire method [17].

The objective of this short communication is to give a straightforward reference to the applied scientist, engineer, and medical personnel who perform research with therapeutic gas mixtures. We anticipate that this information will assist both in the design and interpretation of experiments. Estimates of density, viscosity, mean free path, thermal conductivity, specific heat at constant pressure, and diffusivity are provided over a range of concentrations of He-O2, Xe-O2, and N2O-O2 mixtures at room (or normal) and body temperature, 20 and 37°C, respectively and at atmospheric pressure; based on kinetic theory and compared to experimental values obtained from the literature where it is possible. For further comparison N2-O2 mixtures will be included because this mixture makes up the composition of medical air.

Methods

Density

All of the mixtures can be evaluated as ideal gases under the conditions considered. As such the density is based on the state equation as,
ρ m i x = p R m i x T https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_Equ1_HTML.gif
(1)
where ρmix is the mixture density, p is the pressure, T is the absolute temperature and Rmix is the gas constant defined for the mixture as
R m i x = R u n i v X i M W i + ( 1 - X i ) 32 https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_Equ2_HTML.gif
(2)

In Equation (2) Runiv is the universal gas constant, Xi is the mole fraction of the pure gas component, and MWi is the molecular weight of the pure gas component (32 is the molecular weight for oxygen). The units of Rmix depends on the value chosen for Runiv (e.g., 8314 N-m/kgmol-K).

Viscosity

For viscosity we use a semi-empirical method by Wilke [8] that extends the model for collisions between hard spheres to mixtures.
μ m i x = X i μ i X i + ( 1 - X i ) ϕ i - O 2 + ( 1 - X i ) μ O 2 X i ϕ O 2 - i + ( 1 - X i ) https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_Equ3_HTML.gif
(3a)
ϕ i - O 2 = 1 + μ i μ O 2 32 M W i 1 4 2 8 1 + M W i 32 https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_Equ4_HTML.gif
(3b)
ϕ O 2 - i = 1 + μ O 2 μ i M W i 32 1 4 2 8 1 + 32 M W i https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_Equ5_HTML.gif
(3c)
μ i and μ O 2 https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_IEq1_HTML.gifare the viscosities of the pure gas component and oxygen, respectively. The pure gas viscosity estimates are based on the Lennard-Jones empirical function for the potential:
ϕ ( r ) = 4 ε σ r 12 - σ r 6 https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_Equ6_HTML.gif
(4)
where r is the distance between the molecules, ε is a characteristic energy of the interaction between molecules and σ is a characteristic diameter, or collision diameter. Equation (5) is a viscosity formula based on the Lennard-Jones parameters in units of kg/s-m derived for monatomic gases that has also been shown to work well for polyatomic gases [8],
μ i = 0 . 26 69 3 x 1 0 - 5 M W i T σ 2 Ω μ https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_Equ7_HTML.gif
(5)
where Ω μ is a function of ε. Lennard-Jones parameters are tabulated for common gases [8, 9] and for the gases herein in Table 1.
Table 1

Molecular parameters and Lennard-Jones potential parameters for the pure gas components [9].

Gas

MW

R (J/kg-K)

σ (Å)

ε/κ (°K)

Ωμ

at 20°C

Ωμ

at 37°C

Atomic Diffusion Volume

(Σv)

He

4.003

2076.9

2.551

10.22

0.7061

0.7004

2.67

Xe

131.3

63.3

4.047

231.

1.4140

1.3798

32.7

N 2 O

44.02

188.9

3.828

232.4

1.4190

1.3846

35.9

N 2

28.02

296.7

3.798

71.4

0.9697

0.9535

18.5

O 2

32.00

259.8

3.467

106.7

1.0635

1.047

16.3

Values for Ω have been interpolated from Table B-2 in Bird et al. [8]. κ is the Boltzmann constant.

Mean Free Path

The estimation of mean free path is based on the Chapman-Enskog formulation for hard spheres [18], where the mixture viscosity and density account for the interactions of the different molecules:
λ m i x = 16 μ m i x 5 ρ m i x 2 π R m i x T https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_Equ8_HTML.gif
(6)

The input values are obtained from Equations 1-3.

Specific Heat at Constant Pressure

The specific heat at constant pressure (on a per unit mass basis) for all of the mixtures can be evaluated assuming ideal gas behavior and therefore the specific heat curve is a linear function of the mass fraction, though nonlinear in terms of the mole fraction
c p m i x = X i ρ i ρ m i x c p i + 1 - X i ρ O 2 ρ m i x c p O 2 https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_Equ9_HTML.gif
(7)

where c p m i x https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_IEq2_HTML.gif and c p i https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_IEq3_HTML.gif are the specific heats of the mixture and of the pure gas component, respectively. The pure gas values for the monatomic gases are based on the theoretical value c p i = 2 . 5 R u n i v M W i https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_IEq4_HTML.gif The polyatomic estimates are based on empirically derived 4th order polynomials in temperature found in Poling et al. [9].

Thermal Conductivity

Thermal conductivity is treated in an analogous manner to viscosity, where Equation (8a) is equivalent to Equation (3a) and the coefficients are exactly the same based on the pure gas viscosity values.
μ m i x = X i k i X i + ( 1 - X i ) ϕ i - O 2 + ( 1 - X i ) k O 2 X i ϕ O 2 - i + ( 1 - X i ) https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_Equ10_HTML.gif
(8a)
ϕ i - O 2 = 1 + μ i μ O 2 32 M W i 1 4 2 8 1 + M W i 32 https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_Equ11_HTML.gif
(8b)
ϕ O 2 - i = 1 + μ O 2 μ i M W i 32 1 4 2 8 1 + 32 M W i https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_Equ12_HTML.gif
(8c)
The pure gas conductivity estimates are based on a modified Eucken approximation found in Poling et al. [9].
k i = μ i R i c p i R i - 1 1 . 15 + 2 . 03 c p i R i - 1 https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_Equ13_HTML.gif
(9)

Diffusivity

The self diffusivity for a binary system Dij, represents the movement of species i relative to the mixture, where Dij = Dji. The presentation here is based on the method of Fuller et al. given in Poling et al [9], which uses empirically obtained atomic diffusion volumes (Σv).
D i O 2 = 1 . 43 x 10 - 7 T 1 . 75 2 p 1 M W i + 1 32 - 1 2 Σ v i 1 3 + 16 . 3 1 3 2 https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_Equ14_HTML.gif
(10)

In Equation (10) j always represents oxygen, the diffusivity is in m2/s, T is the temperature in degrees Kelvin, p is the pressure in bar and the atomic diffusion volumes are given in Table 1 for each gas. D i O 2 https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_IEq5_HTML.gifis almost independent of composition at low pressures so only a single value will be calculated for each binary gas pair [8].

Of much practical interest is the diffusivity of water vapor or carbon dioxide through the gas mixtures. Values are calculated for these mixtures based on Blanc's law [9].
D m k = X j D j k + X O 2 D O 2 k - 1 https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_Equ15_HTML.gif
(11)

Where m represents the therapeutic gas mixture considered, j represents the specific therapeutic gas, and k corresponds to H2O or CO2. The diffusion constants in Equation 11 of H2O or CO2 through the therapeutic gas or oxygen are calculated using Equation 10 with atomic diffusion volumes of 13.1 and 26.9 for H2O or CO2, respectively.

Results

The molecular weights, gas constants, Lennard-Jones parameters, and atomic diffusion volumes for the pure gases are given in Table 1. The mixture results are given in tabular and graphical forms. Tables 2, 3, 4, and 5 give the property values for He, Xe, N2O, and N2 with O2 mixtures, as a function of mole fraction at 20°C. Tables 6, 7, 8, and 9 are the analogous tables for 37°C. Table 10 gives binary diffusivities for the gas mixtures. Figures 1, 2, 3, 4, and 5 are plots of the 20°C data of density, viscosity, mean free path, thermal conductivity, and specific heat, respectively.
Table 2

He-O2 property values at 20°C and 1 atm.

He Mole Fraction

ρ (kg/m3)

μ × 105 (kg/s-m)

λ (n m)

k (W/m-K)

cp (J/kg-K)

D H 2 O https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_IEq6_HTML.gif× 105 (m2/s)

D C O 2 https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_IEq7_HTML.gif× 105 (m2/s)

0

1.330

2.029

70.561

0.026

917.5

2.551

1.573

0.05

1.272

2.040

72.547

0.029

945.5

2.641

1.632

0.10

1.214

2.051

74.673

0.032

976.1

2.739

1.695

0.15

1.156

2.063

76.954

0.035

1009.8

2.844

1.764

0.20

1.098

2.074

79.409

0.039

1047.1

2.957

1.838

0.25

1.039

2.086

82.057

0.043

1088.6

3.080

1.919

0.30

0.981

2.097

84.924

0.047

1135.0

3.214

2.007

0.35

0.923

2.109

88.038

0.051

1187.3

3.359

2.104

0.40

0.865

2.120

91.432

0.055

1246.6

3.519

2.210

0.45

0.807

2.131

95.148

0.060

1314.4

3.694

2.328

0.50

0.748

2.141

99.235

0.066

1392.8

3.888

2.459

0.55

0.690

2.149

103.751

0.071

1484.4

4.103

2.606

0.60

0.632

2.156

108.773

0.077

1592.9

4.343

2.772

0.65

0.574

2.161

114.393

0.084

1723.4

4.613

2.960

0.70

0.516

2.162

120.735

0.091

1883.3

4.919

3.175

0.75

0.457

2.158

127.959

0.099

2084.0

5.268

3.424

0.78

0.422

2.152

132.807

0.104

2230.9

5.503

3.593

0.79

0.411

2.150

134.522

0.106

2285.5

5.585

3.653

0.80

0.399

2.147

136.291

0.108

2343.2

5.671

3.715

0.85

0.341

2.127

146.059

0.117

2690.8

6.140

4.060

0.90

0.283

2.092

157.788

0.128

3181.5

6.694

4.477

0.95

0.225

2.037

172.409

0.139

3926.4

7.359

4.988

1.0

0.166

1.952

191.912

0.152

5192.4

8.169

5.632

Table 3

Xe-O2 property values at 20°C and 1 atm.

Xe Mole Fraction

ρ (kg/m3)

μ × 105 (kg/s-m)

λ (nm)

k (W/m-K)

cp (J/kg-K)

D H 2 O https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_IEq6_HTML.gif× 105 (m2/s)

D C O 2 https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_IEq7_HTML.gif× 105 (m2/s)

0

1.330

2.029

70.561

0.026

917.5

2.551

1.573

0.05

1.537

2.084

67.417

0.024

782.7

2.487

1.522

0.10

1.743

2.128

64.637

0.023

679.8

2.427

1.474

0.15

1.950

2.163

62.138

0.021

598.6

2.369

1.429

0.20

2.156

2.192

59.866

0.020

533.1

2.314

1.387

0.25

2.362

2.215

57.783

0.019

478.9

2.262

1.347

0.30

2.569

2.232

55.863

0.017

433.5

2.211

1.309

0.35

2.775

2.247

54.083

0.016

394.9

2.164

1.273

0.40

2.982

2.257

52.428

0.015

361.5

2.118

1.240

0.45

3.188

2.265

50.883

0.014

332.5

2.074

1.208

0.50

3.394

2.271

49.437

0.013

307.1

2.031

1.177

0.55

3.601

2.275

48.080

0.012

284.5

1.991

1.148

0.60

3.807

2.277

46.804

0.011

264.4

1.952

1.121

0.65

4.014

2.278

45.602

0.010

246.4

1.915

1.095

0.70

4.220

2.278

44.467

0.010

230.1

1.878

1.070

0.75

4.427

2.276

43.395

0.009

215.3

1.844

1.046

0.80

4.633

2.274

42.379

0.008

201.9

1.810

1.023

0.85

4.839

2.272

41.415

0.007

189.6

1.778

1.001

0.90

5.046

2.268

40.500

0.007

178.3

1.747

0.980

0.95

5.252

2.265

39.630

0.006

167.9

1.717

0.960

1.0

5.459

2.260

38.801

0.005

158.3

1.688

0.940

Table 4

N2O-O2 property values at 20°C and 1 atm.

N2O Mole Fraction

ρ (kg/m3)

μx105 (kg/s-m)

λ (nm)

k (W/m-K)

cp (J/kg-K)

D H 2 O https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_IEq6_HTML.gif× 105 (m2/s)

D C O 2 https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_IEq7_HTML.gif× 105 (m2/s)

0

1.330

2.029

70.561

0.026

917.5

2.551

1.573

0.05

1.355

1.956

67.394

0.025

914.3

2.500

1.542

0.10

1.380

1.892

64.577

0.025

911.1

2.451

1.511

0.15

1.405

1.835

62.065

0.024

908.1

2.404

1.482

0.20

1.430

1.784

59.820

0.024

905.2

2.358

1.454

0.25

1.455

1.739

57.810

0.023

902.4

2.315

1.426

0.30

1.480

1.699

56.005

0.023

899.7

2.273

1.400

0.35

1.505

1.664

54.383

0.022

897.1

2.232

1.375

0.40

1.530

1.632

52.923

0.022

894.6

2.193

1.351

0.45

1.555

1.605

51.605

0.021

892.1

2.156

1.327

0.50

1.580

1.580

50.414

0.021

889.7

2.119

1.305

0.55

1.605

1.559

49.337

0.020

887.4

2.084

1.283

0.60

1.630

1.540

48.361

0.020

885.2

2.050

1.262

0.65

1.655

1.523

47.475

0.019

883.0

2.017

1.241

0.70

1.680

1.508

46.670

0.019

880.9

1.985

1.221

0.75

1.705

1.496

45.938

0.019

878.9

1.954

1.202

0.80

1.730

1.485

45.271

0.018

876.9

1.924

1.184

0.85

1.755

1.475

44.663

0.018

875.0

1.895

1.166

0.90

1.780

1.467

44.108

0.018

873.1

1.866

1.148

0.95

1.805

1.461

43.601

0.017

871.3

1.839

1.131

1.0

1.830

1.455

43.137

0.017

869.6

1.812

1.115

Table 5

N2-O2 property values at 20°C and 1 atm.

N2 Mole Fraction

ρ (kg/m3)

μ × 105 (kg/s-m)

λ (nm)

k (W/m-K)

cp (J/kg-K)

D H 2 O https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_IEq6_HTML.gif× 105 (m2/s)

D C O 2 https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_IEq7_HTML.gif× 105 (m2/s)

0

1.330

2.029

70.561

0.026

917.5

2.551

1.573

0.05

1.322

2.015

70.289

0.026

922.8

2.548

1.573

0.10

1.314

2.001

70.016

0.026

928.2

2.546

1.573

0.15

1.306

1.987

69.743

0.026

933.7

2.543

1.573

0.20

1.297

1.973

69.468

0.026

939.3

2.541

1.573

0.25

1.289

1.959

69.192

0.026

944.9

2.538

1.573

0.30

1.281

1.945

68.915

0.026

950.6

2.536

1.573

0.35

1.272

1.931

68.637

0.026

956.3

2.533

1.573

0.40

1.264

1.916

68.358

0.026

962.2

2.531

1.574

0.45

1.256

1.902

68.077

0.026

968.1

2.529

1.574

0.50

1.248

1.888

67.796

0.026

974.1

2.526

1.574

0.55

1.239

1.874

67.513

0.026

980.2

2.524

1.574

0.60

1.231

1.860

67.230

0.026

986.3

2.521

1.574

0.65

1.223

1.846

66.945

0.026

992.6

2.519

1.574

0.70

1.215

1.832

66.659

0.026

998.9

2.516

1.574

0.75

1.206

1.818

66.371

0.026

1005.3

2.514

1.574

0.78

1.201

1.809

66.198

0.026

1009.2

2.513

1.574

0.79

1.200

1.806

66.141

0.026

1010.5

2.512

1.574

0.80

1.198

1.803

66.083

0.026

1011.8

2.512

1.574

0.85

1.190

1.789

65.793

0.026

1018.4

2.509

1.574

0.90

1.181

1.775

65.502

0.025

1025.1

2.507

1.574

0.95

1.173

1.761

65.210

0.025

1031.9

2.504

1.574

1.0

1.165

1.747

64.916

0.025

1038.7

2.502

1.574

Table 6

He-O2 property values at 37°C and 1 atm.

He Mole Fraction

ρ (kg/m3)

μ × 105 (kg/s-m)

λ (nm)

k (W/m-K)

cp (J/kg-K)

D H 2 O https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_IEq6_HTML.gif× 105 (m2/s)

D C O 2 https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_IEq7_HTML.gif× 105 (m2/s)

0

1.257

2.113

75.572

0.027

920.7

2.815

1.736

0.05

1.202

2.125

77.716

0.030

948.7

2.915

1.801

0.10

1.147

2.137

80.012

0.034

979.3

3.023

1.871

0.15

1.092

2.149

82.477

0.037

1013.0

3.139

1.947

0.20

1.037

2.162

85.131

0.041

1050.3

3.264

2.029

0.25

0.982

2.175

87.996

0.045

1091.7

3.400

2.118

0.30

0.927

2.188

91.101

0.049

1138.1

3.547

2.215

0.35

0.872

2.200

94.475

0.053

1190.3

3.708

2.322

0.40

0.817

2.213

98.157

0.058

1249.5

3.883

2.440

0.45

0.762

2.225

102.191

0.063

1317.3

4.077

2.570

0.50

0.707

2.236

106.633

0.069

1395.7

4.291

2.714

0.55

0.652

2.246

111.548

0.075

1487.2

4.528

2.876

0.60

0.597

2.255

117.019

0.081

1595.6

4.793

3.059

0.65

0.542

2.261

123.153

0.088

1726.0

5.091

3.266

0.70

0.487

2.264

130.085

0.096

1885.8

5.429

3.504

0.75

0.432

2.262

137.997

0.104

2086.3

5.814

3.779

0.78

0.399

2.258

143.316

0.110

2233.2

6.073

3.965

0.79

0.388

2.256

145.199

0.112

2287.7

6.165

4.032

0.80

0.377

2.254

147.142

0.114

2345.3

6.259

4.100

0.85

0.322

2.235

157.891

0.124

2692.7

6.777

4.481

0.90

0.267

2.202

170.832

0.135

3183.0

7.389

4.941

0.95

0.212

2.149

187.014

0.147

3927.4

8.122

5.505

1.0

0.157

2.064

208.666

0.161

5192.4

9.016

6.216

Table 7

Xe-O2 property values at 37°C and 1 atm.

Xe Mole Fraction

ρ (kg/m3)

μ × 105 (kg/s-m)

λ (nm)

k (W/m-K)

cp (J/kg-K)

D H 2 O https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_IEq6_HTML.gif× 105 (m2/s)

D C O 2 https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_IEq7_HTML.gif× 105 (m2/s)

0

1.257

2.113

75.572

0.027

920.7

2.815

1.736

0.05

1.453

2.173

72.306

0.025

785.3

2.745

1.680

0.10

1.648

2.221

69.409

0.024

682.0

2.678

1.627

0.15

1.843

2.261

66.798

0.022

600.5

2.615

1.577

0.20

2.038

2.293

64.418

0.021

534.7

2.554

1.530

0.25

2.233

2.319

62.231

0.020

480.3

2.496

1.486

0.30

2.428

2.339

60.210

0.018

434.7

2.441

1.445

0.35

2.623

2.356

58.334

0.017

395.9

2.388

1.405

0.40

2.818

2.369

56.586

0.016

362.4

2.337

1.368

0.45

3.013

2.378

54.951

0.015

333.3

2.289

1.333

0.50

3.208

2.386

53.419

0.014

307.7

2.242

1.299

0.55

3.404

2.391

51.980

0.013

285.1

2.197

1.267

0.60

3.599

2.395

50.625

0.012

264.9

2.154

1.237

0.65

3.794

2.397

49.346

0.011

246.7

2.113

1.208

0.70

3.989

2.397

48.138

0.010

230.4

2.073

1.180

0.75

4.184

2.397

46.995

0.009

215.6

2.035

1.154

0.80

4.379

2.396

45.911

0.008

202.1

1.998

1.129

0.85

4.574

2.393

44.882

0.008

189.7

1.962

1.105

0.90

4.769

2.391

43.904

0.007

178.4

1.928

1.081

0.95

4.964

2.387

42.973

0.006

168.0

1.895

1.059

1.0

5.159

2.384

42.086

0.006

158.3

1.863

1.038

Table 8

N2O-O2 property values at 37°C and 1 atm.

N2O Mole Fraction

ρ (kg/m3)

μ × 105 (kg/s-m)

λ (nm)

k (W/m-K)

cp (J/kg-K)

D H 2 O https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_IEq6_HTML.gif× 105 (m2/s)

D C O 2 https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_IEq7_HTML.gif× 105 (m2/s)

0

1.257

2.113

75.572

0.027

920.7

2.815

1.736

0.05

1.281

2.039

72.254

0.027

918.4

2.759

1.701

0.10

1.305

1.974

69.300

0.026

916.2

2.705

1.668

0.15

1.328

1.916

66.666

0.025

914.0

2.653

1.635

0.20

1.352

1.864

64.312

0.025

911.9

2.603

1.604

0.25

1.376

1.819

62.203

0.024

909.9

2.555

1.574

0.30

1.399

1.779

60.311

0.024

908.0

2.509

1.546

0.35

1.423

1.743

58.611

0.023

906.1

2.464

1.518

0.40

1.446

1.712

57.080

0.023

904.3

2.421

1.491

0.45

1.470

1.684

55.700

0.022

902.5

2.379

1.465

0.50

1.494

1.659

54.454

0.022

900.8

2.339

1.440

0.55

1.517

1.638

53.327

0.021

899.1

2.300

1.416

0.60

1.541

1.619

52.307

0.021

897.5

2.262

1.393

0.65

1.564

1.602

51.382

0.021

896.0

2.226

1.370

0.70

1.588

1.588

50.543

0.020

894.5

2.190

1.348

0.75

1.612

1.576

49.780

0.020

893.0

2.156

1.327

0.80

1.635

1.565

49.087

0.020

891.6

2.123

1.306

0.85

1.659

1.556

48.455

0.019

890.2

2.091

1.286

0.90

1.683

1.549

47.880

0.019

888.9

2.060

1.267

0.95

1.706

1.542

47.355

0.019

887.6

2.030

1.248

1.0

1.730

1.537

46.876

0.018

886.3

2.000

1.230

Table 9

N2-O2 property values at 37°C and 1 atm.

N2 Mole Fraction

ρ (kg/m3)

μ × 105 (kg/s-m)

λ (nm)

k (W/m-K)

cp (J/kg-K)

D H 2 O https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_IEq6_HTML.gif× 105 (m2/s)

D C O 2 https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_IEq7_HTML.gif× 105 (m2/s)

0

1.257

2.113

75.572

0.027

920.7

2.815

1.736

0.05

1.250

2.098

75.262

0.027

925.9

2.812

1.736

0.10

1.242

2.083

74.950

0.027

931.2

2.810

1.736

0.15

1.234

2.067

74.638

0.027

936.6

2.807

1.736

0.20

1.226

2.052

74.324

0.027

942.0

2.804

1.737

0.25

1.218

2.037

74.010

0.027

947.5

2.802

1.737

0.30

1.211

2.022

73.694

0.027

953.1

2.799

1.737

0.35

1.203

2.006

73.377

0.027

958.7

2.796

1.737

0.40

1.195

1.991

73.059

0.027

964.4

2.793

1.737

0.45

1.187

1.976

72.740

0.027

970.2

2.791

1.737

0.50

1.179

1.961

72.420

0.027

976.1

2.788

1.737

0.55

1.171

1.946

72.098

0.027

982.0

2.785

1.737

0.60

1.164

1.931

71.776

0.027

988.0

2.783

1.737

0.65

1.156

1.915

71.452

0.027

994.1

2.780

1.737

0.70

1.148

1.900

71.127

0.027

1000.3

2.777

1.737

0.75

1.140

1.885

70.801

0.027

1006.6

2.775

1.737

0.78

1.135

1.876

70.605

0.027

1010.4

2.773

1.737

0.79

1.134

1.873

70.539

0.027

1011.6

2.773

1.737

0.80

1.132

1.870

70.474

0.027

1012.9

2.772

1.737

0.85

1.124

1.855

70.145

0.026

1019.4

2.769

1.737

0.90

1.117

1.840

69.815

0.026

1025.9

2.767

1.737

0.95

1.109

1.824

69.484

0.026

1032.5

2.764

1.737

1.0

1.101

1.809

69.152

0.026

1039.2

2.761

1.737

Table 10

Binary diffusivities at 1 atm.

Gas

D i O 2 https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_IEq8_HTML.gif× 105 (m2/s)

 

20°C

37°C

He-O 2

7.142

7.883

Xe-O 2

1.243

1.372

N 2 O-O 2

1.415

1.561

N 2 -O 2

1.999

2.206

https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_Fig1_HTML.jpg
Figure 1

Density of gas mixtures at 20°C and 1 atm.

https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_Fig2_HTML.jpg
Figure 2

Viscosity of gas mixtures at 20°C and 1 atm.

https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_Fig3_HTML.jpg
Figure 3

Mean free path of gas mixtures at 20°C and 1 atm.

https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_Fig4_HTML.jpg
Figure 4

Thermal conductivity of gas mixtures at 20°C and 1 atm.

https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_Fig5_HTML.jpg
Figure 5

Specific heat of gas mixtures at 20°C and 1 atm.

Discussion

In this paper thermophysical property values have been presented for inhaled therapeutic binary gas mixtures. Pure substance values at 20°C and 37°C and mixing formulas based on kinetic theory were used to estimate the mixture values. The approach was to use relatively simple estimates for nonpolar gases [8]. That is, more complex intermolecular interactions that occur, for example, at high pressure, were not included.

Whereas many therapeutic gases (e.g.; CO and NO) are used at trace concentrations such that property values of the bulk mixture are essentially equivalent to those of air, mixtures considered herein have significantly different properties than air which change as a function of component concentration. Mechanical property values of density and viscosity are fundamental to the understanding of gas transport and airway resistance. The thermal properties of conductivity and capacity are necessary to accurately predict how gas treatments will affect the temperature and humidity of the respiratory tract. They also will influence the thermodynamic interaction of inhaled aerosols with the gas, and thus the deposition distribution which is particularly relevant for helium-oxygen mixtures. Diffusion is a key mode of gas transport deep in the lung potentially affecting exchange with the blood.

Bird et al. [8] note that the concept of the mean free path is applicable only if there are no long range forces associated with the hard sphere kinetic theory models. For this reason it is not typically an element of modern kinetic theory. Nevertheless, it is an important parameter in modeling the interaction of aerosols and gases [19], and thus for combination therapies involving aerosols and gas mixtures. In contrast to the scheme employed by Loeb [20], the estimation method employed here does not directly take into account the molecular collisions. However, Equation (6) for the mean free path does account for the collisions of different molecules through the mixture viscosity. As the utility of this parameter in aerosol mechanics is to estimate a reduced drag on small particles where their size is comparable to the mean free path, this approach would appear to be self consistent.

A comparison of estimated data based on Equation (3) to experimental data for the viscosity at 20°C of helium-oxygen mixtures [14] is shown in Figure 6, along with the linear curve representing the concentration weighted average. The maximum relative difference of 0.9% between the theory and experiment occurs at XHe = 0.82. For the concentration weighted average value the maximum relative error of 7.9% occurs at XHe = 0.67.
https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_Fig6_HTML.jpg
Figure 6

Viscosity of He-O 2 mixtures using Equation (3), based on a weighted average of the molar fractions and from experimental measurements [14].

Figure 7 shows comparisons of experimental thermal conductivity values [17] for helium-oxygen and xenon-oxygen mixtures at 30°C compared to theoretical values calculated using Equation (8). The maximum relative differences between the theory and experiment are 4.2% at XHe = 0.68 and 4.7% at XXe = 0.27, respectively.
https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_Fig7_HTML.jpg
Figure 7

Thermal conductivity at 30°C for He-O 2 and Xe-O 2 mixtures using Equation (8), based on a weighted average of the molar fractions and from experimental measurements [17].

Table 11 shows a good agreement between experimental data for binary diffusivity of He-O2 and Xe-O2 [14, 21] with theoretical data calculated using Equation (10). For the diffusivity of water vapor or carbon dioxide, the simplifying assumption leading to Blanc's law is for a trace component diffusing into a homogeneous, binary mixture. A quantitative definition of trace for the applicability of this assumption was not found. However, experiments testing diffusion of He, CO and SF6 through gas mixtures similar to alveolar gas (14% O2, 6% CO2 and 80% N2) did not show significant departures from values predicted on the basis of binary diffusion coefficient values weighted according to fractional concentrations [22] in agreement with Blanc's law. These experiments were performed with test gas concentrations varying from 0 to 10% suggesting Blanc's law would be appropriate for typical applications of the gases considered herein.
Table 11

Comparison of experimental and theoretical binary diffusivities based on Equation (10).

 

D i - O 2 https://static-content.springer.com/image/art%3A10.1186%2F2045-9912-1-28/MediaObjects/13618_2011_Article_31_IEq9_HTML.gif× 105 (m2/s)

 

T (K)

Experimental

Theoretical

Percent Difference

He-O 2

   

298 [14]

7.06

7.357

4.21

300 [21]

7.441

7.437

0.05

Xe-O 2

   

280 [21]

1.147

1.128

1.68

290 [21]

1.220

1.202

1.50

300 [21]

1.295

1.279

1.25

310 [21]

1.371

1.357

1.03

320 [21]

1.449

1.438

0.76

In conclusion, the methods presented above allow accurate estimation of thermophysical property values for inhaled therapeutic binary gas mixtures, including He-O2, Xe-O2, and N2O-O2, over a range of concentrations.

Declarations

Acknowledgements

We thank Paul Finlay for performing some of the calculations.

Authors’ Affiliations

(1)
Medical Gases Group, Air Liquide Santé International, Centre de Recherche Claude-Delorme
(2)
Department of Mechanical Engineering, Lafayette College
(3)
Scientific Direction, Air Liquide Research and Development, Centre de Recherche Claude-Delorme

References

  1. Anderson M, Svartengren M, Bylin G, Philipson K, Camner P: Deposition in asthmatics of particles inhaled in air or helium-oxygen. Am Rev Respir Dis. 1993, 147: 524-528.View ArticlePubMed
  2. Baumert J-H, Reyle-Hahn M, Hecker K, Tenbrinck R, Kuhien R, Rossaint R: Increased airway resistance during xenon anaesthesia in pigs is attributed to physical properties of the gas. Brit Anaesthesia. 2002, 88: 540-545. 10.1093/bja/88.4.540.View Article
  3. Darquenne C, Prisk GK: Aerosol deposition in the human respiratory tract breathing air and 80:20 heliox. J Aerosol Med. 2004, 17: 278-285. 10.1089/jam.2004.17.278.PubMed CentralView ArticlePubMed
  4. Frazier MD, Cheifetz IM: The role of heliox in paediatric respiratory disease. Paediatric Respiratory Reviews. 2010, 11: 46-53. 10.1016/j.prrv.2009.10.008.View ArticlePubMed
  5. Hess DR, Fink JB, Venkataraman ST, Kim IK, Meyers TR, Tano BD: The history and physics of heliox. Respir Care. 2006, 51: 608-612.PubMed
  6. Mihaescu M, Gutmark E, Murugappan S, Elluru R, Cohen A, Willging P: Modeling flow in a compromised pediatric airway breathing air and heliox. Laryngoscope. 2009, 119: 145-151. 10.1002/lary.20015.View ArticlePubMed
  7. Palange P, Valli G, Onorati P, Antonucci R, Paoletti P, Rosato A, Manfredi F, Serra P: Effect of heliox on lung dynamic hyperinflation, dyspnea, and exercise endurance capacity in COPD patients. J Appl Physiol. 2004, 97: 1637-1642. 10.1152/japplphysiol.01207.2003.View ArticlePubMed
  8. Bird GA, Stewart WE, Lightfoot EN: Transport Phenomena. 1960, New York: John Wiley & Sons
  9. Poling BE, Prausnitz JM, O'Connel JP: The Properties of Gases and Liquids. 2007, New York: McGraw-Hill, 5
  10. Reid RC, Sherwood TK: The Properties of Gases and Liquides: Their Estimation and Correlation. 1966, New York: McGraw-Hill, 2
  11. Bzowski J, Kestin J, Mason EA, Uribe FJ: Equilibrium and transport properties of gas mixtures at low density: Eleven polyatomic gases and five noble gases. J Phys Chem Ref Data. 1990, 19: 1179-1232. 10.1063/1.555867.View Article
  12. Hellemans JM, Kestin J, Ro ST: The viscosity of oxygen and of some of its mixtures with other gases. Physica. 1973, 65 (2): 362-375. 10.1016/0031-8914(73)90351-0.View Article
  13. Hellemans JM, Kestin J, Ro ST: On the properties of multicomponent mixtures of monatomic gases. Physica. 1974, 71 (1): 1-16. 10.1016/0031-8914(74)90043-3.View Article
  14. Kestin J, Khalifa HE, Ro ST, Wakeham WA: The viscosity and diffusion coefficients of eighteen binary gas systems. Physica. 1977, 88A: 242-260.View Article
  15. Kestin J, Khalifa HE, Wakeham WA: The viscosity and diffusion coefficients of the binary mixtures of xenon with the other noble gases. Physica A: Statistical and Theoretical Physics. 1978, 90 (2): 215-228. 10.1016/0378-4371(78)90110-3.View Article
  16. Kestin J, Knierim K, Mason EA, Najafi B, Ro ST, Waldman M: Equilibrium and transport properties of the noble gases and their mixtures at low density. J Phys Chem Ref Data. 1984, 13: 229-303. 10.1063/1.555703.View Article
  17. Srivastava BN, Barua AK: The dilute gas thermal conductivity of the binary mixtures O2 - He, O2 - Ne, O2 - Kr and O2 - Xe is measured at 30 C and 45 C for various compositions by using the thick-wire variant of the hot-wire method. J Chem Phys. 1960, 32: 427-435. 10.1063/1.1730711.View Article
  18. Bird GA: Definition of mean free path for real gases. Phys Fluids. 1983, 26: 3222-3223. 10.1063/1.864095.View Article
  19. Issacs KK, Rosati JA, Martonen TB: Mechanisms of particle deposition. Aerosols Handbook: Measurement, Dosimetry, and Health Effects. Edited by: Ruzer LS, Harley NH. 2005, CRC Press LLC, 73-97.
  20. Loeb LB: The Kinetic Theory of Gases. 1961, New York: Dover Publications, Inc, 3
  21. Dunlop PJ, Bignelli CM: The temperature and concentration dependences of diffusion coefficients of the systems Ne-O2, K-O2, Xe-O2 and He-NO. Ber Bunsen-Ges. 1992, 96: 1847-1848.View Article
  22. Worth H, Piper J: Diffusion of helium, carbon monoxide and sulfur hexafluoride in gas mixtures similar to alveolar gas. Respir Physiol. 1978, 32: 155-166. 10.1016/0034-5687(78)90106-8.View ArticlePubMed

Copyright

© Katz et al; licensee BioMed Central Ltd. 2011

This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://​creativecommons.​org/​licenses/​by/​2.​0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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