Abstract

A common-path interferometer (CPI) system was developed to measure the diffusivity of transparent liquid pairs by real-time visualization of the concentration gradient profile. The CPI is an optical technique that can be used to measure changes in the gradient of the refractive index of transparent materials. The CPI is a shearing interferometer that shares the same optical path from a laser light source to the final imaging plane. Molecular diffusivity of liquids can be determined by use of physical relations between changes in the optical path length and the liquid phase properties. The data obtained by this interferometer are compared with similar results from other techniques. This demonstrates that the instrument is reliable for measurement of the diffusivity of miscible liquids and allows the system to be compact and robust. It can also be useful for studies in interface dynamics as well as other applications in a low-gravity environment.

© 2002 Optical Society of America

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References

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  1. W. Linnik, “Simple interferometer for the investigation of optical systems,” C. R. Acad. Sci. U.R.S.S. 1, 208–210 (1933), abstract in Z. Instrumentenkd. 54, 463 (1934).
  2. R. N. Smartt, J. Strong, “Point-diffraction interferometer,” J. Opt. Soc. Am. 62, 737 (1972).
  3. C. R. Mercer, N. Rashidnia, K. Creath, “High data density temperature measurement for quasi steady-state flows,” Exp. Fluids 21, 11–16 (1996).
    [CrossRef]
  4. C. R. Mercer, N. Rashidnia, “Common-path phase-stepped interferometer for fluid measurements,” in Proceedings of the Eight International Symposium of Flow Visualization, G. M. Carlomango, I. Grant, eds. (1998; available on CD-ROM from Optical Diagnostics in Engineering, http://www.ode-web.demon.co.uk ), pp. 256.1–256.9.
  5. P. Petitjeans, T. Maxworthy, “Miscible displacements in a capillary tube. Part 1: Experiments,” J. Fluid Mech. 326, 37–56 (1996).
    [CrossRef]
  6. A. Sommerfeld, Optics, Lectures in Physics IV (Academic, New York, 1964), p. 347).
  7. W. Merzkirch, Flow Visualization (Academic, New York, 1987), pp. 180–188).
  8. N. Rashidnia, R. Balasubramaniam, J. Kuang, P. Petitjeans, T. Maxworthy, “Measurement of the diffusion coefficient of miscible fluids using both interferometry and Weiners method,” Int. J. Thermophys. 22, 547–555 (2001).
    [CrossRef]
  9. W. Merzkirch, “Generalized analysis of shearing interferometers as applied for gas dynamic studies,” Appl. Opt. 13, 409–413 (1974).
    [CrossRef] [PubMed]
  10. R. B. Bird, W. E. Stewart, E. N. Lightfoot, Transport Phenomena (Wiley, New York, 1960), p. 558).
  11. N. Rashidnia, R. Balasubramaniam, “Optical measurement of concentration gradient near miscible interfaces,” presented at the ASME Proceedings of the Microgravity Transport Processes in Fluid, Thermal, Biological Materials Sciences II, Banff, Alberta, Canada, 30 Sept.–5 Oct. 2001, paper UEF: MTP-01-22.

2001 (1)

N. Rashidnia, R. Balasubramaniam, J. Kuang, P. Petitjeans, T. Maxworthy, “Measurement of the diffusion coefficient of miscible fluids using both interferometry and Weiners method,” Int. J. Thermophys. 22, 547–555 (2001).
[CrossRef]

1996 (2)

C. R. Mercer, N. Rashidnia, K. Creath, “High data density temperature measurement for quasi steady-state flows,” Exp. Fluids 21, 11–16 (1996).
[CrossRef]

P. Petitjeans, T. Maxworthy, “Miscible displacements in a capillary tube. Part 1: Experiments,” J. Fluid Mech. 326, 37–56 (1996).
[CrossRef]

1974 (1)

1972 (1)

R. N. Smartt, J. Strong, “Point-diffraction interferometer,” J. Opt. Soc. Am. 62, 737 (1972).

1933 (1)

W. Linnik, “Simple interferometer for the investigation of optical systems,” C. R. Acad. Sci. U.R.S.S. 1, 208–210 (1933), abstract in Z. Instrumentenkd. 54, 463 (1934).

Balasubramaniam, R.

N. Rashidnia, R. Balasubramaniam, J. Kuang, P. Petitjeans, T. Maxworthy, “Measurement of the diffusion coefficient of miscible fluids using both interferometry and Weiners method,” Int. J. Thermophys. 22, 547–555 (2001).
[CrossRef]

N. Rashidnia, R. Balasubramaniam, “Optical measurement of concentration gradient near miscible interfaces,” presented at the ASME Proceedings of the Microgravity Transport Processes in Fluid, Thermal, Biological Materials Sciences II, Banff, Alberta, Canada, 30 Sept.–5 Oct. 2001, paper UEF: MTP-01-22.

Bird, R. B.

R. B. Bird, W. E. Stewart, E. N. Lightfoot, Transport Phenomena (Wiley, New York, 1960), p. 558).

Creath, K.

C. R. Mercer, N. Rashidnia, K. Creath, “High data density temperature measurement for quasi steady-state flows,” Exp. Fluids 21, 11–16 (1996).
[CrossRef]

Kuang, J.

N. Rashidnia, R. Balasubramaniam, J. Kuang, P. Petitjeans, T. Maxworthy, “Measurement of the diffusion coefficient of miscible fluids using both interferometry and Weiners method,” Int. J. Thermophys. 22, 547–555 (2001).
[CrossRef]

Lightfoot, E. N.

R. B. Bird, W. E. Stewart, E. N. Lightfoot, Transport Phenomena (Wiley, New York, 1960), p. 558).

Linnik, W.

W. Linnik, “Simple interferometer for the investigation of optical systems,” C. R. Acad. Sci. U.R.S.S. 1, 208–210 (1933), abstract in Z. Instrumentenkd. 54, 463 (1934).

Maxworthy, T.

N. Rashidnia, R. Balasubramaniam, J. Kuang, P. Petitjeans, T. Maxworthy, “Measurement of the diffusion coefficient of miscible fluids using both interferometry and Weiners method,” Int. J. Thermophys. 22, 547–555 (2001).
[CrossRef]

P. Petitjeans, T. Maxworthy, “Miscible displacements in a capillary tube. Part 1: Experiments,” J. Fluid Mech. 326, 37–56 (1996).
[CrossRef]

Mercer, C. R.

C. R. Mercer, N. Rashidnia, K. Creath, “High data density temperature measurement for quasi steady-state flows,” Exp. Fluids 21, 11–16 (1996).
[CrossRef]

Merzkirch, W.

Petitjeans, P.

N. Rashidnia, R. Balasubramaniam, J. Kuang, P. Petitjeans, T. Maxworthy, “Measurement of the diffusion coefficient of miscible fluids using both interferometry and Weiners method,” Int. J. Thermophys. 22, 547–555 (2001).
[CrossRef]

P. Petitjeans, T. Maxworthy, “Miscible displacements in a capillary tube. Part 1: Experiments,” J. Fluid Mech. 326, 37–56 (1996).
[CrossRef]

Rashidnia, N.

N. Rashidnia, R. Balasubramaniam, J. Kuang, P. Petitjeans, T. Maxworthy, “Measurement of the diffusion coefficient of miscible fluids using both interferometry and Weiners method,” Int. J. Thermophys. 22, 547–555 (2001).
[CrossRef]

C. R. Mercer, N. Rashidnia, K. Creath, “High data density temperature measurement for quasi steady-state flows,” Exp. Fluids 21, 11–16 (1996).
[CrossRef]

N. Rashidnia, R. Balasubramaniam, “Optical measurement of concentration gradient near miscible interfaces,” presented at the ASME Proceedings of the Microgravity Transport Processes in Fluid, Thermal, Biological Materials Sciences II, Banff, Alberta, Canada, 30 Sept.–5 Oct. 2001, paper UEF: MTP-01-22.

Smartt, R. N.

R. N. Smartt, J. Strong, “Point-diffraction interferometer,” J. Opt. Soc. Am. 62, 737 (1972).

Sommerfeld, A.

A. Sommerfeld, Optics, Lectures in Physics IV (Academic, New York, 1964), p. 347).

Stewart, W. E.

R. B. Bird, W. E. Stewart, E. N. Lightfoot, Transport Phenomena (Wiley, New York, 1960), p. 558).

Strong, J.

R. N. Smartt, J. Strong, “Point-diffraction interferometer,” J. Opt. Soc. Am. 62, 737 (1972).

Appl. Opt. (1)

C. R. Acad. Sci. U.R.S.S. (1)

W. Linnik, “Simple interferometer for the investigation of optical systems,” C. R. Acad. Sci. U.R.S.S. 1, 208–210 (1933), abstract in Z. Instrumentenkd. 54, 463 (1934).

Exp. Fluids (1)

C. R. Mercer, N. Rashidnia, K. Creath, “High data density temperature measurement for quasi steady-state flows,” Exp. Fluids 21, 11–16 (1996).
[CrossRef]

Int. J. Thermophys. (1)

N. Rashidnia, R. Balasubramaniam, J. Kuang, P. Petitjeans, T. Maxworthy, “Measurement of the diffusion coefficient of miscible fluids using both interferometry and Weiners method,” Int. J. Thermophys. 22, 547–555 (2001).
[CrossRef]

J. Fluid Mech. (1)

P. Petitjeans, T. Maxworthy, “Miscible displacements in a capillary tube. Part 1: Experiments,” J. Fluid Mech. 326, 37–56 (1996).
[CrossRef]

J. Opt. Soc. Am. (1)

R. N. Smartt, J. Strong, “Point-diffraction interferometer,” J. Opt. Soc. Am. 62, 737 (1972).

Other (5)

C. R. Mercer, N. Rashidnia, “Common-path phase-stepped interferometer for fluid measurements,” in Proceedings of the Eight International Symposium of Flow Visualization, G. M. Carlomango, I. Grant, eds. (1998; available on CD-ROM from Optical Diagnostics in Engineering, http://www.ode-web.demon.co.uk ), pp. 256.1–256.9.

A. Sommerfeld, Optics, Lectures in Physics IV (Academic, New York, 1964), p. 347).

W. Merzkirch, Flow Visualization (Academic, New York, 1987), pp. 180–188).

R. B. Bird, W. E. Stewart, E. N. Lightfoot, Transport Phenomena (Wiley, New York, 1960), p. 558).

N. Rashidnia, R. Balasubramaniam, “Optical measurement of concentration gradient near miscible interfaces,” presented at the ASME Proceedings of the Microgravity Transport Processes in Fluid, Thermal, Biological Materials Sciences II, Banff, Alberta, Canada, 30 Sept.–5 Oct. 2001, paper UEF: MTP-01-22.

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Figures (4)

Fig. 1
Fig. 1

Schematic of (a) the CPI and (b) the expanded shearing unit.

Fig. 2
Fig. 2

Schematic of the quartz test container (10 mm × 10 mm × 45 mm).

Fig. 3
Fig. 3

Interferogram images near the interface of 10- and 1000-cS silicone oils at (a) 160, (b) 280, (c) 460, and (d) 1000 min after the fluids came into contact.

Fig. 4
Fig. 4

Typical trace of a fringe near the interface after the fluids came into contact. Data points used for calculation of the diffusion coefficient are also shown on the fringe.

Tables (1)

Tables Icon

Table 1 Comparison of Measured Diffusivities (unit of D is cm2/s)

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

Δlx, y=z1z2 nx, y+d2, zdz-z1z2 nx, y-d2, zdz.
Δlx, y=dz1z2y nx, y, zdz.
1λ Δlx, y=0, ±1, ±2, ,
1λ Δlx, y=±12, ±32, .
Δlx, y=dz1z2s nx, y, zdz+x sin α+y cos α.
Δlx, y=dLcos αny+sin αnx+x sin α+y cos α,
Δlx, y=dLβKcy+x+βy.
x-x0=-dLβny=-dLβKcy.
y-y0=-dLαnx=-dLαKcx,
D1-1/e=δ1-1/e2-16 1n1-1/et=δ1-1/e27.34t,
D1/e=δ1/e216t.

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