Abstract

The transmissivity of fogged glass to visible light incident on the dry side is studied with ray tracing to show that condensation can act as an optically thick antireflective coating. A new simulation method is described that uses symmetry relations and analytical expressions for the intersection of rays and surfaces to include all drop–drop and drop–surface interactions between an infinite number of drops. Angle of incidence, droplet contact angle, and surface coverage are varied. The simulation reveals that in the optimal contact angle range, dropwise condensation can decrease the reflectance of glass to below even that of glass coated with a water film.

© 2014 Optical Society of America

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References

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  1. I. V. Pollet, J. G. Pieters, and R. Verschoore, “Impact of water drops on the visible radiation transmittance of glazings under outside radiant conditions,” Sol. Energy 73, 327–335 (2002).
    [CrossRef]
  2. I. V. Pollet and J. G. Pieters, “Condensation and radiation transmittance of greenhouse cladding materials, part 3: results for glass plates and plastic films,” J. Agric. Eng. Res. 77, 419–428 (2000).
    [CrossRef]
  3. C. Hsieh and A. K. Rajvanshi, “The effect of dropwise condensation on glass solar properties,” Sol. Energy 19, 389–393 (1977).
    [CrossRef]
  4. I. V. Pollet, F. P. Thoen, and J. G. Pieters, “Solar energy availability in greenhouses as affected by condensation on cladding materials,” Renew. Energy 16, 769–772 (1999).
    [CrossRef]
  5. P. H. Heinemann and P. N. Walker, “Effects of greenhouse surface heating water on light transmission,” Trans. ASABE 30, 215–220 (1987).
  6. I. V. Pollet and J. G. Pieters, “Condensation and radiation transmittance of greenhouse cladding materials, part 2: results for a complete condensation cycle,” J. Agric. Eng. Res. 75, 65–72 (2000).
    [CrossRef]
  7. I. V. Pollet and J. G. Pieters, “Condensation and radiation transmittance of greenhouse cladding materials: part 1, laboratory measuring unit and performance,” J. Agric. Eng. Res. 74, 369–377 (1999).
    [CrossRef]
  8. I. V. Pollet, J. G. Pieters, J. Deltour, and R. Verschoore, “Diffusion of radiation transmitted through dry and condensate covered transmitting materials,” Sol. Energy Mater. Sol. Cells 86, 177–196 (2005).
    [CrossRef]
  9. B. J. Briscoe and K. P. Galvin, “The effect of surface fog on the transmittance of light,” Sol. Energy 46, 191–197 (1991).
    [CrossRef]
  10. K. McCree, “Test of current definitions of photosynthetically active radiation against leaf photosynthesis data,” Agric. Meteorol. 10, 443–453 (1972).
  11. A. Jaffrin and A. Morisot, “Role of structure, dirt and condensation on the light transmission of greenhouse covers,” Plasticulture 101, 33–44 (1994).
  12. I. V. Pollet and J. G. Pieters, “Forward scattering induced by water drops on a transmissive substrate,” Appl. Opt. 41, 5122–5129 (2002).
    [CrossRef]
  13. S. N. Kasarova, N. G. Sultanova, C. D. Ivanov, and I. D. Nikolov, “Analysis of the dispersion of optical plastic materials,” Opt. Mater. 29, 1481–1490 (2007).
    [CrossRef]
  14. J. Pieters, J. Deltour, and M. Debruyckere, “Light transmission through condensation on glass and polyethylene,” Agricul. Forest Meteorol. 85, 51–62 (1997).
    [CrossRef]
  15. J. Pieters, “Interaction effects in simulating the light transmission through condensation drops on greenhouse covers,” Trans. ASAE 40, 1463–1465 (1997).
    [CrossRef]
  16. W. R. Blevin, “Corrections in optical pyrometry and photometry for the refractive index of air,” Metrologia 8, 146–147 (1972).
    [CrossRef]
  17. G. M. Hale and M. R. Querry, “Optical constants of water in the 200-nm to 200-mu-m wavelength region,” Appl. Opt. 12, 555–563 (1973).
    [CrossRef]
  18. D. H. Eberly, “Intersection of a linear component and a sphere,” in 3D Game Engine Design: A Practical Approach (Academic, 2001), pp. 171–172.
  19. R. Siegel and J. Howell, Thermal Radiation Heat Transfer (Hemisphere, 1972).

2007

S. N. Kasarova, N. G. Sultanova, C. D. Ivanov, and I. D. Nikolov, “Analysis of the dispersion of optical plastic materials,” Opt. Mater. 29, 1481–1490 (2007).
[CrossRef]

2005

I. V. Pollet, J. G. Pieters, J. Deltour, and R. Verschoore, “Diffusion of radiation transmitted through dry and condensate covered transmitting materials,” Sol. Energy Mater. Sol. Cells 86, 177–196 (2005).
[CrossRef]

2002

I. V. Pollet, J. G. Pieters, and R. Verschoore, “Impact of water drops on the visible radiation transmittance of glazings under outside radiant conditions,” Sol. Energy 73, 327–335 (2002).
[CrossRef]

I. V. Pollet and J. G. Pieters, “Forward scattering induced by water drops on a transmissive substrate,” Appl. Opt. 41, 5122–5129 (2002).
[CrossRef]

2000

I. V. Pollet and J. G. Pieters, “Condensation and radiation transmittance of greenhouse cladding materials, part 3: results for glass plates and plastic films,” J. Agric. Eng. Res. 77, 419–428 (2000).
[CrossRef]

I. V. Pollet and J. G. Pieters, “Condensation and radiation transmittance of greenhouse cladding materials, part 2: results for a complete condensation cycle,” J. Agric. Eng. Res. 75, 65–72 (2000).
[CrossRef]

1999

I. V. Pollet and J. G. Pieters, “Condensation and radiation transmittance of greenhouse cladding materials: part 1, laboratory measuring unit and performance,” J. Agric. Eng. Res. 74, 369–377 (1999).
[CrossRef]

I. V. Pollet, F. P. Thoen, and J. G. Pieters, “Solar energy availability in greenhouses as affected by condensation on cladding materials,” Renew. Energy 16, 769–772 (1999).
[CrossRef]

1997

J. Pieters, J. Deltour, and M. Debruyckere, “Light transmission through condensation on glass and polyethylene,” Agricul. Forest Meteorol. 85, 51–62 (1997).
[CrossRef]

J. Pieters, “Interaction effects in simulating the light transmission through condensation drops on greenhouse covers,” Trans. ASAE 40, 1463–1465 (1997).
[CrossRef]

1994

A. Jaffrin and A. Morisot, “Role of structure, dirt and condensation on the light transmission of greenhouse covers,” Plasticulture 101, 33–44 (1994).

1991

B. J. Briscoe and K. P. Galvin, “The effect of surface fog on the transmittance of light,” Sol. Energy 46, 191–197 (1991).
[CrossRef]

1987

P. H. Heinemann and P. N. Walker, “Effects of greenhouse surface heating water on light transmission,” Trans. ASABE 30, 215–220 (1987).

1977

C. Hsieh and A. K. Rajvanshi, “The effect of dropwise condensation on glass solar properties,” Sol. Energy 19, 389–393 (1977).
[CrossRef]

1973

1972

W. R. Blevin, “Corrections in optical pyrometry and photometry for the refractive index of air,” Metrologia 8, 146–147 (1972).
[CrossRef]

K. McCree, “Test of current definitions of photosynthetically active radiation against leaf photosynthesis data,” Agric. Meteorol. 10, 443–453 (1972).

Blevin, W. R.

W. R. Blevin, “Corrections in optical pyrometry and photometry for the refractive index of air,” Metrologia 8, 146–147 (1972).
[CrossRef]

Briscoe, B. J.

B. J. Briscoe and K. P. Galvin, “The effect of surface fog on the transmittance of light,” Sol. Energy 46, 191–197 (1991).
[CrossRef]

Debruyckere, M.

J. Pieters, J. Deltour, and M. Debruyckere, “Light transmission through condensation on glass and polyethylene,” Agricul. Forest Meteorol. 85, 51–62 (1997).
[CrossRef]

Deltour, J.

I. V. Pollet, J. G. Pieters, J. Deltour, and R. Verschoore, “Diffusion of radiation transmitted through dry and condensate covered transmitting materials,” Sol. Energy Mater. Sol. Cells 86, 177–196 (2005).
[CrossRef]

J. Pieters, J. Deltour, and M. Debruyckere, “Light transmission through condensation on glass and polyethylene,” Agricul. Forest Meteorol. 85, 51–62 (1997).
[CrossRef]

Eberly, D. H.

D. H. Eberly, “Intersection of a linear component and a sphere,” in 3D Game Engine Design: A Practical Approach (Academic, 2001), pp. 171–172.

Galvin, K. P.

B. J. Briscoe and K. P. Galvin, “The effect of surface fog on the transmittance of light,” Sol. Energy 46, 191–197 (1991).
[CrossRef]

Hale, G. M.

Heinemann, P. H.

P. H. Heinemann and P. N. Walker, “Effects of greenhouse surface heating water on light transmission,” Trans. ASABE 30, 215–220 (1987).

Howell, J.

R. Siegel and J. Howell, Thermal Radiation Heat Transfer (Hemisphere, 1972).

Hsieh, C.

C. Hsieh and A. K. Rajvanshi, “The effect of dropwise condensation on glass solar properties,” Sol. Energy 19, 389–393 (1977).
[CrossRef]

Ivanov, C. D.

S. N. Kasarova, N. G. Sultanova, C. D. Ivanov, and I. D. Nikolov, “Analysis of the dispersion of optical plastic materials,” Opt. Mater. 29, 1481–1490 (2007).
[CrossRef]

Jaffrin, A.

A. Jaffrin and A. Morisot, “Role of structure, dirt and condensation on the light transmission of greenhouse covers,” Plasticulture 101, 33–44 (1994).

Kasarova, S. N.

S. N. Kasarova, N. G. Sultanova, C. D. Ivanov, and I. D. Nikolov, “Analysis of the dispersion of optical plastic materials,” Opt. Mater. 29, 1481–1490 (2007).
[CrossRef]

McCree, K.

K. McCree, “Test of current definitions of photosynthetically active radiation against leaf photosynthesis data,” Agric. Meteorol. 10, 443–453 (1972).

Morisot, A.

A. Jaffrin and A. Morisot, “Role of structure, dirt and condensation on the light transmission of greenhouse covers,” Plasticulture 101, 33–44 (1994).

Nikolov, I. D.

S. N. Kasarova, N. G. Sultanova, C. D. Ivanov, and I. D. Nikolov, “Analysis of the dispersion of optical plastic materials,” Opt. Mater. 29, 1481–1490 (2007).
[CrossRef]

Pieters, J.

J. Pieters, J. Deltour, and M. Debruyckere, “Light transmission through condensation on glass and polyethylene,” Agricul. Forest Meteorol. 85, 51–62 (1997).
[CrossRef]

J. Pieters, “Interaction effects in simulating the light transmission through condensation drops on greenhouse covers,” Trans. ASAE 40, 1463–1465 (1997).
[CrossRef]

Pieters, J. G.

I. V. Pollet, J. G. Pieters, J. Deltour, and R. Verschoore, “Diffusion of radiation transmitted through dry and condensate covered transmitting materials,” Sol. Energy Mater. Sol. Cells 86, 177–196 (2005).
[CrossRef]

I. V. Pollet and J. G. Pieters, “Forward scattering induced by water drops on a transmissive substrate,” Appl. Opt. 41, 5122–5129 (2002).
[CrossRef]

I. V. Pollet, J. G. Pieters, and R. Verschoore, “Impact of water drops on the visible radiation transmittance of glazings under outside radiant conditions,” Sol. Energy 73, 327–335 (2002).
[CrossRef]

I. V. Pollet and J. G. Pieters, “Condensation and radiation transmittance of greenhouse cladding materials, part 2: results for a complete condensation cycle,” J. Agric. Eng. Res. 75, 65–72 (2000).
[CrossRef]

I. V. Pollet and J. G. Pieters, “Condensation and radiation transmittance of greenhouse cladding materials, part 3: results for glass plates and plastic films,” J. Agric. Eng. Res. 77, 419–428 (2000).
[CrossRef]

I. V. Pollet and J. G. Pieters, “Condensation and radiation transmittance of greenhouse cladding materials: part 1, laboratory measuring unit and performance,” J. Agric. Eng. Res. 74, 369–377 (1999).
[CrossRef]

I. V. Pollet, F. P. Thoen, and J. G. Pieters, “Solar energy availability in greenhouses as affected by condensation on cladding materials,” Renew. Energy 16, 769–772 (1999).
[CrossRef]

Pollet, I. V.

I. V. Pollet, J. G. Pieters, J. Deltour, and R. Verschoore, “Diffusion of radiation transmitted through dry and condensate covered transmitting materials,” Sol. Energy Mater. Sol. Cells 86, 177–196 (2005).
[CrossRef]

I. V. Pollet and J. G. Pieters, “Forward scattering induced by water drops on a transmissive substrate,” Appl. Opt. 41, 5122–5129 (2002).
[CrossRef]

I. V. Pollet, J. G. Pieters, and R. Verschoore, “Impact of water drops on the visible radiation transmittance of glazings under outside radiant conditions,” Sol. Energy 73, 327–335 (2002).
[CrossRef]

I. V. Pollet and J. G. Pieters, “Condensation and radiation transmittance of greenhouse cladding materials, part 2: results for a complete condensation cycle,” J. Agric. Eng. Res. 75, 65–72 (2000).
[CrossRef]

I. V. Pollet and J. G. Pieters, “Condensation and radiation transmittance of greenhouse cladding materials, part 3: results for glass plates and plastic films,” J. Agric. Eng. Res. 77, 419–428 (2000).
[CrossRef]

I. V. Pollet and J. G. Pieters, “Condensation and radiation transmittance of greenhouse cladding materials: part 1, laboratory measuring unit and performance,” J. Agric. Eng. Res. 74, 369–377 (1999).
[CrossRef]

I. V. Pollet, F. P. Thoen, and J. G. Pieters, “Solar energy availability in greenhouses as affected by condensation on cladding materials,” Renew. Energy 16, 769–772 (1999).
[CrossRef]

Querry, M. R.

Rajvanshi, A. K.

C. Hsieh and A. K. Rajvanshi, “The effect of dropwise condensation on glass solar properties,” Sol. Energy 19, 389–393 (1977).
[CrossRef]

Siegel, R.

R. Siegel and J. Howell, Thermal Radiation Heat Transfer (Hemisphere, 1972).

Sultanova, N. G.

S. N. Kasarova, N. G. Sultanova, C. D. Ivanov, and I. D. Nikolov, “Analysis of the dispersion of optical plastic materials,” Opt. Mater. 29, 1481–1490 (2007).
[CrossRef]

Thoen, F. P.

I. V. Pollet, F. P. Thoen, and J. G. Pieters, “Solar energy availability in greenhouses as affected by condensation on cladding materials,” Renew. Energy 16, 769–772 (1999).
[CrossRef]

Verschoore, R.

I. V. Pollet, J. G. Pieters, J. Deltour, and R. Verschoore, “Diffusion of radiation transmitted through dry and condensate covered transmitting materials,” Sol. Energy Mater. Sol. Cells 86, 177–196 (2005).
[CrossRef]

I. V. Pollet, J. G. Pieters, and R. Verschoore, “Impact of water drops on the visible radiation transmittance of glazings under outside radiant conditions,” Sol. Energy 73, 327–335 (2002).
[CrossRef]

Walker, P. N.

P. H. Heinemann and P. N. Walker, “Effects of greenhouse surface heating water on light transmission,” Trans. ASABE 30, 215–220 (1987).

Agric. Meteorol.

K. McCree, “Test of current definitions of photosynthetically active radiation against leaf photosynthesis data,” Agric. Meteorol. 10, 443–453 (1972).

Agricul. Forest Meteorol.

J. Pieters, J. Deltour, and M. Debruyckere, “Light transmission through condensation on glass and polyethylene,” Agricul. Forest Meteorol. 85, 51–62 (1997).
[CrossRef]

Appl. Opt.

J. Agric. Eng. Res.

I. V. Pollet and J. G. Pieters, “Condensation and radiation transmittance of greenhouse cladding materials, part 3: results for glass plates and plastic films,” J. Agric. Eng. Res. 77, 419–428 (2000).
[CrossRef]

I. V. Pollet and J. G. Pieters, “Condensation and radiation transmittance of greenhouse cladding materials, part 2: results for a complete condensation cycle,” J. Agric. Eng. Res. 75, 65–72 (2000).
[CrossRef]

I. V. Pollet and J. G. Pieters, “Condensation and radiation transmittance of greenhouse cladding materials: part 1, laboratory measuring unit and performance,” J. Agric. Eng. Res. 74, 369–377 (1999).
[CrossRef]

Metrologia

W. R. Blevin, “Corrections in optical pyrometry and photometry for the refractive index of air,” Metrologia 8, 146–147 (1972).
[CrossRef]

Opt. Mater.

S. N. Kasarova, N. G. Sultanova, C. D. Ivanov, and I. D. Nikolov, “Analysis of the dispersion of optical plastic materials,” Opt. Mater. 29, 1481–1490 (2007).
[CrossRef]

Plasticulture

A. Jaffrin and A. Morisot, “Role of structure, dirt and condensation on the light transmission of greenhouse covers,” Plasticulture 101, 33–44 (1994).

Renew. Energy

I. V. Pollet, F. P. Thoen, and J. G. Pieters, “Solar energy availability in greenhouses as affected by condensation on cladding materials,” Renew. Energy 16, 769–772 (1999).
[CrossRef]

Sol. Energy

C. Hsieh and A. K. Rajvanshi, “The effect of dropwise condensation on glass solar properties,” Sol. Energy 19, 389–393 (1977).
[CrossRef]

I. V. Pollet, J. G. Pieters, and R. Verschoore, “Impact of water drops on the visible radiation transmittance of glazings under outside radiant conditions,” Sol. Energy 73, 327–335 (2002).
[CrossRef]

B. J. Briscoe and K. P. Galvin, “The effect of surface fog on the transmittance of light,” Sol. Energy 46, 191–197 (1991).
[CrossRef]

Sol. Energy Mater. Sol. Cells

I. V. Pollet, J. G. Pieters, J. Deltour, and R. Verschoore, “Diffusion of radiation transmitted through dry and condensate covered transmitting materials,” Sol. Energy Mater. Sol. Cells 86, 177–196 (2005).
[CrossRef]

Trans. ASABE

P. H. Heinemann and P. N. Walker, “Effects of greenhouse surface heating water on light transmission,” Trans. ASABE 30, 215–220 (1987).

Trans. ASAE

J. Pieters, “Interaction effects in simulating the light transmission through condensation drops on greenhouse covers,” Trans. ASAE 40, 1463–1465 (1997).
[CrossRef]

Other

D. H. Eberly, “Intersection of a linear component and a sphere,” in 3D Game Engine Design: A Practical Approach (Academic, 2001), pp. 171–172.

R. Siegel and J. Howell, Thermal Radiation Heat Transfer (Hemisphere, 1972).

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Figures (9)

Fig. 1.
Fig. 1.

(a) Solid model of the simulated geometry with a single droplet slice removed and light incident on the dry side. (b) A portion of the simulated infinite plane of evenly-spaced droplets, with lines of symmetry shown. (c) Droplet slice used in ray tracing, with perfectly mirrored sidewalls, showing equilibrium contact angle θe and angle of incidence θi.

Fig. 2.
Fig. 2.

Comparison of simulated results with the experimental bidirectional transmission distribution function (BTDF) from Pollet and Pieters [12] of wet glass at normal incidence.

Fig. 3.
Fig. 3.

To illustrate ray behaviors, the fraction of rays scattered into each degree of polar angle is shown for visible light at 40° incidence and 50.9° contact angle. 0° indicates transmission normal to glass. Peaks occur at angles A, B, and C. The inset graphic shows the dominant ray behaviors, with labels A–D corresponding to features in the plot.

Fig. 4.
Fig. 4.

Variation of reflectivity with incident angle for a variety of contact angles at 55% surface coverage plus dry glass and glass with a water film.

Fig. 5.
Fig. 5.

Left: normally incident radiation experiences total internal reflection at the edges of the droplet and reflects back. Right: radiation is incident at a moderate angle such that the most steeply angled part of the droplet is in shadow, reducing the overall reflectance.

Fig. 6.
Fig. 6.

Variation of reflectivity with contact angle for various angles of incidence at 55% surface coverage.

Fig. 7.
Fig. 7.

Illustration of how droplets’ shape gives rays reflected off the water–air interface a second chance to transmit and enables transmittance to exceed that of glass with a water film.

Fig. 8.
Fig. 8.

Reflectivity at normal incidence of fogged glass with 55% and 90% surface coverage is compared to that of dry glass and glass with a water film to show the decline in reflectivity around 25° due to total internal reflection-aided transmission. At 90% coverage and contact angles between 26° and 49°, reflectivity is lower than that of glass with a water film.

Fig. 9.
Fig. 9.

Reflectivity as a function of surface coverage at normal incidence. As coverage is reduced, reflectivity approaches the dry value.

Equations (1)

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θe(0°)>12sin1(ne/nw)=24.4°.

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