Abstract

Properties of large scale water lenses for solar concentration were investigated. These lenses were built from readily available materials, normal tap water and hyper-elastic linear low density polyethylene foil. Exposed to sunlight, the focal lengths and light intensities in the focal spot were measured and calculated. Their optical properties were modeled with a raytracing software based on the lens shape. We have achieved a good match of experimental and theoretical data by considering wavelength dependent concentration factor, absorption and focal length. The change in light concentration as a function of water volume was examined via the resulting load on the foil and the corresponding change of shape. The latter was extracted from images and modeled by a finite element simulation.

© 2015 Optical Society of America

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  1. H. Ren and S. T. Wu, “Variable-focus liquid lens by changing aperture,” Appl. Phys. Lett. 86, 211107 (2005).
    [Crossref]
  2. Q. Yang, P. Kobrin, C. Seabury, S. Narayanaswamy, and W. Christian, “Mechanical modeling of fluid-driven polymer lenses,” Appl. Opt. 47, 3658–3668 (2008).
    [Crossref] [PubMed]
  3. N. T. Nguyen, “Micro-optofluidic lenses: a review,” Biomicrofluidics,  4, 031501 (2010).
    [Crossref] [PubMed]
  4. H. Ren, D. Fox, P. A. Anderson, B. Wu, and S. T. Wu, “Tunable-focus liquid lens controlled using a servo motor,” Opt. Express 14, 8031–8036 (2006).
    [Crossref] [PubMed]
  5. H. Ren and S. T. Wu, “Variable-focus liquid lens,” Opt. Express 15, 5931–5936 (2007).
    [Crossref] [PubMed]
  6. A. S. Alvarado, J. G. García, F. I. Jiménez, M. C. García, V. M. C. Martinez, and R. Patrick, “Simulating the functioning of variable focus length liquid filled lenses using the finite element method (FEM),” Int. J. Light Electron Opt. 124, 1003–1010 (2013).
    [Crossref]
  7. L. Wang, H. Oku, and M. Ishikawa, “An improved low-optical-power variable focus lens with a large aperture,” Opt. Express 22, 19448–19456 (2014).
    [Crossref] [PubMed]
  8. N. Sugiura and S. Morita, “Variable-focus liquid-filled optical lens,” Appl. Opt. 32, 4181–4186 (1993).
    [Crossref] [PubMed]
  9. F. Duerr, Y. Meuret, and H. Thienpont, “Miniaturization of fresnel lenses for solar concentration: a quantitative investigation,” Appl. Opt. 49, 2339–2346 (2010).
    [Crossref] [PubMed]
  10. G. I. Kweon and C. H. Kim, “Aspherical lens design by using a numerical analysis,” J. Korean Phys. Soc. 51, 93–103 (2007).
    [Crossref]
  11. T. Grindley and J. E. Lind, “PVT properties of water and mercury,” J. Chem. Phys. 54, 3983–3989 (1971).
    [Crossref]
  12. P. Schiebener, J. Straub, J. M. H. L. Sengers, and J. S. Gallagehr, “Refractive index of water and steam as function of wavelength, temperature and density,” J Phys. Chem. Ref. Data 19, 677–717 (1990).
    [Crossref]
  13. A. N. Bashkatov and E. A. Genina, “Water refractive index in dependence on temperature and wavelength : a simple approximation,” Proc. SPIE 5068, 393–395 (2003).
    [Crossref]
  14. S. E. Salih, A. F. Hamood, and A. H. A. Alsalam, “Comparison of the characteristics of LDPE : PP and HDPE : PP polymer blends,” Mod. Appl. Sci. 7, 33–42 (2013).
    [Crossref]
  15. B. Kolgjini, G. Schoukens, and P. Kiekens, “Three-phase characterization of uniaxially stretched linear low-density polyethylene,” Int. J. Polym. Sci. 2011, 731708 (2011).
    [Crossref]
  16. M. Delin, R. W. Rychwalski, M. J. Kubát, and J. Kubát, “Volume changes during stress relaxation in polyethylene,” Rheol. Acta 34, 182–195 (1995).
    [Crossref]
  17. D. Nwabunma and T. Kyu, Polyolefin Blends (John Wiley & Sons Inc., 2008), Chap. 3.
  18. A. Durmus, A. Kaşgöz, and C. W. Macosko, “Mechanical properties of linear low-density polyethylene (LLDPE)/clay nanocomposites: estimation of aspect ratio and interfacial strength by composite models,” J. Macromol. Sci. Part-B: Phys. 47, 608–619 (2008).
    [Crossref]
  19. P. A. L. S. Martins, R. M. N. Jorge, and A. J. M. Ferreira, “A comparative study of several material models for prediction of hyperelastic properties: application to silicone-rubber and soft tissues,” Strain 42, 135–147 (2006).
    [Crossref]
  20. D. C. Pamplona and D. E. J. S. Mota, “Numerical and experimental analysis of inflating a circular hyperelastic membrane over a rigid and elastic foundation,” Int. J. Mech. Sci. 65, 18–23 (2012).
    [Crossref]
  21. G. Tamadapu and A. DasGupta, “Finite inflation analysis of a hyperelastic toroidal membrane of initially circular cross-section,” Int. J. Non-Linear Mech. 49, 31–39 (2013).
    [Crossref]
  22. J. C. Selby and M. A. Shannon, “Inflation of a circular elastomeric membrane into a horizontally semi-infinite liquid reservoir of finite vertical depth: Quasi-static deformation model,” Int. J. Eng. Sci. 47, 700–717 (2009).
    [Crossref]
  23. A. Patil and A. DasGupta, “Finite inflation of an initially stretched hyperelastic circular membrane,” Eur. J. Mech. A-Solids 41, 28–36 (2013).
    [Crossref]
  24. J. D. Humphrey, “Computer methods in membrane biomechanics,” Comput. Method Biomech. Biomed. Eng. 1, 171–210 (1998).
    [Crossref]
  25. J. C. Selby and M. A. Shannon, “Inflation of a circular elastomeric membrane into a horizontally semi-infinite liquid reservoir of finite vertical depth: estimation of material parameters from volume–pressure data,” Int. J. Eng. Sci. 47, 718–734 (2009).
    [Crossref]
  26. D. Pamplona, P. Gonçalves, M. Davidovich, and H. I. Weber, “Finite axisymmetric deformations of an initially stressed fluid- filled cylindrical membrane,” Int. J. Solid Struct. 38, 2033–2047, (2001).
    [Crossref]
  27. A. P. S. Selvadurai and M. Shi, “Fluid pressure loading of a hyperelastic membrane,” Int. J. Non-Linear Mech. 47, 228–239 (2012).
    [Crossref]
  28. D. M. Haughton, “Axisymmetric elastic membranes subjected to fluid loading,” IMA J. Appl. Math. 56, 303–320 (1996).
    [Crossref]
  29. D. L. Boyer and W. Gutkowski, “Liquid filled membranes,” Int. J. Non-Linear Mech. 5, 299–310 (1970).
    [Crossref]
  30. A. M. Kolesnikov, “Equilibrium of an elastic spherical shell filled with a heavy fluid under pressure,” J Appl. Mech. Tech. Phys. 51, 744–750 (2010).
    [Crossref]

2014 (1)

2013 (4)

A. S. Alvarado, J. G. García, F. I. Jiménez, M. C. García, V. M. C. Martinez, and R. Patrick, “Simulating the functioning of variable focus length liquid filled lenses using the finite element method (FEM),” Int. J. Light Electron Opt. 124, 1003–1010 (2013).
[Crossref]

S. E. Salih, A. F. Hamood, and A. H. A. Alsalam, “Comparison of the characteristics of LDPE : PP and HDPE : PP polymer blends,” Mod. Appl. Sci. 7, 33–42 (2013).
[Crossref]

G. Tamadapu and A. DasGupta, “Finite inflation analysis of a hyperelastic toroidal membrane of initially circular cross-section,” Int. J. Non-Linear Mech. 49, 31–39 (2013).
[Crossref]

A. Patil and A. DasGupta, “Finite inflation of an initially stretched hyperelastic circular membrane,” Eur. J. Mech. A-Solids 41, 28–36 (2013).
[Crossref]

2012 (2)

A. P. S. Selvadurai and M. Shi, “Fluid pressure loading of a hyperelastic membrane,” Int. J. Non-Linear Mech. 47, 228–239 (2012).
[Crossref]

D. C. Pamplona and D. E. J. S. Mota, “Numerical and experimental analysis of inflating a circular hyperelastic membrane over a rigid and elastic foundation,” Int. J. Mech. Sci. 65, 18–23 (2012).
[Crossref]

2011 (1)

B. Kolgjini, G. Schoukens, and P. Kiekens, “Three-phase characterization of uniaxially stretched linear low-density polyethylene,” Int. J. Polym. Sci. 2011, 731708 (2011).
[Crossref]

2010 (3)

N. T. Nguyen, “Micro-optofluidic lenses: a review,” Biomicrofluidics,  4, 031501 (2010).
[Crossref] [PubMed]

A. M. Kolesnikov, “Equilibrium of an elastic spherical shell filled with a heavy fluid under pressure,” J Appl. Mech. Tech. Phys. 51, 744–750 (2010).
[Crossref]

F. Duerr, Y. Meuret, and H. Thienpont, “Miniaturization of fresnel lenses for solar concentration: a quantitative investigation,” Appl. Opt. 49, 2339–2346 (2010).
[Crossref] [PubMed]

2009 (2)

J. C. Selby and M. A. Shannon, “Inflation of a circular elastomeric membrane into a horizontally semi-infinite liquid reservoir of finite vertical depth: estimation of material parameters from volume–pressure data,” Int. J. Eng. Sci. 47, 718–734 (2009).
[Crossref]

J. C. Selby and M. A. Shannon, “Inflation of a circular elastomeric membrane into a horizontally semi-infinite liquid reservoir of finite vertical depth: Quasi-static deformation model,” Int. J. Eng. Sci. 47, 700–717 (2009).
[Crossref]

2008 (2)

A. Durmus, A. Kaşgöz, and C. W. Macosko, “Mechanical properties of linear low-density polyethylene (LLDPE)/clay nanocomposites: estimation of aspect ratio and interfacial strength by composite models,” J. Macromol. Sci. Part-B: Phys. 47, 608–619 (2008).
[Crossref]

Q. Yang, P. Kobrin, C. Seabury, S. Narayanaswamy, and W. Christian, “Mechanical modeling of fluid-driven polymer lenses,” Appl. Opt. 47, 3658–3668 (2008).
[Crossref] [PubMed]

2007 (2)

H. Ren and S. T. Wu, “Variable-focus liquid lens,” Opt. Express 15, 5931–5936 (2007).
[Crossref] [PubMed]

G. I. Kweon and C. H. Kim, “Aspherical lens design by using a numerical analysis,” J. Korean Phys. Soc. 51, 93–103 (2007).
[Crossref]

2006 (2)

P. A. L. S. Martins, R. M. N. Jorge, and A. J. M. Ferreira, “A comparative study of several material models for prediction of hyperelastic properties: application to silicone-rubber and soft tissues,” Strain 42, 135–147 (2006).
[Crossref]

H. Ren, D. Fox, P. A. Anderson, B. Wu, and S. T. Wu, “Tunable-focus liquid lens controlled using a servo motor,” Opt. Express 14, 8031–8036 (2006).
[Crossref] [PubMed]

2005 (1)

H. Ren and S. T. Wu, “Variable-focus liquid lens by changing aperture,” Appl. Phys. Lett. 86, 211107 (2005).
[Crossref]

2003 (1)

A. N. Bashkatov and E. A. Genina, “Water refractive index in dependence on temperature and wavelength : a simple approximation,” Proc. SPIE 5068, 393–395 (2003).
[Crossref]

2001 (1)

D. Pamplona, P. Gonçalves, M. Davidovich, and H. I. Weber, “Finite axisymmetric deformations of an initially stressed fluid- filled cylindrical membrane,” Int. J. Solid Struct. 38, 2033–2047, (2001).
[Crossref]

1998 (1)

J. D. Humphrey, “Computer methods in membrane biomechanics,” Comput. Method Biomech. Biomed. Eng. 1, 171–210 (1998).
[Crossref]

1996 (1)

D. M. Haughton, “Axisymmetric elastic membranes subjected to fluid loading,” IMA J. Appl. Math. 56, 303–320 (1996).
[Crossref]

1995 (1)

M. Delin, R. W. Rychwalski, M. J. Kubát, and J. Kubát, “Volume changes during stress relaxation in polyethylene,” Rheol. Acta 34, 182–195 (1995).
[Crossref]

1993 (1)

1990 (1)

P. Schiebener, J. Straub, J. M. H. L. Sengers, and J. S. Gallagehr, “Refractive index of water and steam as function of wavelength, temperature and density,” J Phys. Chem. Ref. Data 19, 677–717 (1990).
[Crossref]

1971 (1)

T. Grindley and J. E. Lind, “PVT properties of water and mercury,” J. Chem. Phys. 54, 3983–3989 (1971).
[Crossref]

1970 (1)

D. L. Boyer and W. Gutkowski, “Liquid filled membranes,” Int. J. Non-Linear Mech. 5, 299–310 (1970).
[Crossref]

Alsalam, A. H. A.

S. E. Salih, A. F. Hamood, and A. H. A. Alsalam, “Comparison of the characteristics of LDPE : PP and HDPE : PP polymer blends,” Mod. Appl. Sci. 7, 33–42 (2013).
[Crossref]

Alvarado, A. S.

A. S. Alvarado, J. G. García, F. I. Jiménez, M. C. García, V. M. C. Martinez, and R. Patrick, “Simulating the functioning of variable focus length liquid filled lenses using the finite element method (FEM),” Int. J. Light Electron Opt. 124, 1003–1010 (2013).
[Crossref]

Anderson, P. A.

Bashkatov, A. N.

A. N. Bashkatov and E. A. Genina, “Water refractive index in dependence on temperature and wavelength : a simple approximation,” Proc. SPIE 5068, 393–395 (2003).
[Crossref]

Boyer, D. L.

D. L. Boyer and W. Gutkowski, “Liquid filled membranes,” Int. J. Non-Linear Mech. 5, 299–310 (1970).
[Crossref]

Christian, W.

DasGupta, A.

G. Tamadapu and A. DasGupta, “Finite inflation analysis of a hyperelastic toroidal membrane of initially circular cross-section,” Int. J. Non-Linear Mech. 49, 31–39 (2013).
[Crossref]

A. Patil and A. DasGupta, “Finite inflation of an initially stretched hyperelastic circular membrane,” Eur. J. Mech. A-Solids 41, 28–36 (2013).
[Crossref]

Davidovich, M.

D. Pamplona, P. Gonçalves, M. Davidovich, and H. I. Weber, “Finite axisymmetric deformations of an initially stressed fluid- filled cylindrical membrane,” Int. J. Solid Struct. 38, 2033–2047, (2001).
[Crossref]

Delin, M.

M. Delin, R. W. Rychwalski, M. J. Kubát, and J. Kubát, “Volume changes during stress relaxation in polyethylene,” Rheol. Acta 34, 182–195 (1995).
[Crossref]

Duerr, F.

Durmus, A.

A. Durmus, A. Kaşgöz, and C. W. Macosko, “Mechanical properties of linear low-density polyethylene (LLDPE)/clay nanocomposites: estimation of aspect ratio and interfacial strength by composite models,” J. Macromol. Sci. Part-B: Phys. 47, 608–619 (2008).
[Crossref]

Ferreira, A. J. M.

P. A. L. S. Martins, R. M. N. Jorge, and A. J. M. Ferreira, “A comparative study of several material models for prediction of hyperelastic properties: application to silicone-rubber and soft tissues,” Strain 42, 135–147 (2006).
[Crossref]

Fox, D.

Gallagehr, J. S.

P. Schiebener, J. Straub, J. M. H. L. Sengers, and J. S. Gallagehr, “Refractive index of water and steam as function of wavelength, temperature and density,” J Phys. Chem. Ref. Data 19, 677–717 (1990).
[Crossref]

García, J. G.

A. S. Alvarado, J. G. García, F. I. Jiménez, M. C. García, V. M. C. Martinez, and R. Patrick, “Simulating the functioning of variable focus length liquid filled lenses using the finite element method (FEM),” Int. J. Light Electron Opt. 124, 1003–1010 (2013).
[Crossref]

García, M. C.

A. S. Alvarado, J. G. García, F. I. Jiménez, M. C. García, V. M. C. Martinez, and R. Patrick, “Simulating the functioning of variable focus length liquid filled lenses using the finite element method (FEM),” Int. J. Light Electron Opt. 124, 1003–1010 (2013).
[Crossref]

Genina, E. A.

A. N. Bashkatov and E. A. Genina, “Water refractive index in dependence on temperature and wavelength : a simple approximation,” Proc. SPIE 5068, 393–395 (2003).
[Crossref]

Gonçalves, P.

D. Pamplona, P. Gonçalves, M. Davidovich, and H. I. Weber, “Finite axisymmetric deformations of an initially stressed fluid- filled cylindrical membrane,” Int. J. Solid Struct. 38, 2033–2047, (2001).
[Crossref]

Grindley, T.

T. Grindley and J. E. Lind, “PVT properties of water and mercury,” J. Chem. Phys. 54, 3983–3989 (1971).
[Crossref]

Gutkowski, W.

D. L. Boyer and W. Gutkowski, “Liquid filled membranes,” Int. J. Non-Linear Mech. 5, 299–310 (1970).
[Crossref]

Hamood, A. F.

S. E. Salih, A. F. Hamood, and A. H. A. Alsalam, “Comparison of the characteristics of LDPE : PP and HDPE : PP polymer blends,” Mod. Appl. Sci. 7, 33–42 (2013).
[Crossref]

Haughton, D. M.

D. M. Haughton, “Axisymmetric elastic membranes subjected to fluid loading,” IMA J. Appl. Math. 56, 303–320 (1996).
[Crossref]

Humphrey, J. D.

J. D. Humphrey, “Computer methods in membrane biomechanics,” Comput. Method Biomech. Biomed. Eng. 1, 171–210 (1998).
[Crossref]

Ishikawa, M.

Jiménez, F. I.

A. S. Alvarado, J. G. García, F. I. Jiménez, M. C. García, V. M. C. Martinez, and R. Patrick, “Simulating the functioning of variable focus length liquid filled lenses using the finite element method (FEM),” Int. J. Light Electron Opt. 124, 1003–1010 (2013).
[Crossref]

Jorge, R. M. N.

P. A. L. S. Martins, R. M. N. Jorge, and A. J. M. Ferreira, “A comparative study of several material models for prediction of hyperelastic properties: application to silicone-rubber and soft tissues,” Strain 42, 135–147 (2006).
[Crossref]

Kasgöz, A.

A. Durmus, A. Kaşgöz, and C. W. Macosko, “Mechanical properties of linear low-density polyethylene (LLDPE)/clay nanocomposites: estimation of aspect ratio and interfacial strength by composite models,” J. Macromol. Sci. Part-B: Phys. 47, 608–619 (2008).
[Crossref]

Kiekens, P.

B. Kolgjini, G. Schoukens, and P. Kiekens, “Three-phase characterization of uniaxially stretched linear low-density polyethylene,” Int. J. Polym. Sci. 2011, 731708 (2011).
[Crossref]

Kim, C. H.

G. I. Kweon and C. H. Kim, “Aspherical lens design by using a numerical analysis,” J. Korean Phys. Soc. 51, 93–103 (2007).
[Crossref]

Kobrin, P.

Kolesnikov, A. M.

A. M. Kolesnikov, “Equilibrium of an elastic spherical shell filled with a heavy fluid under pressure,” J Appl. Mech. Tech. Phys. 51, 744–750 (2010).
[Crossref]

Kolgjini, B.

B. Kolgjini, G. Schoukens, and P. Kiekens, “Three-phase characterization of uniaxially stretched linear low-density polyethylene,” Int. J. Polym. Sci. 2011, 731708 (2011).
[Crossref]

Kubát, J.

M. Delin, R. W. Rychwalski, M. J. Kubát, and J. Kubát, “Volume changes during stress relaxation in polyethylene,” Rheol. Acta 34, 182–195 (1995).
[Crossref]

Kubát, M. J.

M. Delin, R. W. Rychwalski, M. J. Kubát, and J. Kubát, “Volume changes during stress relaxation in polyethylene,” Rheol. Acta 34, 182–195 (1995).
[Crossref]

Kweon, G. I.

G. I. Kweon and C. H. Kim, “Aspherical lens design by using a numerical analysis,” J. Korean Phys. Soc. 51, 93–103 (2007).
[Crossref]

Kyu, T.

D. Nwabunma and T. Kyu, Polyolefin Blends (John Wiley & Sons Inc., 2008), Chap. 3.

Lind, J. E.

T. Grindley and J. E. Lind, “PVT properties of water and mercury,” J. Chem. Phys. 54, 3983–3989 (1971).
[Crossref]

Macosko, C. W.

A. Durmus, A. Kaşgöz, and C. W. Macosko, “Mechanical properties of linear low-density polyethylene (LLDPE)/clay nanocomposites: estimation of aspect ratio and interfacial strength by composite models,” J. Macromol. Sci. Part-B: Phys. 47, 608–619 (2008).
[Crossref]

Martinez, V. M. C.

A. S. Alvarado, J. G. García, F. I. Jiménez, M. C. García, V. M. C. Martinez, and R. Patrick, “Simulating the functioning of variable focus length liquid filled lenses using the finite element method (FEM),” Int. J. Light Electron Opt. 124, 1003–1010 (2013).
[Crossref]

Martins, P. A. L. S.

P. A. L. S. Martins, R. M. N. Jorge, and A. J. M. Ferreira, “A comparative study of several material models for prediction of hyperelastic properties: application to silicone-rubber and soft tissues,” Strain 42, 135–147 (2006).
[Crossref]

Meuret, Y.

Morita, S.

Mota, D. E. J. S.

D. C. Pamplona and D. E. J. S. Mota, “Numerical and experimental analysis of inflating a circular hyperelastic membrane over a rigid and elastic foundation,” Int. J. Mech. Sci. 65, 18–23 (2012).
[Crossref]

Narayanaswamy, S.

Nguyen, N. T.

N. T. Nguyen, “Micro-optofluidic lenses: a review,” Biomicrofluidics,  4, 031501 (2010).
[Crossref] [PubMed]

Nwabunma, D.

D. Nwabunma and T. Kyu, Polyolefin Blends (John Wiley & Sons Inc., 2008), Chap. 3.

Oku, H.

Pamplona, D.

D. Pamplona, P. Gonçalves, M. Davidovich, and H. I. Weber, “Finite axisymmetric deformations of an initially stressed fluid- filled cylindrical membrane,” Int. J. Solid Struct. 38, 2033–2047, (2001).
[Crossref]

Pamplona, D. C.

D. C. Pamplona and D. E. J. S. Mota, “Numerical and experimental analysis of inflating a circular hyperelastic membrane over a rigid and elastic foundation,” Int. J. Mech. Sci. 65, 18–23 (2012).
[Crossref]

Patil, A.

A. Patil and A. DasGupta, “Finite inflation of an initially stretched hyperelastic circular membrane,” Eur. J. Mech. A-Solids 41, 28–36 (2013).
[Crossref]

Patrick, R.

A. S. Alvarado, J. G. García, F. I. Jiménez, M. C. García, V. M. C. Martinez, and R. Patrick, “Simulating the functioning of variable focus length liquid filled lenses using the finite element method (FEM),” Int. J. Light Electron Opt. 124, 1003–1010 (2013).
[Crossref]

Ren, H.

Rychwalski, R. W.

M. Delin, R. W. Rychwalski, M. J. Kubát, and J. Kubát, “Volume changes during stress relaxation in polyethylene,” Rheol. Acta 34, 182–195 (1995).
[Crossref]

Salih, S. E.

S. E. Salih, A. F. Hamood, and A. H. A. Alsalam, “Comparison of the characteristics of LDPE : PP and HDPE : PP polymer blends,” Mod. Appl. Sci. 7, 33–42 (2013).
[Crossref]

Schiebener, P.

P. Schiebener, J. Straub, J. M. H. L. Sengers, and J. S. Gallagehr, “Refractive index of water and steam as function of wavelength, temperature and density,” J Phys. Chem. Ref. Data 19, 677–717 (1990).
[Crossref]

Schoukens, G.

B. Kolgjini, G. Schoukens, and P. Kiekens, “Three-phase characterization of uniaxially stretched linear low-density polyethylene,” Int. J. Polym. Sci. 2011, 731708 (2011).
[Crossref]

Seabury, C.

Selby, J. C.

J. C. Selby and M. A. Shannon, “Inflation of a circular elastomeric membrane into a horizontally semi-infinite liquid reservoir of finite vertical depth: estimation of material parameters from volume–pressure data,” Int. J. Eng. Sci. 47, 718–734 (2009).
[Crossref]

J. C. Selby and M. A. Shannon, “Inflation of a circular elastomeric membrane into a horizontally semi-infinite liquid reservoir of finite vertical depth: Quasi-static deformation model,” Int. J. Eng. Sci. 47, 700–717 (2009).
[Crossref]

Selvadurai, A. P. S.

A. P. S. Selvadurai and M. Shi, “Fluid pressure loading of a hyperelastic membrane,” Int. J. Non-Linear Mech. 47, 228–239 (2012).
[Crossref]

Sengers, J. M. H. L.

P. Schiebener, J. Straub, J. M. H. L. Sengers, and J. S. Gallagehr, “Refractive index of water and steam as function of wavelength, temperature and density,” J Phys. Chem. Ref. Data 19, 677–717 (1990).
[Crossref]

Shannon, M. A.

J. C. Selby and M. A. Shannon, “Inflation of a circular elastomeric membrane into a horizontally semi-infinite liquid reservoir of finite vertical depth: estimation of material parameters from volume–pressure data,” Int. J. Eng. Sci. 47, 718–734 (2009).
[Crossref]

J. C. Selby and M. A. Shannon, “Inflation of a circular elastomeric membrane into a horizontally semi-infinite liquid reservoir of finite vertical depth: Quasi-static deformation model,” Int. J. Eng. Sci. 47, 700–717 (2009).
[Crossref]

Shi, M.

A. P. S. Selvadurai and M. Shi, “Fluid pressure loading of a hyperelastic membrane,” Int. J. Non-Linear Mech. 47, 228–239 (2012).
[Crossref]

Straub, J.

P. Schiebener, J. Straub, J. M. H. L. Sengers, and J. S. Gallagehr, “Refractive index of water and steam as function of wavelength, temperature and density,” J Phys. Chem. Ref. Data 19, 677–717 (1990).
[Crossref]

Sugiura, N.

Tamadapu, G.

G. Tamadapu and A. DasGupta, “Finite inflation analysis of a hyperelastic toroidal membrane of initially circular cross-section,” Int. J. Non-Linear Mech. 49, 31–39 (2013).
[Crossref]

Thienpont, H.

Wang, L.

Weber, H. I.

D. Pamplona, P. Gonçalves, M. Davidovich, and H. I. Weber, “Finite axisymmetric deformations of an initially stressed fluid- filled cylindrical membrane,” Int. J. Solid Struct. 38, 2033–2047, (2001).
[Crossref]

Wu, B.

Wu, S. T.

Yang, Q.

Appl. Opt. (3)

Appl. Phys. Lett. (1)

H. Ren and S. T. Wu, “Variable-focus liquid lens by changing aperture,” Appl. Phys. Lett. 86, 211107 (2005).
[Crossref]

Biomicrofluidics (1)

N. T. Nguyen, “Micro-optofluidic lenses: a review,” Biomicrofluidics,  4, 031501 (2010).
[Crossref] [PubMed]

Comput. Method Biomech. Biomed. Eng. (1)

J. D. Humphrey, “Computer methods in membrane biomechanics,” Comput. Method Biomech. Biomed. Eng. 1, 171–210 (1998).
[Crossref]

Eur. J. Mech. A-Solids (1)

A. Patil and A. DasGupta, “Finite inflation of an initially stretched hyperelastic circular membrane,” Eur. J. Mech. A-Solids 41, 28–36 (2013).
[Crossref]

IMA J. Appl. Math. (1)

D. M. Haughton, “Axisymmetric elastic membranes subjected to fluid loading,” IMA J. Appl. Math. 56, 303–320 (1996).
[Crossref]

Int. J. Eng. Sci. (2)

J. C. Selby and M. A. Shannon, “Inflation of a circular elastomeric membrane into a horizontally semi-infinite liquid reservoir of finite vertical depth: estimation of material parameters from volume–pressure data,” Int. J. Eng. Sci. 47, 718–734 (2009).
[Crossref]

J. C. Selby and M. A. Shannon, “Inflation of a circular elastomeric membrane into a horizontally semi-infinite liquid reservoir of finite vertical depth: Quasi-static deformation model,” Int. J. Eng. Sci. 47, 700–717 (2009).
[Crossref]

Int. J. Light Electron Opt. (1)

A. S. Alvarado, J. G. García, F. I. Jiménez, M. C. García, V. M. C. Martinez, and R. Patrick, “Simulating the functioning of variable focus length liquid filled lenses using the finite element method (FEM),” Int. J. Light Electron Opt. 124, 1003–1010 (2013).
[Crossref]

Int. J. Mech. Sci. (1)

D. C. Pamplona and D. E. J. S. Mota, “Numerical and experimental analysis of inflating a circular hyperelastic membrane over a rigid and elastic foundation,” Int. J. Mech. Sci. 65, 18–23 (2012).
[Crossref]

Int. J. Non-Linear Mech. (3)

G. Tamadapu and A. DasGupta, “Finite inflation analysis of a hyperelastic toroidal membrane of initially circular cross-section,” Int. J. Non-Linear Mech. 49, 31–39 (2013).
[Crossref]

A. P. S. Selvadurai and M. Shi, “Fluid pressure loading of a hyperelastic membrane,” Int. J. Non-Linear Mech. 47, 228–239 (2012).
[Crossref]

D. L. Boyer and W. Gutkowski, “Liquid filled membranes,” Int. J. Non-Linear Mech. 5, 299–310 (1970).
[Crossref]

Int. J. Polym. Sci. (1)

B. Kolgjini, G. Schoukens, and P. Kiekens, “Three-phase characterization of uniaxially stretched linear low-density polyethylene,” Int. J. Polym. Sci. 2011, 731708 (2011).
[Crossref]

Int. J. Solid Struct. (1)

D. Pamplona, P. Gonçalves, M. Davidovich, and H. I. Weber, “Finite axisymmetric deformations of an initially stressed fluid- filled cylindrical membrane,” Int. J. Solid Struct. 38, 2033–2047, (2001).
[Crossref]

J Appl. Mech. Tech. Phys. (1)

A. M. Kolesnikov, “Equilibrium of an elastic spherical shell filled with a heavy fluid under pressure,” J Appl. Mech. Tech. Phys. 51, 744–750 (2010).
[Crossref]

J Phys. Chem. Ref. Data (1)

P. Schiebener, J. Straub, J. M. H. L. Sengers, and J. S. Gallagehr, “Refractive index of water and steam as function of wavelength, temperature and density,” J Phys. Chem. Ref. Data 19, 677–717 (1990).
[Crossref]

J. Chem. Phys. (1)

T. Grindley and J. E. Lind, “PVT properties of water and mercury,” J. Chem. Phys. 54, 3983–3989 (1971).
[Crossref]

J. Korean Phys. Soc. (1)

G. I. Kweon and C. H. Kim, “Aspherical lens design by using a numerical analysis,” J. Korean Phys. Soc. 51, 93–103 (2007).
[Crossref]

J. Macromol. Sci. Part-B: Phys. (1)

A. Durmus, A. Kaşgöz, and C. W. Macosko, “Mechanical properties of linear low-density polyethylene (LLDPE)/clay nanocomposites: estimation of aspect ratio and interfacial strength by composite models,” J. Macromol. Sci. Part-B: Phys. 47, 608–619 (2008).
[Crossref]

Mod. Appl. Sci. (1)

S. E. Salih, A. F. Hamood, and A. H. A. Alsalam, “Comparison of the characteristics of LDPE : PP and HDPE : PP polymer blends,” Mod. Appl. Sci. 7, 33–42 (2013).
[Crossref]

Opt. Express (3)

Proc. SPIE (1)

A. N. Bashkatov and E. A. Genina, “Water refractive index in dependence on temperature and wavelength : a simple approximation,” Proc. SPIE 5068, 393–395 (2003).
[Crossref]

Rheol. Acta (1)

M. Delin, R. W. Rychwalski, M. J. Kubát, and J. Kubát, “Volume changes during stress relaxation in polyethylene,” Rheol. Acta 34, 182–195 (1995).
[Crossref]

Strain (1)

P. A. L. S. Martins, R. M. N. Jorge, and A. J. M. Ferreira, “A comparative study of several material models for prediction of hyperelastic properties: application to silicone-rubber and soft tissues,” Strain 42, 135–147 (2006).
[Crossref]

Other (1)

D. Nwabunma and T. Kyu, Polyolefin Blends (John Wiley & Sons Inc., 2008), Chap. 3.

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Figures (14)

Fig. 1
Fig. 1 Optical properties of water: Refractive index and extinction coefficient as used in the optical simulation. The total transmittance and the absorbance for the thickness of 10 cm are calculated from the refractive index and the extinction coefficient.

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Fig. 2
Fig. 2 The experimental stress- strain data of LLDPE presented in [17] are used to extract the constants of the first order Mooney-Rivlin model. Although the model shows slight deviation from the original material behavior, this model is chosen for the simplicity and applicability.

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Fig. 3
Fig. 3 The experimental setup of the water lens of 10 liter water volume. The water radius, water height and the foil deformations are the tree main mechanical parameters which changes due to the change of water volume.

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Fig. 4
Fig. 4 The lens shapes obtained from the measurement photo are approximated by an equation and their match has been evaluated with coefficient of determination (R2). The perfect match would result in the ideal value, R2 = 1. With the increase of the water volume, the approximation is nearing the ideal value. Also, the average of R2 for all the water volume is close to the ideal value.

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Fig. 5
Fig. 5 In the upper picture the water lens maximum height as a function of water volume is compared for the simulation, the measurement and the lens shape represented by the shape equation. The picture in the bottom compares the water lens aperture-radius or semi-diameter as a function of water volume for the same processes.

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Fig. 6
Fig. 6 The simulation and the experimental results of the water loading on the LLDPE foil are compared for four different volume. The simulated foil deformations are represented by lines where as the measured deformations are represented by the symbols.

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Fig. 7
Fig. 7 the focal length of water lens as a function of volume has been compared for the simulation, the measurement and the lens extracted from photo.

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Fig. 8
Fig. 8 The intensity distribution for different volume of water obtained form the ray tracing has been compared. The intensity increases with the increase of the water volume.

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Fig. 9
Fig. 9 Intensity and concentration factor as a function of the wavelength has been plotted. Here in (a), the simulated intensity for the calculated lens and the equation based lens are shown, whereas in (c) the corresponding spectrometer measurements are depicted. The concentration factor obtained by employing the input spectrum with the spectrum in (a) and (c) are presented in (b) and (d) respectively.

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Fig. 10
Fig. 10 The average concentration factor over the whole spectral range has been compared for the simulated lens, the equation based lens and the measurement as a function of water volume.

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Fig. 11
Fig. 11 The incident solar radiation for different water volume as a function of the wavelength are shown. It was recorded after each of the focal plane measurement.

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Fig. 12
Fig. 12 The loss of water lenses for different water volumes as a function of wavelength are compared for the simulated lenses and the equation based lenses.

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Fig. 13
Fig. 13 Intensity, concentration factor and loss of 10 liter water lens as a function of the wavelength have been compared for the simulation, the lens based on equation and the measurement.

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Fig. 14
Fig. 14 Comparison of the aspheric lens and the photo extracted water lens of 10 liter water volume. The upper picture compares the focusing capability as well as lens shape mismatch. The lower left graph compares the intensity profile in the focal spot. The lower right graph shows the intensity and concentration factor comparison as a function of wavelength.

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Equations (15)

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

W = f ( I 1 , I 2 , I 3 ) ,
I 1 = λ 1 2 + λ 2 2 + λ 3 2 ,
I 2 = λ 1 2 λ 2 2 + λ 2 2 λ 3 2 + λ 3 2 λ 1 2 ,
I 3 = λ 1 2 λ 2 2 λ 3 2 ,
λ i = ε i + 1 ,
λ 3 = 1 λ 1 λ 2 ,
I 1 = λ 1 2 + λ 2 2 + 1 λ 1 2 λ 1 2 ,
I 2 = 1 λ 1 2 + 1 λ 1 2 + λ 1 2 λ 2 2 ,
I 3 = 1 ,
W = f ( I 1 , I 2 ) ,
W = ∑ i + j = 1 N C i j ( I 1 − 3 ) i ( I 2 − 3 ) j + ∑ k = 1 N 1 D k ( J − 3 ) 2 k ,
J 2 = I 3 ,
W = C 1 ( I 1 − 3 ) + C 2 ( I 2 − 3 ) ,
C = A 1 A 2 = I 2 A 2 I 1 A 1 ,
z ( r ) = ρ r 2 1 + 1 − ( 1 + κ ) ( ρ r ) 2 + ∑ i = 1 A i r 2 + 2 i ,

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