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Diffusion measurements by optical methods: Recent advances and applications
ARTICLE IN PRESS Optics and Lasers in Engineering 46 (2008) 849–851
Contents lists available at ScienceDirect
Optics and Lasers in Engineering journal homepage: www.elsevier.com/locate/optlaseng
Guest Editorial
Diffusion measurements by optical methods: Recent advances and applications
1. Introduction Diffusion, a pervasive phenomenon, fundamental in chemistry, biology and medicine, occurs in many applications, such as chemical, biochemical, aerospace and mechanical engineering [1,2]. It can be concisely described as a process, which leads to an equalization of concentration within a single phase. On the other hand, optical methods, known as effective and flexible tools [3–5] for visualizing flows and performing measurements in transparent fluids, have been used in diffusion measurements since the 19th century. The papers in this special issue on diffusion measurement using optical methods are all contributed by renowned specialists. Before briefly introducing the issue, we will provide a short historical perspective with special emphasis on optical experimental methods that have left their marks on the field.
2. Historical perspective In a noteworthy book published in 1860 [6], diffusion is introduced as ‘‘a curious phenomenon, discovered first by Priestley; brought again under notice by Dalton, and of recent years very fully investigated by Dr. Thomas Grahamy Adolf Fick of Zurich has recently made an interesting attempt to develop a fundamental law.’’ As a matter of fact, our modern ideas on diffusion are largely due to these two men, Graham and Fick. Thomas Graham, a Scottish chemist, performed systematic measurements of diffusion in gases between 1828 and 1833 and later in liquids. His measurements, the first quantitative experiments on diffusion, were remarkably accurate. Furthermore, he devised correctly many aspects of the phenomenon [2]. However, as Fick stated in his famous paper published in 1855 [7] ‘‘A few years ago, Graham published an extensive investigation on the diffusion of salts in watery. It appears to me a matter of regret, however, that in such an exceedingly valuable and extensive investigation, the development of a fundamental law, for the operation of diffusion in a single element of space, was neglected, and I have therefore endeavoured to supply this omission.’’ Adolf Eugen Fick was a physiologist fond of mathematics, an area to which he initially planned to dedicate his career [2]. Fick derived his laws of diffusion in close analogy with Fourier’s law of heat conduction. While the approaches used by either Graham or Fick were macroscopic and phenomenological in nature, the 0143-8166/$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlaseng.2008.08.006
connection between the microscopic and the macroscopic natures was first established by Einstein in 1905 [8]. The year 2005, marking two anniversaries (1855 and 1905), moreover, provided the occasion to look back to the original papers and to the development of diffusion concepts in their historical context [9]. The interested reader is referred to this paper for more details. Main developments in diffusion measurement using optical methods are briefly outlined in the next section. 2.1. Optical methods for diffusion measurements Scientists have realized since long (see [10] as an example) that the gradient of refractive index that accompanies a temperature gradient has the effect of bending the light. It is this bending which is at the basis of the mirage phenomenon. The same bending effect can be produced by a concentration gradient (see [11] for examples). It is however relatively unknown, that William Hyde Wollaston, in the years around 1800, was among the first to use diffusion phenomena to artificially reproduce a mirage [12]. Louis George Gouy in 1880 was one of the first to suggest concentration measurement by using the beam deflection properties of the diffusion phenomena [13]. Although Gouy did not perform quantitative measurements, he clearly described light propagation through the diffusion region (Fig. 1). The source, an illuminated horizontal slit, not shown in the figure, is focused by a lens L in the plane G. In case of no diffusion in the cell C (pure solvent) emerging wave represented by the arc ab is focused at xo in the plane G. However, in the presence of concentration gradient, the emerging wave is distorted, giving rise to a system of alternate light and dark bands [13]. For more details on the modern use of Gouy’s diffusiometer the reader is referred to [14]. O. Wiener made the first quantitative measurements in diffusion in 1893 [15]. Fig. 2 shows a sketch of his optical system. Monochromatic light from a narrow slit S, inclined at 451 to the horizontal, is focused by a lens L on a distant screen G. If the solution in the cell C is homogeneous (no diffusion) the slit image is a straight line, practically a magnified image of the original slit. In the presence of a concentration gradient the image is distorted [1,13]. Although Wiener also provided the necessary mathematical treatment, no photographs of his results are known to have survived. Wiener’s method is elegant and inexpensive and is still considered to be very useful and effective. It was improved by J. Thovert between 1902 and 1904 [1,13] using a point source S,
ARTICLE IN PRESS 850
Guest Editorial / Optics and Lasers in Engineering 46 (2008) 849–851
Fig. 1. Gouy’s description of light propagation through a diffusion cell. Redrawn from [13]. Fig. 4. Schematic view of Lamm’s scale method. Redrawn from [1].
Fig. 5. Lamm’s slit method. Redrawn from [1].
Fig. 2. Schematic view of Wiener’s experimental setup.
Fig. 3. Thovert’s cylindrical lens system. Redrawn from [13].
a cylindrical lens E and a 451 inclined slit positioned on the front of the diffusion cell C (Fig. 3). This arrangement has the distinctive feature to give the gradient curve directly in rectangular coordinates [13]. A further modification proposed by O. Lamm in the 1930s [1] requires a scale S to be photographed through a diffusion cell C (Fig. 4). During a diffusion experiment, the scale is distorted because of different deflections of light beams passing through the diffusion cell. As stated explicitly by Hubert Schardin [16], Lamm’s method is a Schlieren process; in particular, according to Schardin’s classification, it is (Schardin) Schlieren #2. Gary Settles’ book [17] for example contains a modern discussion of Schardin’s canonical Schlieren arrangements. Lamm also used the so-called slit method [1], Fig. 5, which, once again, is a special form of the Schlieren method. The principle is the following: the light from the first slit (S1) passes through lens L1 and a cell C to reach the S2 plane. In the case there is no deflection (due to concentration gradients in the cell), the light from the first slit (S1) will pass through the second slit (S2). Cell is observed using a telescope, consisting of lens L2 and an
ocular at A. In the case of diffusion in the cell, a vertical shift of S1 will be needed to have the deflected light pass through S2. Deflection can be related to the vertical shift. Further modifications of these methods are described in [1] and references therein. Examples of interference methods for the determination of concentration in diffusion measurements are to be found in the works of H. Ro¨gener, 1941–1950 [1] and E. Calvet and R. Chevalerias, 1946–1947 [1]. Both works employ Young interferometers. For more details on diffusion measurements by interference methods, the reader is referred to [14].
3. This issue This special issue, devoted to recent advances and applications in diffusion measurements by optical methods, is a collection of 8 papers contributed by some frontline research groups currently working in the field. The first paper by Ambrosini et al. is a review of optical techniques in diffusivity measurements with main emphasis on recent contributions and on quantitative analysis. Axellson and Marucci discuss the use of holographic interferometry and electronic speckle pattern interferometry (ESPI) for diffusion measurements in biochemical and pharmaceutical applications. Diffusion in gel is discussed for the biomedical application. The third paper by Fernandez-Sempere et al. describes the use of holographic interferometry to study concentration profiles near membranes and elucidate the transport mechanism. The next paper by Chhaniwal et al. suggests a method for measuring diffusion coefficients in transparent media through polarization imaging. Viner and Poyman report on the study of partially miscible systems using Laser Line Deflection. The paper by Lewis et al. shows how Wiener’s method can be used to determine the diffusive behaviour of glass (high molecular weight) polymers. A comparison with other techniques, such as fluorescence, NMR, IR imaging, gravimetric techniques, optical microscopy, is also
ARTICLE IN PRESS Guest Editorial / Optics and Lasers in Engineering 46 (2008) 849–851
given. Ghosn et al. describe how Optical Coherence Tomography (OCT) can give information about glucose diffusion through ocular tissue. In the last contribution, Genina et al. address the problem of the diffusion of Retinalamin (an important medicament in ophthalmology) in human sclera: the diffusion coefficients are obtained by optical spectroscopy and Montecarlo simulations. This issue describes recent advances and application of optical methods in diffusion measurements through an interdisciplinary calibrated and balanced state-of the-art description featuring trends for future developments and interspersed with some striking applications in chemical and pharmaceutical engineering and in medicine and biology. The authors present in this special issue continue to make significant contributions to the field. We would like to use this opportunity to thank each of them for having made this issue possible. We would also like to thank the referees personally for their efforts and for their valuable comments. References [1] Jost W. Diffusion in solids, liquids, gases. New York: Academic Press; 1960. [2] Cussler EL. Diffusion—mass transfer in fluid systems. 2nd ed. Cambridge: Cambridge University Press; 1997. [3] Merzkirch W. Flow visualization. 2nd ed. Orlando: Academic Press; 1987. [4] Kleine H. Measurement techniques and diagnostics. Handbook of shock waves, vol. 1. London: Academic Press; 2001. p. 683–740. [5] Ambrosini D, Rastogi PK. editors. Special issue on: optical methods in heat transfer and fluid flow. Opt Lasers Eng 2006; 44: 155–350. [6] Nichol JP. A Cyclopædia of the physical sciences. London & Glasgow: Richard Griffin & Co.; 1860. p. 196. [7] Fick A. On liquid diffusion. Philos Mag S.4 1855;10:30–9. [8] Einstein A. Ann Phys 1905;17:549–60 English translation: Investigations on the theory of the Brownian movement, edited with notes by R. Fu¨rth. New York: Dover publications; 1926, reprinted 1956.
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[9] Philibert J. One and a half century of diffusion: Fick, Einstein, before and beyond. Diffusion Fundam 2006;4:6.1–6.19 Available online at /www.diffusiononline.orgS. [10] Huygens C. Traite´ de la lumie`re, 1690. English translation: treatise on light. London: Macmillan and Co.; 1912. [11] Ambrosini D, Ponticiello A, Schirripa Spagnolo G, Borghi R, Gori F. Bouncing light beams and the Hamiltonian analogy. Eur J Phys 1997;18:284–9. [12] The London Enciclopædia, vol. 16. London: Thomas Tegg; 1829. p. 234–235. [13] Longsworth LG. The diffusion of electrolytes and macromolecules in solution: a historical survey. Ann NY Acad Sci 1945;46:211–41. [14] Miller DG, Albright JG. Optical methods. In: Wakeham WA, Nagashima A, Sengers JV, editors. Measurements of the transport properties of fluids. Oxford: Blackwell Scientific Publication; 1991. p. 272–94. [15] Wiener O. Darstellung gekrummter Lichtstrahlen und Verwerthung derselben zur Untersuchung von Diffusion und Warmeleitung. Ann Phys Chem 1893;49:105–49. [16] Schardin H. Schlieren methods and their applications. Ergeb Exakten Naturwiss 1942;20:303–439 [English translation: NASA TT F-12,732]. [17] Settles GS. Schlieren and shadowgraph techniques: visualizing phenomena in transparent media. Berlin: Springer; 2001.
Dario Ambrosini ` dell’Aquila, Loc. Monteluco di Roio, I-67040 Roio DIMEG, Universita Poggio (AQ), Italy E-mail address: [email protected] URL: http://dau.ing.univaq.it/laser
Pramod K. Rastogi Applied Computing and Mechanics Laboratory, IMAC-IS-ENAC, Ecole ´de´rale de Lausanne, CH-1015 Lausanne, Switzerland Polytechnique Fe E-mail address: pramod.rastogi@epfl.ch URL: http://imac.epfl.ch/Team/Rastogi/rastogi.jsp
Contents lists available at ScienceDirect
Optics and Lasers in Engineering journal homepage: www.elsevier.com/locate/optlaseng
Guest Editorial
Diffusion measurements by optical methods: Recent advances and applications
1. Introduction Diffusion, a pervasive phenomenon, fundamental in chemistry, biology and medicine, occurs in many applications, such as chemical, biochemical, aerospace and mechanical engineering [1,2]. It can be concisely described as a process, which leads to an equalization of concentration within a single phase. On the other hand, optical methods, known as effective and flexible tools [3–5] for visualizing flows and performing measurements in transparent fluids, have been used in diffusion measurements since the 19th century. The papers in this special issue on diffusion measurement using optical methods are all contributed by renowned specialists. Before briefly introducing the issue, we will provide a short historical perspective with special emphasis on optical experimental methods that have left their marks on the field.
2. Historical perspective In a noteworthy book published in 1860 [6], diffusion is introduced as ‘‘a curious phenomenon, discovered first by Priestley; brought again under notice by Dalton, and of recent years very fully investigated by Dr. Thomas Grahamy Adolf Fick of Zurich has recently made an interesting attempt to develop a fundamental law.’’ As a matter of fact, our modern ideas on diffusion are largely due to these two men, Graham and Fick. Thomas Graham, a Scottish chemist, performed systematic measurements of diffusion in gases between 1828 and 1833 and later in liquids. His measurements, the first quantitative experiments on diffusion, were remarkably accurate. Furthermore, he devised correctly many aspects of the phenomenon [2]. However, as Fick stated in his famous paper published in 1855 [7] ‘‘A few years ago, Graham published an extensive investigation on the diffusion of salts in watery. It appears to me a matter of regret, however, that in such an exceedingly valuable and extensive investigation, the development of a fundamental law, for the operation of diffusion in a single element of space, was neglected, and I have therefore endeavoured to supply this omission.’’ Adolf Eugen Fick was a physiologist fond of mathematics, an area to which he initially planned to dedicate his career [2]. Fick derived his laws of diffusion in close analogy with Fourier’s law of heat conduction. While the approaches used by either Graham or Fick were macroscopic and phenomenological in nature, the 0143-8166/$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlaseng.2008.08.006
connection between the microscopic and the macroscopic natures was first established by Einstein in 1905 [8]. The year 2005, marking two anniversaries (1855 and 1905), moreover, provided the occasion to look back to the original papers and to the development of diffusion concepts in their historical context [9]. The interested reader is referred to this paper for more details. Main developments in diffusion measurement using optical methods are briefly outlined in the next section. 2.1. Optical methods for diffusion measurements Scientists have realized since long (see [10] as an example) that the gradient of refractive index that accompanies a temperature gradient has the effect of bending the light. It is this bending which is at the basis of the mirage phenomenon. The same bending effect can be produced by a concentration gradient (see [11] for examples). It is however relatively unknown, that William Hyde Wollaston, in the years around 1800, was among the first to use diffusion phenomena to artificially reproduce a mirage [12]. Louis George Gouy in 1880 was one of the first to suggest concentration measurement by using the beam deflection properties of the diffusion phenomena [13]. Although Gouy did not perform quantitative measurements, he clearly described light propagation through the diffusion region (Fig. 1). The source, an illuminated horizontal slit, not shown in the figure, is focused by a lens L in the plane G. In case of no diffusion in the cell C (pure solvent) emerging wave represented by the arc ab is focused at xo in the plane G. However, in the presence of concentration gradient, the emerging wave is distorted, giving rise to a system of alternate light and dark bands [13]. For more details on the modern use of Gouy’s diffusiometer the reader is referred to [14]. O. Wiener made the first quantitative measurements in diffusion in 1893 [15]. Fig. 2 shows a sketch of his optical system. Monochromatic light from a narrow slit S, inclined at 451 to the horizontal, is focused by a lens L on a distant screen G. If the solution in the cell C is homogeneous (no diffusion) the slit image is a straight line, practically a magnified image of the original slit. In the presence of a concentration gradient the image is distorted [1,13]. Although Wiener also provided the necessary mathematical treatment, no photographs of his results are known to have survived. Wiener’s method is elegant and inexpensive and is still considered to be very useful and effective. It was improved by J. Thovert between 1902 and 1904 [1,13] using a point source S,
ARTICLE IN PRESS 850
Guest Editorial / Optics and Lasers in Engineering 46 (2008) 849–851
Fig. 1. Gouy’s description of light propagation through a diffusion cell. Redrawn from [13]. Fig. 4. Schematic view of Lamm’s scale method. Redrawn from [1].
Fig. 5. Lamm’s slit method. Redrawn from [1].
Fig. 2. Schematic view of Wiener’s experimental setup.
Fig. 3. Thovert’s cylindrical lens system. Redrawn from [13].
a cylindrical lens E and a 451 inclined slit positioned on the front of the diffusion cell C (Fig. 3). This arrangement has the distinctive feature to give the gradient curve directly in rectangular coordinates [13]. A further modification proposed by O. Lamm in the 1930s [1] requires a scale S to be photographed through a diffusion cell C (Fig. 4). During a diffusion experiment, the scale is distorted because of different deflections of light beams passing through the diffusion cell. As stated explicitly by Hubert Schardin [16], Lamm’s method is a Schlieren process; in particular, according to Schardin’s classification, it is (Schardin) Schlieren #2. Gary Settles’ book [17] for example contains a modern discussion of Schardin’s canonical Schlieren arrangements. Lamm also used the so-called slit method [1], Fig. 5, which, once again, is a special form of the Schlieren method. The principle is the following: the light from the first slit (S1) passes through lens L1 and a cell C to reach the S2 plane. In the case there is no deflection (due to concentration gradients in the cell), the light from the first slit (S1) will pass through the second slit (S2). Cell is observed using a telescope, consisting of lens L2 and an
ocular at A. In the case of diffusion in the cell, a vertical shift of S1 will be needed to have the deflected light pass through S2. Deflection can be related to the vertical shift. Further modifications of these methods are described in [1] and references therein. Examples of interference methods for the determination of concentration in diffusion measurements are to be found in the works of H. Ro¨gener, 1941–1950 [1] and E. Calvet and R. Chevalerias, 1946–1947 [1]. Both works employ Young interferometers. For more details on diffusion measurements by interference methods, the reader is referred to [14].
3. This issue This special issue, devoted to recent advances and applications in diffusion measurements by optical methods, is a collection of 8 papers contributed by some frontline research groups currently working in the field. The first paper by Ambrosini et al. is a review of optical techniques in diffusivity measurements with main emphasis on recent contributions and on quantitative analysis. Axellson and Marucci discuss the use of holographic interferometry and electronic speckle pattern interferometry (ESPI) for diffusion measurements in biochemical and pharmaceutical applications. Diffusion in gel is discussed for the biomedical application. The third paper by Fernandez-Sempere et al. describes the use of holographic interferometry to study concentration profiles near membranes and elucidate the transport mechanism. The next paper by Chhaniwal et al. suggests a method for measuring diffusion coefficients in transparent media through polarization imaging. Viner and Poyman report on the study of partially miscible systems using Laser Line Deflection. The paper by Lewis et al. shows how Wiener’s method can be used to determine the diffusive behaviour of glass (high molecular weight) polymers. A comparison with other techniques, such as fluorescence, NMR, IR imaging, gravimetric techniques, optical microscopy, is also
ARTICLE IN PRESS Guest Editorial / Optics and Lasers in Engineering 46 (2008) 849–851
given. Ghosn et al. describe how Optical Coherence Tomography (OCT) can give information about glucose diffusion through ocular tissue. In the last contribution, Genina et al. address the problem of the diffusion of Retinalamin (an important medicament in ophthalmology) in human sclera: the diffusion coefficients are obtained by optical spectroscopy and Montecarlo simulations. This issue describes recent advances and application of optical methods in diffusion measurements through an interdisciplinary calibrated and balanced state-of the-art description featuring trends for future developments and interspersed with some striking applications in chemical and pharmaceutical engineering and in medicine and biology. The authors present in this special issue continue to make significant contributions to the field. We would like to use this opportunity to thank each of them for having made this issue possible. We would also like to thank the referees personally for their efforts and for their valuable comments. References [1] Jost W. Diffusion in solids, liquids, gases. New York: Academic Press; 1960. [2] Cussler EL. Diffusion—mass transfer in fluid systems. 2nd ed. Cambridge: Cambridge University Press; 1997. [3] Merzkirch W. Flow visualization. 2nd ed. Orlando: Academic Press; 1987. [4] Kleine H. Measurement techniques and diagnostics. Handbook of shock waves, vol. 1. London: Academic Press; 2001. p. 683–740. [5] Ambrosini D, Rastogi PK. editors. Special issue on: optical methods in heat transfer and fluid flow. Opt Lasers Eng 2006; 44: 155–350. [6] Nichol JP. A Cyclopædia of the physical sciences. London & Glasgow: Richard Griffin & Co.; 1860. p. 196. [7] Fick A. On liquid diffusion. Philos Mag S.4 1855;10:30–9. [8] Einstein A. Ann Phys 1905;17:549–60 English translation: Investigations on the theory of the Brownian movement, edited with notes by R. Fu¨rth. New York: Dover publications; 1926, reprinted 1956.
851
[9] Philibert J. One and a half century of diffusion: Fick, Einstein, before and beyond. Diffusion Fundam 2006;4:6.1–6.19 Available online at /www.diffusiononline.orgS. [10] Huygens C. Traite´ de la lumie`re, 1690. English translation: treatise on light. London: Macmillan and Co.; 1912. [11] Ambrosini D, Ponticiello A, Schirripa Spagnolo G, Borghi R, Gori F. Bouncing light beams and the Hamiltonian analogy. Eur J Phys 1997;18:284–9. [12] The London Enciclopædia, vol. 16. London: Thomas Tegg; 1829. p. 234–235. [13] Longsworth LG. The diffusion of electrolytes and macromolecules in solution: a historical survey. Ann NY Acad Sci 1945;46:211–41. [14] Miller DG, Albright JG. Optical methods. In: Wakeham WA, Nagashima A, Sengers JV, editors. Measurements of the transport properties of fluids. Oxford: Blackwell Scientific Publication; 1991. p. 272–94. [15] Wiener O. Darstellung gekrummter Lichtstrahlen und Verwerthung derselben zur Untersuchung von Diffusion und Warmeleitung. Ann Phys Chem 1893;49:105–49. [16] Schardin H. Schlieren methods and their applications. Ergeb Exakten Naturwiss 1942;20:303–439 [English translation: NASA TT F-12,732]. [17] Settles GS. Schlieren and shadowgraph techniques: visualizing phenomena in transparent media. Berlin: Springer; 2001.
Dario Ambrosini ` dell’Aquila, Loc. Monteluco di Roio, I-67040 Roio DIMEG, Universita Poggio (AQ), Italy E-mail address: [email protected] URL: http://dau.ing.univaq.it/laser
Pramod K. Rastogi Applied Computing and Mechanics Laboratory, IMAC-IS-ENAC, Ecole ´de´rale de Lausanne, CH-1015 Lausanne, Switzerland Polytechnique Fe E-mail address: pramod.rastogi@epfl.ch URL: http://imac.epfl.ch/Team/Rastogi/rastogi.jsp