Abstract
We used a direct imaging technique to investigate concentration fluctuations enhanced by thermal fluctuations in a ternary mixture of methanol (Me), cyclohexane (C), and partially deuterated cyclohexane (C*) within 1mK above its consolute critical point. The experimental setup used a low-coherence white-light source and a red filter to visualize fluctuation images. The red-filtered images were analyzed off-line using a differential dynamic microscopy algorithm that allowed us to determine the correlation time, τ, of concentration fluctuations. From τ, we determined the mutual mass diffusion coefficient, D, very near and above the critical point of Me-CC* mixtures. We also numerically estimated both the background and critical contributions to D and compared the results against our experimental values determined from τ. We found that the experimental value of D is close to the prediction based on Stokes-Einstein diffusion law with Kawasaki’s correction.
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References
C. Houessou, P. Guenoun, R. Gastaud, F. Perrot, D. Beysens, Phys. Rev. A 32, 1818 (1985).
D. Beysens, P. Guenoun, F. Perrot, Phys. Rev. A 38, 4173 (1988).
C. Knobler, N.-C. Wong, J. Phys. Chem. 85, 1972 (1981).
C. Domb, The Critical Point: A Historical Introduction To The Modern Theory Of Critical Phenomena (Taylor and Francis Ltd, 1996).
H. Stanley, Introduction to Phase Transitions and Critical Phenomena (Oxford University Press, 1987).
R. Griffiths, J. Wheeler, Phys. Rev. A 2, 1047 (1970).
J. Sengers, J. Shanks, J. Stat. Phys. 137, 857 (2009).
D. Cannell, Phys. Rev. A 12, 225 (1975).
J. Le Guillou, J. Zinn-Justin, Phys. Rev. Lett. 39, 95 (1977).
R. Cerbino, V. Trappe, Phys. Rev. Lett. 100, 188102 (2008).
F. Giavazzi, B. Brogioli, V. Trappe, T. Bellini, R. Cerbino, Phys. Rev. E 80, 031403 (2009).
P. Kaplan, V. Trappe, D. Weitz, Appl. Opt. 38, 4151 (1999).
M. Valentine, A. Popp, P. Kaplan, D. Weitz, Opt. Lett. 26, 890 (2001).
L.G. Wilson, V.A. Martinez, J. Schwarz-Linek, J. Tailleur, G. Bryant, P.N. Pusey, W.C.K. Poon, Phys. Rev. Lett. 106, 018101 (2011).
V. Martinez, R. Besseling, O. Croze, J. Tailleur, M. Reufer, J. Schwarz-Linek, L. Wilson, M. Bees, W. Poon, Biophys. J. 103, 1637 (2012).
P.J. Lu, F. Giavazzi, T.E. Angelini, E. Zaccarelli, F. Jargstorff, A.B. Schofield, J.N. Wilking, M.B. Romanowsky, D.A. Weitz, R. Cerbino, Phys. Rev. Lett. 108, 218103 (2012).
M. Reufer, V.A. Martinez, P. Schurtenberger, W.C.K. Poon, Langmuir 28, 4618 (2012).
A. Oprisan, Fluctuations, Phase Separation and Wetting Films near Liquid-Gas Critical Point, PhD thesis (University of New Orleans, 2006).
J.J. Hegseth, A. Oprisan, Y. Garrabos, D. Beysens, Phys. Rev. E 90, 022127 (2014).
R. Kopelman, R. Gammon, M. Moldover, Phys. Rev. A 29, 2048 (1984).
P. Guenoun, F. Perrot, D. Beysens, Phys. Rev. Lett. 63, 1152 (1989).
P. Guenoun, R. Gastaud, F. Perrot, D. Beysens, Phys. Rev. A 36, 4876 (1987).
J. Dainty, Laser speckle and related phenomena, Topics in Applied Physics (Springer-Verlag, 1984).
F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, D. Cannell, Ann. N.Y. Acad. Sci. 1077, 365 (2006).
S. Trainoff, D. Cannell, Phys. Fluids 14, 1340 (2002).
F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, D. Cannell, Appl. Opt. 45, 2166 (2006).
F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, D. Cannell, Phys. Rev. E 76, 041112 (2007).
F. Croccolo, H. Bataller, F. Scheffold, J. Chem. Phys. 137, 234202 (2012).
K. Kawasaki, Ann. Phys. (N.Y.) 61, 1 (1970).
C. Sorensen, R. Mockler, W. O’Sullivan, Phys. Rev. A 16, 365 (1977).
C. Hartley, D. Jacobs, R. Mockler, W. O’Sullivan, Phys. Rev. Lett. 33, 1129 (1974).
Y. Yosida, Phys. Lett. A 65, 161 (1978).
A. Oprisan, B. Bayley, S. Oprisan, J. Hegseth, Y. Garrabos, C. Lecoutre, D. Beysens, Thermal fluctuation exponents for two near-critical point systems, in SPIE, Visual Information Processing XIX, Vol. 7701, edited by Z.-u. Rahman, S.E. Reichenbach, M.A. Neifeld (SPIE, 2010).
D. Jacobs, Phys. Rev. A 33, 2605 (1986).
R. Behrends, U. Kaatze, M. Schach, J. Chem. Phys. 119, 7957 (2003).
A. Kostko, M. Anisimov, J. Sengers, Phys. Rev. E 76, 021804 (2007).
H. Swinney, D. Henry, Phys. Rev. A 8, 2586 (1973).
H. Burstyn, J. Sengers, J. Bhattacharjee, R. Ferrell, Phys. Rev. A 28, 1567 (1983).
J. Sengers, Int. J. Thermophys. 6, 203 (1985).
J. Sengers, Effects of critical fluctuations on the thermodynamic and transport properties of supercritical fluids, in Supercritical Fluids: Fundamentals for Application, edited by E. Kiran, J.M.H. Levelt Sengers (Kluwer Academic, Dordrecht, 1994) pp. 231--271.
J. Sengers, J. Luettmer-Strathmann, The critical enhancements, in Properties of Fluids, edited by J.H. Dymond, J. Millat, C.A. Nieto de Castro (Cambridge University Press, Cambridge, UK, 1995) pp. 131--159.
L. Mistura, Nuovo Cimento B 12, 35 (1972).
A. Onuki, Phys. Rev. E 55, 403 (1997).
P. Hohenberg, B. Halperin, Rev. Mod. Phys. 49, 435 (1977).
R. Folk, G. Moser, Phys. Rev. Lett. 75, 2706 (1995).
J. Luettmer-Strathmann, Thermodiffusion in the critical region, in Thermal Nonequilibrium Phenomena in Fluid Mixtures, edited by K. Werner, S. Wiegand, Vol. 584 of Springer Lecture Notes in Physics (Springer, Berlin, Heidelberg, 2002) pp. 24--37.
H. Burstyn, J. Sengers, Phys. Rev. A 25, 448 (1982).
H. Leister, J. Allegra, G. Allen, J. Chem. Phys. 51, 3701 (1969).
A. Alekhin, O. Bilous, Ukr. J. Phys. 52, 793 (2007).
H. Hao, Aspects of Dynamic Critical Phenomena in a Single Component Fluid, PhD thesis (University of Maryland, College Park, Maryland, 1991).
H. Hao, R. Ferrell, J. Bhattacharjee, Phys. Rev. E 71, 021201 (2005).
R. Berg, M. Moldover, G. Zimmerli, Phys. Rev. E 60, 4079 (1999).
A. Stein, J. Allegra, G. Allen, J. Chem. Phys. 55, 4265 (1971).
C. Sorensen, Int. J. Thermophys. 3, 365 (1982).
D. Oxtoby, W. Gelbart, J. Chem. Phys. 61, 2957 (1974).
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Contribution to the Topical Issue “Thermal nonequilibrium phenomena in multi-component fluids” edited by Fabrizio Croccolo and Henri Bataller.
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Oprisan, A., Oprisan, S.A., Hegseth, J.J. et al. Direct imaging of long-range concentration fluctuations in a ternary mixture. Eur. Phys. J. E 38, 17 (2015). https://doi.org/10.1140/epje/i2015-15017-4
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DOI: https://doi.org/10.1140/epje/i2015-15017-4