Abstract.
This work reports a detailed numerical study of the behavior of ellipsoid-shaped particles adsorbed at fluid interfaces. Former experiments have shown that micrometer-sized prolate ellipsoids aggregate under the action of strong and long-ranged capillary interactions. The latter are due to nonplanar contact lines and to the resulting deformations of the interface in the vicinity of the trapped objects. We first consider the case of a single ellipsoid and examine in detail the influence of contact angle and ellipsoid aspect ratio on interfacial distortions. We then focus on two contacting ellipsoids and study the optimum packing configuration depending on their size and/or aspect ratio mismatch. We thoroughly explore the variety of contact configurations between both ellipsoids and provide corresponding energy maps. Whereas the side-by-side configuration is the most stable state for identical ellipsoids, we find that the mismatched pair adopts an “arrow” configuration in which a finite angle exists between the particles long axes. Such arrows are actually seen in experiments with micron-sized ellipsoids and similarly with millimeter-sized mosquito eggs. These results complement our previous work (J.C. Loudet, B. Pouligny, EPL 85, 28003 (2009)) and highlight the importance of geometrical factors to explain the morphology of aggregated structures at fluid interfaces.
Similar content being viewed by others
References
Courtesy of J.F. Franetich, INSERM U511 - Université Paris 6, Faculté de médecine La Pitié-Salpêtrière
A zoomed-in view of a mosquito egg reveals the presence of two side floats (anchored along the egg long axis) which may prevent it from sinking
P. Pieranski, Phys. Rev. Lett. 45, 569 (1980)
K. Zahn, R. Lenke, G. Maret, Phys. Rev. Lett. 82, 2721 (1999)
S. Reynaert, P. Moldenaers, J. Vermant, Langmuir 22, 4936 (2006)
S.U. Pickering, J. Chem. Soc. 91, 2001 (1907)
R. Aveyard, B.P. Binks, J.H. Clint, Adv. Colloid Interface Sci. 100-102, 503 (2003)
B.P. Binks, Phys. Chem. Chem. Phys. 9, 6298 (2007)
A.R. Bausch, M.J. Bowick, A. Cacciuto, A.D. Dinsmore, M.F. Hsu, D.R. Nelson, M.G. Nikolaides, A. Travesset, D.A. Weitz, Science 299, 1716 (2003)
C. Zeng, H. Bissig, A.D. Dinsmore, Solid State Commun. 139, 547 (2006)
M. Kleman, O.D. Lavrentovich, Soft Matter Physics (Springer, New York, 2003)
M.M. Nicolson, Proc. Cambridge Philos. Soc. 45, 288 (1949)
D.Y. Chan, J.D. Henry, L.R. White, J. Colloid Interface Sci. 79, 410 (1981)
V.N. Paunov, P.A. Kralchevsky, N.D. Denkov, K. Nagayama, J. Colloid Interface Sci. 157, 100 (1993)
C. Allain, M. Cloitre, J. Colloid Interface Sci. 157, 261 (1993) 269
D. Vella, L. Mahadevan, Am. J. Phys. 73, 814 (2005)
R. Aveyard et al., Phys. Rev. Lett. 88, 246102 (2002)
M.G. Nikolaides, A.R. Bausch, M.F. Hsu, A.D. Dinsmore, M. Brenner, C. Gay, D.A. Weitz, Nature 420, 299 (2002)
T.S. Horozov, R. Aveyard, J.H. Clint, B.P. Binks, Langmuir 19, 2822 (2003)
M. Megens, J. Aizenberg, Nature (London) 424, 1014 (2003)
L. Foret, A. Würger, Phys. Rev. Lett. 92, 058302 (2004)
M. Oettel, A. Dominguez, S. Dietrich, Phys. Rev. E 71, 051401 (2005)
A. Würger, L. Foret, J. Phys. Chem. B 109, 16435 (2005)
M. Oettel, A. Dominguer, S. Dietrich, J. Phys.: Condens. Matter 17, L337 (2005)
K.D. Danov, P.A. Ktalchevsky, M.P. Boneva, Langmuir 22, 2653 (2006)
M.E. Leunissen, A. van Blaaderen, A.D. Hollingsworth, M.T. Sullivan, P.M. Chaikin, Proc. Natl. Acad. Sci. U.S.A. 104, 2585 (2007)
M.P. Boneva, K.D. Danov, N.C. Christov, P.A. Kralchevsky, Langmuir 25, 9129 (2009)
K.P. Velikov, F. Durst, O.D. Velev, Langmuir 14, 1148 (1998)
P.A. Kralchevsky, K. Nagayama, Adv. Colloid Interface Sci. 85, 145 (2000)
K.D. Danov, B. Pouligny, P.A. Kralchevsky, Langmuir 17, 6599 (2001)
R. Di Leonardo, F. Saglimbeni, G. Ruocco, Phys. Rev. Lett. 100, 106103 (2008)
D. Stamou, C. Duschl, D. Johannsmann, Phys. Rev. E 62, 5263 (2000)
P.A. Kralchevsky, N.D. Denkov, K.D. Danov, Langmuir 17, 7694 (2001)
J.-B. Fournier, P. Galatola, Phys. Rev. E 65, 031601 (2002)
K.D. Danov, P.A. Kralchevsky, B.N. Naydenov, G. Brenn, J. Colloid Interface Sci. 287, 121 (2005)
J. Lucassen, Colloids Surf. 65, 131 (1992)
A.B.D. Brown, C.G. Smith, A.R. Rennie, Phys. Rev. E 62, 951 (2000)
E.A. van Nierop, M.A. Stijnman, S. Hilgenfeldt, Europhys. Lett. 72, 671 (2005)
J.C. Loudet, A.M. Alsayed, J. Zhang, A.G. Yodh, Phys. Rev. Lett. 94, 018301 (2005)
J.C. Loudet, A.G. Yodh, B. Pouligny, Phys. Rev. Lett. 97, 018304 (2006)
H. Lehle, E. Noruzifar, M. Oettel, Eur. Phys. J. E 26, 151 (2008)
E.P. Lewandowski, J.A. Bernate, P.C. Searson, K.J. Stebe, Langmuir 24, 9302 (2008)
E.P. Lewandowski, J.A. Bernate, A. Tseng, P.C. Searson, K.J. Stebe, Soft Matter 5, 886 (2009)
J.C. Loudet, B. Pouligny, Europhys. Lett. 85, 28003 (2009)
B. Madivala, J. Fransaer, J. Vermant, Langmuir 25, 2718 (2009)
M. Oettel, S. Dietrich, Langmuir 24, 1425 (2008)
J.A. Champion, Y.K. Katare, S. Mitragotri, Proc. Natl. Acad. Sci. U.S.A. 104, 11901 (2007)
K.J. Lee, J. Yoon, J. Lahann, Curr. Opin. Colloid Interface Sci. 16, 195 (2011)
S. Sacanna, D.J. Pine, Curr. Opin. Colloid Interface Sci. 16, 96 (2011)
D.B. Wolfe, A. Snead, C. Mao, N.B. Bowden, G.M. Whitesides, Langmuir 19, 2206 (2003)
K.J. Stebe, E. Lewandowski, M. Ghosh, Science 325, 159 (2009)
A. Dominguez, M. Oettel, S. Dietrich, J. Chem. Phys. 128, 114904 (2008)
R. Finn, Equilibrium Capillary Surfaces (Springer-Verlag, 1986)
C. Pozrikidis, Boundary Element Methods (Chapman & Hall/CRC, 2002)
In our model, the assumption of small interface slopes starts to break down at the ellipsoid tips for $k>6$ and $\theta_c$ close to its maximum value. Indeed, $|\nabla u_c|>0.3$, which is no longer negligible with respect to unity. The full nonlinear Young-Laplace equation of capillarity would be required for more precise computations
The darker regions within the dashed elliptical curve in fig. fig2a are due to (inevitable) unwrapping phase errors (see ghiglia,robinson). The latter occur because of a complex interference pattern (in this region only) combining reflections coming from both solid-air and solid-water interfaces
D.C. Ghiglia, M.D. Pritt, Two-Dimensional Phase Unwrapping (John Wiley & Sons, 1998)
D.W. Robinson, G.T. Reid, Interferogram Analysis (Institute of Physics Publishing, 1995)
J. Yang, Felicity R.A.J. Rose, N. Gadegaard, M.R. Alexander, Langmuir 25, 2567 (2009)
W. Chen, S. Tan, T.-K. Ng, W.T. Ford, P. Tong, Phys. Rev. Lett. 95, 218301 (2005)
W. Chen, S. Tan, Z. Huang, T.-K. Ng, W.T. Ford, P. Tong, Phys. Rev. E 74, 021406 (2006)
In the energy maps of fig. umaps, the typical numerical error for the energy is about $4\cdot10^6k_BT$. As mentioned in the text, this means that shallow wells or hills in the map are not significant or physically relevant. The amplitude of the numerical error is mainly due to the coarse sampling in $\psi_2$
A typical calculation for an ellipsoids pair takes about several minutes to converge on our old DIGITAL AlphaServer DS20 500MHz machine
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Loudet, J.C., Pouligny, B. How do mosquito eggs self-assemble on the water surface?. Eur. Phys. J. E 34, 76 (2011). https://doi.org/10.1140/epje/i2011-11076-9
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1140/epje/i2011-11076-9