Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-18T07:35:51.535Z Has data issue: false hasContentIssue false
  • English
  • Français

Autophoresis of two adsorbing/desorbing particles in an electrolyte solution

Published online by Cambridge University Press:  20 February 2019

Fan Yang Open the ORCID record for Fan Yang [Opens in a new window] ,
Bhargav Rallabandi Open the ORCID record for Bhargav Rallabandi [Opens in a new window]  and
Howard A. Stone
Fan Yang
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
Bhargav Rallabandi
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
Howard A. Stone*
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
*
†Email address for correspondence: hastone@princeton.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Classical diffusiophoresis describes the motion of particles in an electrolyte or non-electrolyte solution with an imposed concentration gradient. We investigate the autophoresis of two particles in an electrolyte solution where the concentration gradient is produced by either adsorption or desorption of ions at the particle surfaces. We find that when the sorption fluxes are large, the ion concentration near the particle surfaces, and consequently the Debye length, is strongly modified, resulting in a nonlinear dependence of the phoretic speed on the sorption flux. In particular, we show that the phoretic velocity saturates at a finite value for large desorption fluxes, but depends superlinearly on the flux for adsorption fluxes, where both conclusions are in contrast with previous results that predict a linear relationship between autophoretic velocity and sorption flux. Our theory can also be applied to precipitation/dissolution and other surface chemical processes.

JFM classification

Complex Fluids: Colloids
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 865 , 25 April 2019 , pp. 440 - 459
Copyright
© 2019 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

‡

Present address: Department of Mechanical Engineering, University of California, Riverside, CA 92521, USA

References

Anderson, J. L. 1989 Colloid transport by interfacial forces. Annu. Rev. Fluid Mech. 21, 61–99.10.1146/annurev.fl.21.010189.000425Google Scholar
Anderson, J. L., Lowell, M. E. & Prieve, D. C. 1982 Motion of a particle generated by chemical gradients. Part 1. Non-electrolytes. J. Fluid Mech. 117, 107–121.10.1017/S0022112082001542Google Scholar
Baraban, L., Tasinkevych, M., Popescu, M. N., Sanchez, S., Dietrich, S. & Schmidt, O. G. 2012 Transport of cargo by catalytic Janus micro-motors. Soft Matt. 8, 48–52.10.1039/C1SM06512BGoogle Scholar
Bazant, M. Z., Kilic, M. S., Storey, B. D. & Ajdari, A. 2009 Towards an understanding of induced-charge electrokinetics at large applied voltages in concentrated solutions. Adv. Colloid Interface Sci. 152, 48–88.10.1016/j.cis.2009.10.001Google Scholar
Bird, R. B., Stewart, W. E. & Lightfoot, E. N. 1960 Transport Phenomena. Wiley.Google Scholar
Brady, J. F. 2011 Particle motion driven by solute gradients with application to autonomous motion: continuum and colloidal perspectives. J. Fluid Mech. 667, 216–259.Google Scholar
Brenner, H. 1961 The slow motion of a sphere through a viscous fluid towards a plane surface. Chem. Engng Sci. 16 (3), 242–251.10.1016/0009-2509(61)80035-3Google Scholar
Brown, A. & Poon, W. 2014 Ionic effects in self-propelled Pt-coated Janus swimmers. Soft Matt. 10, 4016–4027.10.1039/C4SM00340CGoogle Scholar
Córdova-Figueroa, U. M. & Brady, J. F. 2008 Osmotic propulsion: the osmotic motor. Phys. Rev. Lett. 100, 158303.10.1103/PhysRevLett.100.158303Google Scholar
Dash, S., Murth, P. N., Nath, L. & Chowdhury, P. 2010 Kinetic modeling on drug release from controlled drug delivery systems. Acta Pol. Pharm. 67 (3), 217–223.Google Scholar
Derjaguin, B. V., Sidorenkov, G. P., Zubashchenkov, E. A. & Kiseleva, E. V. 1947 Kinetic phenomena in boundary films of liquids. Kolloidn. Z. 9, 335–347.Google Scholar
Ebbens, S., Gregory, D. A., Dunderdale, G., Howse, J. R., Ibrahim, Y., Liverpool, T. B. & Golestanian, R. 2014 Electrokinetic effects in catalytic platinum-insulator Janus swimmers. Europhys. Lett. 106, 58003.Google Scholar
Figliuzzi, B., Chan, W. H. R., Moran, J. L. & Buie, C. R. 2014 Nonlinear electrophoresis of ideally polarizable particles. Phys. Fluids 26, 102002.10.1063/1.4897262Google Scholar
Golestanian, R., Liverpool, T. B. & Ajdari, A. 2007 Designing phoretic micro- and nano-swimmers. New J. Phys. 9, 126.10.1088/1367-2630/9/5/126Google Scholar
Happel, J. & Brenner, H. 1983 Low Reynolds Number Hydrodynamics. Martinus Nijhoff Publishers.Google Scholar
Howse, J. R., Jones, R. A. L., Ryan, A. J., Gough, T., Vafabakhsh, R. & Golestanian, R. 2007 Self-motile colloidal particles: from directed propulsion to random walk. Phys. Rev. Lett. 99, 048102.10.1103/PhysRevLett.99.048102Google Scholar
Ibrahim, Y., Golestanian, R. & Liverpool, T. B. 2017 Multiple phoretic mechanisms in the self-propulsion of a Pt-insulator Janus swimmer. J. Fluid Mech. 828, 318–352.10.1017/jfm.2017.502Google Scholar
Israelachvili, J. 2011 Intermolecular and Surface Forces, 3rd edn. Academic Press.Google Scholar
Izri, Z., van der Linden, M. N., Michelin, S. & Dauchot, O. 2014 Self-propulsion of pure water droplets by spontaneous Marangoni-stress-driven motion. Phys. Rev. Lett. 113, 248302.10.1103/PhysRevLett.113.248302Google Scholar
Jeffery, G. B. 1912 On a form of the solution of Laplace’s equation suitable for problems relating to two spheres. Proc. R. Soc. Lond. A 87 (593), 109–120.Google Scholar
Johnson, K. A. & Goody, R. S. 2011 The original Michaelis constant: translation of the 1913 Michaelis–Menten paper. Biochem. 50, 8264–8269.10.1021/bi201284uGoogle Scholar
Kilic, M. S., Bazant, M. Z. & Ajdari, A. 2007 Steric effects in the dynamics of electrolytes at large applied voltages. I. Double-layer charging. Phys. Rev. E 75, 021502.Google Scholar
Leal, L. G. 2007 Advanced Transport Phenomena: Fluid Mechanics and Convective Transport Processes. Cambridge University Press.10.1017/CBO9780511800245Google Scholar
Mancinelli, R., Botti, A., Bruni, F., Ricci, M. A. & Soper, A. K. 2007 Hydration of sodium, potassium, and chloride ions in solution and the concept of structure maker/breaker. J. Phys. Chem. B 111, 13570–13577.10.1021/jp075913vGoogle Scholar
Michaelis, L. & Menten, M. L. 1913 Die kinetik der invertinwirkung. Biochem. Z. 49, 333–369.Google Scholar
Michelin, S. & Lauga, E. 2014 Phoretic self-propulsion at finite Peclet numbers. J. Fluid Mech. 747, 572–604.10.1017/jfm.2014.158Google Scholar
Michelin, S. & Lauga, E. 2015 Autophoretic locomotion from geometric asymmetry. Eur. Phys. J. E 38, 7.Google Scholar
Michelin, S., Lauga, E. & Bartolo, D. 2013 Spontaneous autophoretic motion of isotropic particles. Phys. Fluids 25, 061701.Google Scholar
Moerman, P. G., Moyses, H. W., van der Wee, E. B., Grier, D. G., van Blaaderen, A., Kegel, W. K., Groenewold, J. & Brujic, J. 2017 Solute-mediated interactions between active droplets. Phys. Rev. E 96, 032607.Google Scholar
Moran, J. L. & Posner, J. D. 2011 Electrokinetic locomotion due to reaction-induced charge auto-electrophoresis. J. Fluid Mech. 680, 31–66.10.1017/jfm.2011.132Google Scholar
Moran, J. L. & Posner, J. D. 2014 Role of solution conductivity in reaction induced charge auto-electrophoresis. Phys. Fluids 26, 042001.10.1063/1.4869328Google Scholar
Moran, J. L. & Posner, J. D. 2017 Phoretic self-propulsion. Annu. Rev. Fluid Mech. 49, 511–540.10.1146/annurev-fluid-122414-034456Google Scholar
Mozaffari, A., Sharifi-Mood, N., Koplik, J. & Maldarelli, C. 2016 Self-diffusiophoretic colloidal propulsion near a solid boundary. Phys. Fluids 28, 053107.10.1063/1.4948398Google Scholar
Palacci, J., Abécassis, B., Cottin-Bizonne, C., Ybert, C. & Bocquet, L. 2010 Colloidal motility and pattern formation under rectified diffusiophoresis. Phys. Rev. Lett. 104, 138302.Google Scholar
Papavassiliou, D. & Alexander, G. P. 2015 The many-body reciprocal theorem and swimmer hydrodynamics. Europhys. Lett. 110, 44001.10.1209/0295-5075/110/44001Google Scholar
Paxton, W. F., Baker, P. T., Kline, T. R., Wang, Y., Mallouk, T. E. & Sen, A. 2006 Catalytically induced electrokinetics for motors and micropumps. J. Am. Chem. Soc. 128, 14881–14888.10.1021/ja0643164Google Scholar
Paxton, W. F., Sen, A. & Mallouk, T. E. 2005 Motility of catalytic nanoparticles through self-generated forces. Chem. Eur. J. 11, 6462–6470.Google Scholar
Prieve, D. C., Anderson, J. L., Ebel, J. P. & Lowell, M. E. 1984 Motion of a particle generated by chemical gradients. Part 2. Electrolytes. J. Fluid Mech. 148, 247–269.10.1017/S0022112084002330Google Scholar
Rallabandi, B., Hilgenfeldt, S. & Stone, H. A. 2017 Hydrodynamic force on a sphere normal to an obstacle due to non-uniform flow. J. Fluid Mech. 818, 407–434.Google Scholar
Rallabandi, B., Yang, F. & Stone, H. A.2019 Motion of hydrodynamically interacting active particles. arXiv:1901.04311.Google Scholar
Rubinstein, I. & Zaltzman, B. 2001 Electro-osmotic slip of the second kind and instability in concentration polarization at electrodialysis membranes. Math. Models Meth. Appl. Sci. 11 (2), 263–300.10.1142/S0218202501000866Google Scholar
Sabass, B. & Seifert, U. 2012 Dynamics and efficiency of a self-propelled, diffusiophoretic swimmer. J. Chem. Phys. 136, 064508.Google Scholar
Safdar, M., Khan, S. U. & Jänis, J. 2018 Progress toward catalytic micro- and nanomotors for biomedical and environmental applications. Adv. Mater. 30, 1703660.10.1002/adma.201703660Google Scholar
Schnitzer, O. & Yariv, E. 2015 Osmotic self-propulsion of slender particles. Phys. Fluids 27, 031701.Google Scholar
Sen, A., Ibele, M., Hong, Y. & Velegol, D. 2009 Chemo- and phototactic nano/microbots. Faraday Discuss. 143, 15–27.Google Scholar
Sharifi-Mood, N., Koplik, J. & Maldarelli, C. 2013 Diffusiophoretic self-propulsion of colloids driven by a surface reaction: the submicron particle regime for exponential and van der Waals interactions. Phys. Fluids 25, 012001.Google Scholar
Shin, S., Um, E., Sabass, B., Ault, J. T., Rahimi, M., Warren, P. B. & Stone, H. A. 2016 Size-dependent control of colloid transport via solute gradients in dead-end channels. Proc. Natl Acad. Sci. USA 113 (2), 257–261.10.1073/pnas.1511484112Google Scholar
Shklyaev, S., Brady, J. F. & Córdova-Figueroa, U. M. 2014 Non-spherical osmotic motor: chemical sailing. J. Fluid Mech. 748, 488–520.Google Scholar
Stimson, M. & Jeffery, G. B. 1926 The motion of two spheres in a viscous fluid. Proc. R. Soc. Lond. A 111 (757), 110–116.10.1098/rspa.1926.0053Google Scholar
Stone, H. A. & Samuel, A. D. T. 1996 Propulsion of microorganisms by surface distortions. Phys. Rev. Lett. 77 (19), 4102–4104.10.1103/PhysRevLett.77.4102Google Scholar
Tătulea-Codrean, M. & Lauga, E. 2018 Artificial chemotaxis of phoretic swimmers: instantaneous and long-time behaviour. J. Fluid Mech. 856, 921–957.10.1017/jfm.2018.718Google Scholar
Varma, A., Montenegro-Johnson, T. D. & Michelin, S. 2018 Clustering-induced self-propulsion of isotropic autophoretic particles. Soft Matt. 14, 7155–7173.10.1039/C8SM00690CGoogle Scholar
Velegol, D., Garg, A., Guha, R., Kar, A. & Kumar, M. 2016 Origins of concentration gradients for diffusiophoresis. Soft Matt. 12 (21), 4686–4703.Google Scholar
Wang, W., Chiang, T., Velegol, D. & Mallouk, T. E. 2013 Understanding the efficiency of autonomous nano- and microscale motors. J. Am. Chem. Soc. 135, 10557–10565.10.1021/ja405135fGoogle Scholar
Yariv, E. 2011 Electrokinetic self-propulsion by inhomogeneous surface kinetics. Proc. R. Soc. Lond. A 467, 1645–1664.10.1098/rspa.2010.0503Google Scholar
Yariv, E. 2016 Wall-induced self-diffusiophoresis of active isotropic colloids. Phys. Rev. Fluids. 1, 032101.10.1103/PhysRevFluids.1.032101Google Scholar
Zaltzman, B. & Rubinstein, I. 2007 Electro-osmotic slip and electroconvective instability. J. Fluid Mech. 579, 173–226.10.1017/S0022112007004880Google Scholar