Hostname: page-component-848d4c4894-5nwft Total loading time: 0 Render date: 2024-05-29T21:23:48.564Z Has data issue: false hasContentIssue false

Drop deformation during diffusiophoresis

Published online by Cambridge University Press:  28 September 2022

Brian E. McKenzie
Affiliation:
Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA Center for Complex Fluids Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA
Henry C.W. Chu
Affiliation:
Department of Chemical Engineering, University of Florida, Gainesville, FL 32611, USA
Stephen Garoff
Affiliation:
Center for Complex Fluids Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213, USA
Robert D. Tilton
Affiliation:
Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA Center for Complex Fluids Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA Department of Biomedical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA
Aditya S. Khair*
Affiliation:
Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA Center for Complex Fluids Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA
*
Email address for correspondence: akhair@andrew.cmu.edu

Abstract

Diffusiophoresis refers to the motion of a colloidal particle in a solute concentration gradient, animated by particle–solute interactions. We present a theoretical analysis of the diffusiophoretic motion of a viscous drop in a gradient of neutral solute at zero Reynolds number. In a spatially uniform gradient, the translational velocity of a spherical drop was found by Anderson et al. (J. Fluid Mech., vol. 117, 1982, pp. 107–121). Here, we show additionally that the drop experiences no tendency to deform, regardless of the magnitude of the interfacial tension at the interface of the drop and suspending fluid. Next, we consider a non-uniform gradient, where the ambient solute concentration takes the form of a quadrupole around the drop centroid. This gradient does not induce drop translation, due to symmetry, but does induce a deformation in the drop shape, which is spheroidal to first order in the capillary number $Ca=\beta k_B T R^2 K/\gamma$, where $\beta$ is the magnitude of the quadrupolar variation in solute concentration, $k_B T$ is the thermal energy, $R$ is the drop radius, $K$ is the Gibbs adsorption length, and $\gamma$ is the interfacial tension. Whether the drop becomes prolate or oblate depends on whether the solute–drop interaction is attractive or repulsive. Therefore, our work shows that in principle, a drop could undergo deformation during diffusiophoresis in a non-uniform solute gradient.

Type
JFM Papers
Copyright
© The Author(s), 2022. Published by 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.)

References

REFERENCES

Abécassis, B., Cottin-Bizonne, C., Ybert, C., Ajdari, A. & Bocquet, L. 2009 Osmotic manipulation of particles for microfluidic applications. New J. Phys. 11 (7), 785789.CrossRefGoogle Scholar
Anderson, J.L. 1989 Colloid transport by interfacial forces. Annu. Rev. Fluid Mech. 21, 6199.CrossRefGoogle 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, 107121.CrossRefGoogle Scholar
Anderson, J.L. & Prieve, D.C. 1990 Diffusiophoresis caused by gradients of strongly adsorbing solutes. Langmuir 7, 403406.CrossRefGoogle Scholar
Ault, J.T., Warren, P.B., Shin, S. & Stone, H.A. 2017 Diffusiophoresis in one-dimensional solute gradients. Soft Matt. 13, 90159023.CrossRefGoogle ScholarPubMed
Banerjee, A., Williams, I., Nery-Azevedo, R., Helgeson, M.E. & Squires, T.M. 2016 Soluto-inertial phenomena: designing long-range, long-lasting, surface-specific interactions in suspensions. Proc. Natl Acad. Sci. USA 113 (31), 86128617.CrossRefGoogle ScholarPubMed
Baygents, J.C. & Saville, D.A. 1988 The migration of charged drops and bubbles in electrolyte gradients: diffusiophoresis. Physico-Chem. Hydrodyn. 10, 543560.Google Scholar
Baygents, J.C. & Saville, D.A. 1991 Electrophoresis of drops and bubbles. J. Chem. Soc. Faraday Trans. 87, 18831898.CrossRefGoogle Scholar
Decayeux, J., Dahirel, V., Jardat, M. & Illien, P. 2021 Spontaneous propulsion of an isotropic colloid in a phase-separating environment. Phys. Rev. E 104, 034602.CrossRefGoogle Scholar
Derjaguin, B.V., Sidorenkov, G.P., Zubashchenkov, E.A. & Kiseleva, E.V. 1947 Kinetic phenomena in boundary films of liquids. Kolloidn. Z. 9, 335347.Google Scholar
Kar, A., Chiang, T.Y., Ortiz Rivera, I., Sen, A. & Velegol, D. 2015 Enhanced transport into and out of dead-end pores. ACS Nano 9, 746753.CrossRefGoogle ScholarPubMed
Keh, H.J. & Wang, J.C. 2001 Diffusiophoresis of colloidal spheres in nonelectrolyte gradients at small but finite Péclet numbers. Colloid Polym. Sci. 279, 305311.CrossRefGoogle Scholar
Khair, A.S. 2013 Diffusiophoresis of colloidal particles in neutral solute gradients at finite Péclet number. J. Fluid Mech. 731, 6494.CrossRefGoogle Scholar
Leal, L.G. 2007 Advanced Transport Phenomena: Fluid Mechanics and Convective Transport Processes. Cambridge University Press.CrossRefGoogle Scholar
Marbach, S., Yoshida, H. & Bocquet, L. 2020 Local and global force balance for diffusiophoretic transport. J. Fluid Mech. 892, A6.CrossRefGoogle ScholarPubMed
Michelin, S. & Lauga, E. 2014 Phoretic self-propulsion at finite Péclet numbers. J. Fluid Mech. 747, 572604.CrossRefGoogle Scholar
Moran, J.L. & Posner, J.D. 2017 Phoretic self-propulsion. Annu. Rev. Fluid Mech. 49 (1), 511540.CrossRefGoogle Scholar
Morrison, F.A. 1970 Electrophoresis of a particle of arbitrary shape. J. Colloid Interface Sci. 34, 210214.CrossRefGoogle Scholar
Nery-Azevedo, R., Banerjee, A. & Squires, T.M. 2017 Diffusiophoresis in ionic surfactant gradients. Langmuir 33, 96949702.CrossRefGoogle ScholarPubMed
Palacci, J., Cottin-Bizonne, C., Ybert, C. & Bocquet, L. 2012 Osmotic traps for colloids and macromolecules based on logarithmic sensing in salt taxis. Soft Matt. 8, 980994.CrossRefGoogle Scholar
Paxton, W.F., Kistler, K.C., Olmeda, C.C., Sen, A., St. Angelo, S.K., Cao, Y., Mallouk, T.E., Lammert, P.E. & Crespi, V.H. 2004 Catalytic nanomotors: autonomous movement of striped nanorods. J. Am. Chem. Soc. 126, 1342413431.CrossRefGoogle ScholarPubMed
Prieve, D.C., Ebel, J.P. & Lowell, M.E. 1984 Motion of a particle generated by chemical gradients. Part 2. Electrolytes. J. Fluid Mech. 148, 247269.CrossRefGoogle Scholar
Ramachandran, A. & Leal, L.G. 2012 The effect of interfacial slip on the rheology of a dilute emulsion of drops for small capillary numbers. J. Rheol. 56 (6), 15551587.CrossRefGoogle Scholar
Ramm, B., Goychuk, A., Khmelinskaia, A., Blumhardt, P., Eto, H., Ganzinger, K.A., Frey, E. & Schwille, P. 2021 A diffusiophoretic mechanism for ATP-driven transport without motor proteins. Nat. Phys. 17, 850858.CrossRefGoogle Scholar
Ruckenstein, E. 1981 Can phoretic motions be treated as interfacial tension gradient driven phenomena? J. Colloid Interface Sci. 83, 7781.CrossRefGoogle Scholar
Sear, R.P. 2019 Diffusiophoresis in cells: a general nonequilibrium, nonmotor mechanism for the metabolism-dependent transport of particles in cells. Phys. Rev. Lett. 122, 128101.CrossRefGoogle ScholarPubMed
Shin, S. 2020 Diffusiophoretic separation of colloids in microfluidic flows. Phys. Fluids 32 (10), 101302.CrossRefGoogle 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, 257261.CrossRefGoogle ScholarPubMed
Shin, S., Warren, P.B. & Stone, H.A. 2018 Cleaning by surfactant gradients: particulate removal from porous materials and the significance of rinsing in laundry detergency. Phys. Rev. Appl. 9, 034012.CrossRefGoogle Scholar
Taylor, T.D. & Acrivos, A. 1964 On the deformation and drag of a falling viscous drop at low Reynolds number. J. Fluid Mech. 18, 466476.CrossRefGoogle Scholar
Velegol, D., Garg, A., Guha, R., Kar, A. & Kumar, M. 2016 Origins of concentration gradients for diffusiophoresis. Soft Matt. 12, 46864703.CrossRefGoogle ScholarPubMed
Warren, P.B. 2020 Non-Faradaic electric currents in the Nernst–Planck equations and nonlocal diffusiophoresis of suspended colloids in crossed salt gradients. Phys. Rev. Lett. 124, 248004.CrossRefGoogle ScholarPubMed
Yang, F., Shin, S. & Stone, H.A. 2018 Diffusiophoresis of a charged drop. J. Fluid Mech. 852, 3759.CrossRefGoogle Scholar
Young, N.O., Goldstein, J.S. & Block, M.J. 1959 The motion of bubbles in a vertical temperature gradient. J. Fluid Mech. 6, 350356.CrossRefGoogle Scholar