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Motion of a hot particle in viscous fluids
Phys. Rev. Fluids 1, 014001 – Published 18 May, 2016
DOI: https://doi.org/10.1103/PhysRevFluids.1.014001
Abstract
We study the motion of a hot particle in a viscous liquid at low Reynolds numbers, which is inspired by recent experiments with Brownian particles heated by a laser. The difference in temperature between a particle and the ambient fluid causes a spatial variation of the viscosity in the vicinity of the solid body. We derive a general analytical expression determining the force and the torque on a particle for low Péclet numbers by exploiting the Lorentz reciprocal theorem. For small temperature and viscosity variations, a perturbation analysis is implemented to evaluate the leading-order correction to the hydrodynamic force and torque on the particle. The results are applied to describe dynamics of a uniformly hot spherical particle and to spherical particles with a nonuniform surface temperature described by dipole and quadrupole moments. Among other results, we find for dipolar thermal fields that there is coupling of the translational and rotational motions when there are local viscosity variations; such coupling is absent in an isothermal fluid.
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References (18)
- R. Golestanian, T. B. Liverpool, and A. Ajdari, Designing phoretic micro-and nano-swimmers, New J. Phys. 9, 126 (2007).
- S. Iacopini and R. Piazza, Thermophoresis in protein solutions, Europhys. Lett. 63, 247 (2003).
- R. Piazza and A. Parola, Thermophoresis in colloidal suspensions, J. Phys.: Condens. Matter 20, 153102 (2008).
- A. Würger, Thermophoresis in Colloidal Suspensions Driven by Marangoni Forces, Phys. Rev. Lett. 98, 138301 (2007).
- T. Bickel, A. Majee, and A. Würger, Flow pattern in the vicinity of self-propelling hot Janus particles, Phys. Rev. E 88, 012301 (2013).
- D. Chakraborty, M. V. Gnann, D. Rings, J. Glaser, F. Otto, F. Cichos, and K. Kroy, Generalised Einstein relation for hot Brownian motion, Europhys. Lett. 96, 60009 (2011).
- D. Rings, R. Schachoff, M. Selmke, F. Cichos, and K. Kroy, Hot Brownian Motion, Phys. Rev. Lett. 105, 090604 (2010).
- R. T. Schermer, C. C. Olson, J. P. Coleman, and F. Bucholtz, Laser-induced thermophoresis of individual particles in a viscous liquid, Opt. Express 19, 10571 (2011).
- A. Ansari and S. Morris, The effects of a strongly temperature-dependent viscosity on Stokes's drag law: experiments and theory, J. Fluid Mech. 159, 459 (1985).
- J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics (Prentice-Hall, Englewood Cliffs, NJ, 1965), p. 85.
- B. P. Ho and L. G. Leal, Migration of rigid spheres in a two-dimensional unidirectional shear flow of a second-order fluid, J. Fluid Mech. 76, 783 (1976).
- L. G. Leal, Particle motions in a viscous fluid, Annu. Rev. Fluid Mech. 12, 435 (1980).
- L. E. Becker, G. H. McKinley, and H. A. Stone, Sedimentation of a sphere near a plane wall: weak non-Newtonian and inertial effects, J. Non-Newtonian Fluid Mech. 63, 201 (1996).
- P. M. Lovalenti and J. F. Brady, The hydrodynamic force on a rigid particle undergoing arbitrary time-dependent motion at small Reynolds number, J. Fluid Mech. 256, 561 (1993).
- M. Teubner, The motion of charged colloidal particles in electric fields, J. Chem. Phys. 76, 5564 (1982).
- L. G. Leal, Advanced Transport Phenomena: Fluid Mechanics and Convective Transport Processes (Cambridge University Press, Cambridge, 2007).
- J. D. Jackson, Classical Electrodynamics (John Wiley, New York, 1999).
- J. W. Swan and A. S. Khair, On the hydrodynamics of ‘slip-stick’ spheres, J. Fluid Mech. 606, 115 (2008).