Abstract
In the article, the boundary integral technique is used to solve the hydrodynamic movement of a train of deformable fluid particles in a tube. When a fluid particle is in a tube, the total normal stress difference is not constant any more, this fore tends to distend and elongate the particle. We find that the difference between the velocity of a deformable fluid particle and a sphere (with the same radius) increases as the distance between the particles decreases, and that the increase in velocity with L′/a′ is greater the capillary number, and this increase becomes less pronounced as radius decreases.
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References
H. Wang and R. Skalak, Viscous flow in a cylindrical tube containing a line of spherical particles,J. Fluid Mech.,38 (1986), 75.
W. A. Hyman and R. Skalak, Non-Newtonian behavior of a suspension of liquid drops in tube flow,AIChE J.,181 (1972), 149–160.
W. A. Hyman and R. Skalak, Viscous flow of a suspension of liquid dropes in a cylindrical tube,Appl. Sci. Res.,26 (1972) 27–52.
C. Pozrikidis, The buoyancy-driven motion of a train of viscous drops within a cylindrical tube,J. Fluid Mech.,237 (1992), 627–648.
H. Happel and H. Brenner,Low Reynolds Number Hydrodynamics, Noordhoof International Pub., Leyden (1973).
G. K. Youngren and A. Acrivos, Stokes flow past a particle of arbitrary shape: a numerical method of solution,J. Fluid Mech.,69 (1975), 377–403.
C. Pozrikidis,Boundary Integral and Singularity Methods for Linearized Viscous Flow, Cambridge University Press (1992).
H. Tozeren, Boundary integral equation method for some Stokes flow problem,Intl. J. Numer. Mech. Fluids,4 (1984), 159–170.
M. Abramowitz and I. A. Stegun,Handbook of Mathematical Functions, Dover (1972).
M. J. Lighthill,An Introduction to Fourier Analysis and Generalized Functions, Cambridge University Press (1958).
O. A. Ladyzhenskaya,The Mathematical Theory of Viscous Incompressible Flow, Gordon & Breach (1963).
Chen Jinnan, Z. Dagan and C. Maldarelli, The axisymmetric thermocapillary motion of a particle in a tube,J. Fluid Mech.,233 (1991), 405–437.
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Communicated by Wu Wangyi
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Jinnan, C., Maldarelli, C. Flow of a train of deformable fluid particles in a tube. Appl Math Mech 19, 651–661 (1998). https://doi.org/10.1007/BF02452373
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DOI: https://doi.org/10.1007/BF02452373