TY - JOUR
T1 - Motion of a sphere parallel to plane walls in a Poiseuille flow. Application to field-flow fractionation and hydrodynamic chromatography
AU - Pasol, L.
AU - Martin, M.
AU - Ekiel-Jezewska, M. L.
AU - Wajnryb, E.
AU - Bławzdziewicz, J.
AU - Feuillebois, F.
N1 - Funding Information:
M.L.E.J. and E.W. were supported in part by the Polish Ministry of Science and Higher Education Grant no. N N501 156538 .
Funding Information:
J.B. acknowledges support from NSF Grant CBET-1059745 .
PY - 2011/9/15
Y1 - 2011/9/15
N2 - The motion of a solid spherical particle entrained in a Poiseuille flow between parallel plane walls has various applications to separation methods, like field-flow fractionation and hydrodynamic chromatography. Various handy formulae are presented here to describe the particle motion, with these applications in mind. Based on the assumption of a low Reynolds number, the multipole expansion method coupled to a Cartesian representation is applied to provide accurate results for various friction factors in the motion of a solid spherical particle embedded in a viscous fluid between parallel planes. Accurate results for the velocity of a freely moving solid spherical particle are then obtained. These data are fitted so as to obtain handy formulae, providing e.g. the velocity of the freely moving sphere with a 1% error. For cases where the interaction with a single wall is sufficient, simpler fitting formulae are proposed, based on earlier results using the bispherical coordinates method. It appears that the formulae considering only the interaction with a nearest wall are applicable for a surprisingly wide range of particle positions and channel widths. As an example of application, it is shown how in hydrodynamic chromatography earlier models ignoring the particle-wall hydrodynamic interactions fail to predict the proper choice of channel width for a selective separation. The presented formulae may also be used for modeling the transport of macromolecular or colloidal objects in microfluidic systems.
AB - The motion of a solid spherical particle entrained in a Poiseuille flow between parallel plane walls has various applications to separation methods, like field-flow fractionation and hydrodynamic chromatography. Various handy formulae are presented here to describe the particle motion, with these applications in mind. Based on the assumption of a low Reynolds number, the multipole expansion method coupled to a Cartesian representation is applied to provide accurate results for various friction factors in the motion of a solid spherical particle embedded in a viscous fluid between parallel planes. Accurate results for the velocity of a freely moving solid spherical particle are then obtained. These data are fitted so as to obtain handy formulae, providing e.g. the velocity of the freely moving sphere with a 1% error. For cases where the interaction with a single wall is sufficient, simpler fitting formulae are proposed, based on earlier results using the bispherical coordinates method. It appears that the formulae considering only the interaction with a nearest wall are applicable for a surprisingly wide range of particle positions and channel widths. As an example of application, it is shown how in hydrodynamic chromatography earlier models ignoring the particle-wall hydrodynamic interactions fail to predict the proper choice of channel width for a selective separation. The presented formulae may also be used for modeling the transport of macromolecular or colloidal objects in microfluidic systems.
KW - Creeping flow
KW - Interaction with walls
KW - Particle
KW - Selectivity
KW - Separations
KW - Suspension
UR - http://www.scopus.com/inward/record.url?scp=79960250999&partnerID=8YFLogxK
U2 - 10.1016/j.ces.2011.05.033
DO - 10.1016/j.ces.2011.05.033
M3 - Article
AN - SCOPUS:79960250999
SN - 0009-2509
VL - 66
SP - 4078
EP - 4089
JO - Chemical Engineering Science
JF - Chemical Engineering Science
IS - 18
ER -