Partner: François Feuillebois

Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur (FR)

Recent publications
1.Feuillebois F., Ekiel-Jeżewska M.L., Wajnryb E., Sellier A., Bławzdziewicz J., High-frequency effective viscosity of a dilute suspension of particles in Poiseuille flow between parallel walls, JOURNAL OF FLUID MECHANICS, ISSN: 0022-1120, DOI: 10.1017/jfm.2016.378, Vol.800, pp.111-139, 2016
Abstract:

It is shown that the formal expression for the effective viscosity of a dilute suspension of arbitrary-shaped particles in Poiseuille flow contains a novel quadrupole term, besides the expected stresslet. This term becomes important for a very confined geometry. For a high-frequency flow field (in the sense used in Feuillebois et al. (J. Fluid Mech., vol. 764, 2015, pp. 133–147), the suspension rheology is Newtonian at first order in volume fraction. The effective viscosity is calculated for suspensions of N-bead rods and of prolate spheroids with the same length, volume and aspect ratio (up to 6), entrained by the Poiseuille flow between two infinite parallel flat hard walls. The numerical computations, based on solving the Stokes equations, indicate that the quadrupole term gives a significant positive contribution to the intrinsic viscosity [μ] if the distance between the walls is less than ten times the particle width, or less. It is found that the intrinsic viscosity in bounded Poiseuille flow is generally smaller than the corresponding value in unbounded flow, except for extremely narrow gaps when it becomes larger because of lubrication effects. The intrinsic viscosity is at a minimum for a gap between walls of the order of 1.5–2 particle width. For spheroids, the intrinsic viscosity is generally smaller than for chains of beads with the same aspect ratio, but when normalized by its value in the bulk, the results are qualitatively the same. Therefore, a rigid chain of beads can serve as a simple model of an orthotropic particle with a more complicated shape. The important conclusion is that the intrinsic viscosity in shear flow is larger than in the Poiseuille flow between two walls, and the difference is significant even for relatively wide channels, e.g. three times wider than the particle length. For such confined geometries, the hydrodynamic interactions with the walls are significant and should be taken into account.

Keywords:

low-Reynolds-number flows

Affiliations:
Feuillebois F.-Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur (FR)
Ekiel-Jeżewska M.L.-IPPT PAN
Wajnryb E.-IPPT PAN
Sellier A.-École Polytechnique (FR)
Bławzdziewicz J.-Texas Tech University (US)
2.Feuillebois F., Ekiel-Jeżewska M.L., Wajnryb E., Sellier A., Bławzdziewicz J., High-frequency viscosity of a dilute suspension of elongated particles in a linear shear flow between two walls, JOURNAL OF FLUID MECHANICS, ISSN: 0022-1120, DOI: 10.1017/jfm.2014.690, Vol.764, pp.133-147, 2015
Abstract:

A general expression for the effective viscosity of a dilute suspension of arbitrary-shaped particles in linear shear flow between two parallel walls is derived in terms of the induced stresslets on particles. This formula is applied to N-bead rods and to prolate spheroids with the same length, aspect ratio and volume. The effective viscosity of non-Brownian particles in a periodic shear flow is considered here. The oscillating frequency is high enough for the particle orientation and centre-of-mass distribution to be practically frozen, yet small enough for the flow to be quasi-steady. It is known that for spheres, the intrinsic viscosity [μ] increases monotonically when the distance H between the walls is decreased. The dependence is more complex for both types of elongated particles. Three regimes are theoretically predicted here: (i) a ‘weakly confined’ regime (for H>l, where l is the particle length), where [μ] is slightly larger for smaller H; (ii) a ‘semi-confined’ regime, when H becomes smaller than l, where [μ] rapidly decreases since the geometric constraints eliminate particle orientations corresponding to the largest stresslets; (iii) a ‘strongly confined’ regime when H becomes smaller than 2–3 particle widths d, where [μ] rapidly increases owing to the strong hydrodynamic coupling with the walls. In addition, for sufficiently slender particles (with aspect ratio larger than 5–6) there is a domain of narrow gaps for which the intrinsic viscosity is smaller than that in unbounded fluid.

Keywords:

complex fluids, low-Reynolds-number flows, suspensions

Affiliations:
Feuillebois F.-Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur (FR)
Ekiel-Jeżewska M.L.-IPPT PAN
Wajnryb E.-IPPT PAN
Sellier A.-École Polytechnique (FR)
Bławzdziewicz J.-Texas Tech University (US)
3.Pasol L., Martin M., Ekiel-Jeżewska M.L., Wajnryb E., Bławzdziewicz J., Feuillebois F., Corrigendum to ‘‘Motion of a sphere parallel to plane walls in a Poiseuille flow. Application to field-flow fractionation and hydrodynamic chromatography’’, CHEMICAL ENGINEERING SCIENCE, ISSN: 0009-2509, DOI: 10.1016/j.ces.2012.12.020, Vol.90, pp.51-52, 2013
Abstract:

The authors report that there is a confusion in the definition of the friction factors, pffp, pccp in Pasol et al. (2011).

Keywords:

friction factors, Poiseuille flow, spherical particle, field-flow fractionation, hydrodynamic chromatotography

Affiliations:
Pasol L.-Université Pierre et Marie Curie (FR)
Martin M.-CNRS (FR)
Ekiel-Jeżewska M.L.-IPPT PAN
Wajnryb E.-IPPT PAN
Bławzdziewicz J.-Texas Tech University (US)
Feuillebois F.-Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur (FR)
4.Pasol L., Martin M., Ekiel-Jeżewska M.L., Wajnryb E., Bławzdziewicz J., Feuillebois F., Motion of a sphere parallel to plane walls in a Poiseuille flow. Application to field-flow fractionation and hydrodynamic chromatography, CHEMICAL ENGINEERING SCIENCE, ISSN: 0009-2509, DOI: 10.1016/j.ces.2011.05.033, Vol.66, pp.4078-4089, 2011
Abstract:

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.

Keywords:

Creeping flow, Particle, Suspension, Interaction with walls, Separations, Selectivity

Affiliations:
Pasol L.-Université Pierre et Marie Curie (FR)
Martin M.-CNRS (FR)
Ekiel-Jeżewska M.L.-IPPT PAN
Wajnryb E.-IPPT PAN
Bławzdziewicz J.-Texas Tech University (US)
Feuillebois F.-Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur (FR)
5.Mongruela A., Lecoq N., Wajnryb E., Cichocki B., Feuillebois F., Motion of a sphero-cylindrical particle in a viscous fluid in confined geometry, EUROPEAN JOURNAL OF MECHANICS B-FLUIDS, ISSN: 0997-7546, DOI: 10.1016/j.euromechflu.2011.04.005, Vol.30, pp.405-408, 2011
Abstract:

The motion of a millimeter size spherocylinder particle settling in a very viscous oil in a closed container is measured by laser interferometry, with the goal to model the motion of a particle of this shape in a fluid at microscales. The container is a cylinder with vertical axis and closed at both ends by horizontal plates. The displacement of the particle along the container axis is recorded with a resolution of the order of 100 nm, that is much smaller than the particle–wall separation when in the lubrication regime. The particle friction coefficient, measured as a function of the particle–wall distance, is then used to test the theoretical predictions of an accurate hydrodynamic analysis. The Stokes flow problem is solved by using the hydromultipole method, that is in general appropriate for spheres but is extended here to a non-spherical particle by using a compound of overlapping spheres. The lateral wall effect is negligible but the two parallel horizontal end plane walls are accurately taken into account. The result of the theoretical model is in good quantitative agreement with experiment for the whole settling motion of the spherocylinder, that is for any position between the walls.

Keywords:

Stokes flows, Suspensions, Sedimentation

Affiliations:
Mongruela A.-CNRS (FR)
Lecoq N.-Université de Rouen (FR)
Wajnryb E.-IPPT PAN
Cichocki B.-University of Warsaw (PL)
Feuillebois F.-Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur (FR)
6.Feuillebois F., Ekiel-Jeżewska M.L., Suspensions de particules et interactions hydrodynamiques dans fun luide visqueux, Annales / Centre Scientifique de l'Académie Polonaise des Sciences, Vol.12, pp.44-61, 2010
Abstract:

Un groupe polonais (dont les responsables ont été B. Cichocki durant la période 1996-1997 et M. L. Ekiel-Jeżewska depuis 1998 jusqu’à ce jour, en 2010) et un groupe français (dont le responsable est F. Feuillebois) collaborent depuis 1996 dans le cadre des échanges entre le CNRS (Laboratoires PMMH jusqu’à fin 2009, puis maintenant LIMSI) et l’Académie des Sciences de Pologne (IPPT PAN). Le domaine d’étude de cette collaboration en Mécanique des Fluides concerne les suspensions de particules dans des fluides visqueux et en particulier les interactions hydrodynamiques dans les suspensions.

Keywords:

suspensions, hydrodynamic interactions, viscous fluids, microscale

Affiliations:
Feuillebois F.-Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur (FR)
Ekiel-Jeżewska M.L.-IPPT PAN
7.Ekiel-Jeżewska M.L., Wajnryb E., Bławzdziewicz J., Feuillebois F., Lubrication approximation for microparticles moving along parallel walls, JOURNAL OF CHEMICAL PHYSICS, ISSN: 0021-9606, DOI: 10.1063/1.3009251, Vol.129, pp.181102-1-4, 2008
Abstract:

Lubrication expressions for the friction coefficients of a spherical particle moving in a fluid between and along two parallel solid walls are explicitly evaluated in the low-Reynolds-number regime. They are used to determine lubrication expression for the particle free motion under an ambient Poiseuille flow. The range of validity and the accuracy of the lubrication approximation are determined by comparing with the corresponding results of the accurate multipole procedure. The results are applicable for thin, wide, and long microchannels, or quasi-two-dimensional systems.

Keywords:

Lubrication, Friction, Poiseuille flow, Particle velocity, Fluid equations

Affiliations:
Ekiel-Jeżewska M.L.-IPPT PAN
Wajnryb E.-IPPT PAN
Bławzdziewicz J.-Texas Tech University (US)
Feuillebois F.-Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur (FR)