Soft Matter and Complex Systems Seminar
sala 228, IPPT PAN, ul. Pawińskiego 5B
2019-12-06 (09:30) 
Francois Feuillebois (LIMSI-CNRS, Orsay, France)
Effective viscosity of a dilute suspension between parallel slip walls
Uwaga – Seminarium odbędzie się o godz. 9:30 w Instytucie Podstawowych Problemów Techniki PAN w Warszawie przy ul. Pawińskiego 5B w sali 228 na drugim piętrze.
François FEUILLEBOIS
LIMSI-CNRS, Orsay, France
Coauthors:
Néjiba GHALYA, Antoine SELLIER, Maria L. EKIEL-JEZEWSKA
The energy cost for transporting suspensions in micro-channels may be reduced by using slipping walls. A theoretical model is presented here. Navier's(1823) slip condition is applied on the walls. We consider a suspension of identical solid spherical particles. The suspension is dilute, so that hydrodynamic interactions between particles are neglected. The ambient Poiseuille flow between the parallel slip walls has a high frequency, so that particles are uniformly distributed. The pressure drop for driving particles is derived by using Lorentz reciprocal theorem. The effective viscosity is obtained from the relationship between this pressure drop and the volume flow rate. It involves (as is classical for the viscosity of suspensions) the stresslet on a particle, that is the symmetric first moment of stresses on its surface. It also involves the quadrupole, second moment of stresses. These quantities are calculated from analytical solutions of the Stokes equations for the flow around a spherical particle near a slip wall, using the bispherical coordinates technique. Then two models are used, and validated, to describe the hydrodynamic interactions with both walls: the nearest wall and superposed walls approximations. The effective viscosity of the suspension is found to be very sensitive to the slip length on the walls. For instance for a gap width of two diameters, the contribution of particles to the effective viscosity (described by the 'intrinsic' viscosity [mu]) is divided by 3 when the slip length on walls is increased from 0 to the size of a particle radius. It is divided by 5 as compared with Einstein's (1905) result for an unbounded suspension. A handy fitting formula for [mu] is provided. Finally, outlooks for experiments are proposed.
François FEUILLEBOIS
LIMSI-CNRS, Orsay, France
Coauthors:
Néjiba GHALYA, Antoine SELLIER, Maria L. EKIEL-JEZEWSKA
The energy cost for transporting suspensions in micro-channels may be reduced by using slipping walls. A theoretical model is presented here. Navier's(1823) slip condition is applied on the walls. We consider a suspension of identical solid spherical particles. The suspension is dilute, so that hydrodynamic interactions between particles are neglected. The ambient Poiseuille flow between the parallel slip walls has a high frequency, so that particles are uniformly distributed. The pressure drop for driving particles is derived by using Lorentz reciprocal theorem. The effective viscosity is obtained from the relationship between this pressure drop and the volume flow rate. It involves (as is classical for the viscosity of suspensions) the stresslet on a particle, that is the symmetric first moment of stresses on its surface. It also involves the quadrupole, second moment of stresses. These quantities are calculated from analytical solutions of the Stokes equations for the flow around a spherical particle near a slip wall, using the bispherical coordinates technique. Then two models are used, and validated, to describe the hydrodynamic interactions with both walls: the nearest wall and superposed walls approximations. The effective viscosity of the suspension is found to be very sensitive to the slip length on the walls. For instance for a gap width of two diameters, the contribution of particles to the effective viscosity (described by the 'intrinsic' viscosity [mu]) is divided by 3 when the slip length on walls is increased from 0 to the size of a particle radius. It is divided by 5 as compared with Einstein's (1905) result for an unbounded suspension. A handy fitting formula for [mu] is provided. Finally, outlooks for experiments are proposed.
Please note that the Seminar will take place at the Institute of Fundamental Technological Research, Pawinskiego St. 5b, room 228,second floor.
François FEUILLEBOIS
LIMSI-CNRS, Orsay, France
Coauthors:
Néjiba GHALYA, Antoine SELLIER, Maria L. EKIEL-JEZEWSKA
The energy cost for transporting suspensions in micro-channels may be reduced by using slipping walls. A theoretical model is presented here. Navier's(1823) slip condition is applied on the walls. We consider a suspension of identical solid spherical particles. The suspension is dilute, so that hydrodynamic interactions between particles are neglected. The ambient Poiseuille flow between the parallel slip walls has a high frequency, so that particles are uniformly distributed. The pressure drop for driving particles is derived by using Lorentz reciprocal theorem. The effective viscosity is obtained from the relationship between this pressure drop and the volume flow rate. It involves (as is classical for the viscosity of suspensions) the stresslet on a particle, that is the symmetric first moment of stresses on its surface. It also involves the quadrupole, second moment of stresses. These quantities are calculated from analytical solutions of the Stokes equations for the flow around a spherical particle near a slip wall, using the bispherical coordinates technique. Then two models are used, and validated, to describe the hydrodynamic interactions with both walls: the nearest wall and superposed walls approximations. The effective viscosity of the suspension is found to be very sensitive to the slip length on the walls. For instance for a gap width of two diameters, the contribution of particles to the effective viscosity (described by the 'intrinsic' viscosity [mu]) is divided by 3 when the slip length on walls is increased from 0 to the size of a particle radius. It is divided by 5 as compared with Einstein's (1905) result for an unbounded suspension. A handy fitting formula for [mu] is provided. Finally, outlooks for experiments are proposed.
François FEUILLEBOIS
LIMSI-CNRS, Orsay, France
Coauthors:
Néjiba GHALYA, Antoine SELLIER, Maria L. EKIEL-JEZEWSKA
The energy cost for transporting suspensions in micro-channels may be reduced by using slipping walls. A theoretical model is presented here. Navier's(1823) slip condition is applied on the walls. We consider a suspension of identical solid spherical particles. The suspension is dilute, so that hydrodynamic interactions between particles are neglected. The ambient Poiseuille flow between the parallel slip walls has a high frequency, so that particles are uniformly distributed. The pressure drop for driving particles is derived by using Lorentz reciprocal theorem. The effective viscosity is obtained from the relationship between this pressure drop and the volume flow rate. It involves (as is classical for the viscosity of suspensions) the stresslet on a particle, that is the symmetric first moment of stresses on its surface. It also involves the quadrupole, second moment of stresses. These quantities are calculated from analytical solutions of the Stokes equations for the flow around a spherical particle near a slip wall, using the bispherical coordinates technique. Then two models are used, and validated, to describe the hydrodynamic interactions with both walls: the nearest wall and superposed walls approximations. The effective viscosity of the suspension is found to be very sensitive to the slip length on the walls. For instance for a gap width of two diameters, the contribution of particles to the effective viscosity (described by the 'intrinsic' viscosity [mu]) is divided by 3 when the slip length on walls is increased from 0 to the size of a particle radius. It is divided by 5 as compared with Einstein's (1905) result for an unbounded suspension. A handy fitting formula for [mu] is provided. Finally, outlooks for experiments are proposed.