TY - JOUR
T1 - Three-sphere swimmer in a nonlinear viscoelastic medium
AU - Curtis, Mark P.
AU - Gaffney, Eamonn A.
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: This publication is based on work supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). We are grateful to Qixuan Wang (School of Mathematics, University of Minnesota) for discussions in the early phases of this work.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
PY - 2013/4/10
Y1 - 2013/4/10
N2 - A simple model for a swimmer consisting of three colinearly linked spheres attached by rods and oscillating out of phase to break reciprocal motion is analyzed. With a prescribed forcing of the rods acting on the three spheres, the swimming dynamics are determined analytically in both a Newtonian Stokes fluid and a zero Reynolds number, nonlinear, Oldroyd-B viscoelastic fluid with Deborah numbers of order one (or less), highlighting the effects of viscoelasticity on the net displacement of swimmer. For instance, the model predicts that the three-sphere swimmer with a sinusoidal, but nonreciprocal, forcing cycle within an Oldroyd-B representation of a polymeric Boger fluid moves a greater distance with enhanced efficiency in comparison with its motility in a Newtonian fluid of the same viscosity. Furthermore, the nonlinear contributions to the viscoelastic constitutive relation, while dynamically nontrivial, are predicted a posteriori to have no effect on swimmer motility at leading order, given a prescribed forcing between spheres. © 2013 American Physical Society.
AB - A simple model for a swimmer consisting of three colinearly linked spheres attached by rods and oscillating out of phase to break reciprocal motion is analyzed. With a prescribed forcing of the rods acting on the three spheres, the swimming dynamics are determined analytically in both a Newtonian Stokes fluid and a zero Reynolds number, nonlinear, Oldroyd-B viscoelastic fluid with Deborah numbers of order one (or less), highlighting the effects of viscoelasticity on the net displacement of swimmer. For instance, the model predicts that the three-sphere swimmer with a sinusoidal, but nonreciprocal, forcing cycle within an Oldroyd-B representation of a polymeric Boger fluid moves a greater distance with enhanced efficiency in comparison with its motility in a Newtonian fluid of the same viscosity. Furthermore, the nonlinear contributions to the viscoelastic constitutive relation, while dynamically nontrivial, are predicted a posteriori to have no effect on swimmer motility at leading order, given a prescribed forcing between spheres. © 2013 American Physical Society.
UR - http://hdl.handle.net/10754/600021
UR - https://link.aps.org/doi/10.1103/PhysRevE.87.043006
UR - http://www.scopus.com/inward/record.url?scp=84876924933&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.87.043006
DO - 10.1103/PhysRevE.87.043006
M3 - Article
C2 - 23679512
SN - 1539-3755
VL - 87
JO - Physical Review E
JF - Physical Review E
IS - 4
ER -