TY - JOUR
T1 - A Stokesian viscoelastic flow
T2 - Transition to oscillations and mixing
AU - Thomases, Becca
AU - Shelley, Michael
AU - Thiffeault, Jean Luc
N1 - Funding Information:
The authors would like to thank Steve Childress for many stimulating years of discussion and collaboration. Additionally, the authors would like to thank E. Wolfson at the Courant Institute for assistance. The first author was partially supported by NSF grant DMS-0757813 . The second author was partially supported by DOE grant DE-FG02-88ER25053 and NSF grant DMS-0652795 .
PY - 2011/10/1
Y1 - 2011/10/1
N2 - To understand observations of low Reynolds number mixing and flow transitions in viscoelastic fluids, we study numerically the dynamics of the Oldroyd-B viscoelastic fluid model. The fluid is driven by a simple time-independent forcing that, in the absence of viscoelastic stresses, creates a cellular flow with extensional stagnation points. We find that at O(1) Weissenberg number, these flows lose their slaving to the forcing geometry of the background force, become oscillatory with multiple frequencies, and show continual formation and destruction of small-scale vortices. This drives flow mixing, the details of which we closely examine. These new flow states are dominated by a single-quadrant vortex, which may be stationary or cycle persistently from cell to cell.
AB - To understand observations of low Reynolds number mixing and flow transitions in viscoelastic fluids, we study numerically the dynamics of the Oldroyd-B viscoelastic fluid model. The fluid is driven by a simple time-independent forcing that, in the absence of viscoelastic stresses, creates a cellular flow with extensional stagnation points. We find that at O(1) Weissenberg number, these flows lose their slaving to the forcing geometry of the background force, become oscillatory with multiple frequencies, and show continual formation and destruction of small-scale vortices. This drives flow mixing, the details of which we closely examine. These new flow states are dominated by a single-quadrant vortex, which may be stationary or cycle persistently from cell to cell.
KW - Instability
KW - Microfluidics
KW - Mixing
KW - Viscoelasticity
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U2 - 10.1016/j.physd.2011.06.011
DO - 10.1016/j.physd.2011.06.011
M3 - Article
AN - SCOPUS:80054026934
SN - 0167-2789
VL - 240
SP - 1602
EP - 1614
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
IS - 20
ER -