2013 proceedings - the Virginia Modeling, Analysis and Simulation ...

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Fig. 1: The simulation on a 1 × 1 square domain with N = 1,
and ζ a = −4. (a) Velocity field superimposed to the density plot of
concentration. (b) Polarity director. (c) Nematic orientation. (d) The
domain averaged cosine angle between the particle polarity director
and the fluid velocity.
director goes against the flow direction (indicated by the value
-1 of the cosine angle).
Another simulation is performed in a rectangular region for
N = 0.5 and ζ a = −2.5. Strongly oscillatory spatio-temporal
structure is also observed. Figure 2 shows the snapshots of the
flow field (superimposed to the local concentration) and the
polarity director field. There are two shear layers (roughly
the top half and the bottom half) with opposite flow and
polarity directions. At the concentration valley, the flow field is
strong, while at the concentration peak, the velocity is almost
quiescent. A movie of this structure shows rapid flow reversal
when these two layers change direction.
V. CONCLUSION
This research conducts 2D numerical simulations of active
nematic polymers using the kinetic model [1]. Local
concentration, velocity field, polar direction, and nematic
orientational order are explored in the dilute regime where the
stable passive isotopic phase is driven out of the equilibrium.
Due to the active stress, rapid concentration fluctuation is
observed in the physical domain for some concentration and
active parameters. Polarity and the orientational directors are
closely correlated with the flow field in the period of structure
oscillations. These findings are in agreement with reports in
[5] when a linear model is used.
Time
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Fig. 2: The polarization direction on a 4 × 1 rectangle domain with
N = 0.5, and ζ a = −2.5. (a) Velocity field superimposed to the
density plot of the concentration. (b) Polarity director.
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REFERENCES
[1] M.G. Forest, Q. Wang, R. Zhou, Kinetic Theory and Simulations
of Active Nematic Polymers, Soft Matter (accepted 2013)
[2] A. J. Chorin, Numerical solution of the Navier-Stokes equations,
Math. Comp., 22 (1968), 745762.
[3] C. Hirt, B. Nichols, N. Romero, A Numerical Solution Algorithm
for Transient Fluid Flows, Technical Report (1975)
[4] C. M. Tome, S. McKee, GENSMAC: A Computational marker
and cell method for free surface flows in general domains, J.
Comput. Phys.,110 (1994), 171-186
[5] D. Saintillan and M. J. Shelly, Instabilities, Pattern Formation
and Mixing in Active Suspensions, Phys. Fluids 20, 123304
(2008)
This work is supported by NSF grant DMS-0908409 and Modeling &
Simulation Scholarships from Old Dominion University.
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