| Summary: | Simulations of a simple dipolar fluid under planar Couette shear flow were performed
using nonequilibrium molecular dynamics. This fluid consisted of either Lennard-Jones
or soft-sphere particles each embedded with a point dipole. Under shear flow, the fluid's
spatial structure becomes distorted or spatially anisotropic. If the fluid was orientationally
disordered or isotropic at equilibrium (no flow), then the dipoles responded to this
distortion by aligning parallel to the compression axis, the direction along which the
fluid's structure was most compressed. Although there was a strong correlation between
the alignment of the director, which describes the average orientation of all the dipoles,
and the geometry of this distortion, the degree of orientational order induced from the
shear flow was not substantial at low dipole moments. At very high shear rates above
a critical value, γ[sub cr], a string phase formed where the particles organized themselves into
strings along the flow direction with hexagonal symmetry. The strings were accompanied
by a pronounced orientational ordering of the dipoles; the nature of this order depended
on how the dipole-dipole pair interactions were treated. Under shear flow heat is produced
which can be dissipated by introducing thermostats into the translational and rotational
equations of motion of the particles. The simulation results appeared insensitive to the
choice of rotational thermostat; by contrast, the existence of the string phase and the
accompanying orientational order depended on the whether the translational thermostat
was biased or unbiased. Given a biased thermostat, a string phase was found at very
high shear rates; however, upon switching to an unbiased thermostat, the string phase
disappeared.
Increasing the dipole moment while maintaining the orientationally disordered fluid at equilibrium, shifts the critical shear rate, γ[sub cr], to higher values. In addition, this increase
also increases the degree of orientational order at low shear rates. For a dipolar soft-sphere
fluid with conducting boundary conditions, we observed the formation of a ferroelectric
fluid at low shear rates. Again, the director aligned parallel to the direction where the
fluid's spatial structure was most compressed. However, increasing the shear rate above
a critical value, γ[sub cr], we observed a drop in the degree of this orientational order. This
critical shear rate is much lower than the critical shear rate, γ[sub cr], where steady-state
planar Couette flow ceases to be stable. Given the results of several director-constrained
simulations, we concluded that this drop could be attributed to the onset of fluctuations
in the director's alignment at γ[sub d, cr].
At high dipole moment, the dipolar soft-sphere fluid exists in a ferrolectric liquid
crystal phase at equilibrium, characterized by long-range orientational order but no longrange
spatial correlations. Under shear, the director was flow unstable, continually rotating
about the axis perpendicular to the shear flow and shear gradient directions. Th6
director's angular velocity was on average approximately equal to the vorticity of the
background shear flow; however, this rotational motion was not uniform. The director
rotated fastest when it was oriented parallel to the direction of flow. At these "critical"
orientations, the instantaneous order parameter dropped rapidly. As the shear rate
was increased, these critical orientations were encountered more frequently, yielding an
overall drop in orientational order with increasing shear rate. By fixing the director at
various orientations with respect to the direction of flow, we determined all the shear
and twist viscosities relating the pressure and the strain (shear) rate tensors. Given
the twist viscosities, the flow unstable behavior of the director was predicted; given the
shear and twist viscosities, the shear stress responses of the ferroelectric liquid crystal
and tetragonal I lattice were found to be similar.
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