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Simple dipolar fluids under shear flow McWhirter, James Liam Yates

Abstract

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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