Continuum modeling of micro-particle electrorotation in Couette and Poiseuille flows—The zero spin viscosity limit

Huang, Hsin‐Fu; Zahn, M.; Lemaire, Élisabeth

doi:10.1016/j.elstat.2010.05.001

Cited by 14 publications

(15 citation statements)

References 33 publications

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“…When an external shear flow is applied (for instance in a Couette device or in pressure-driven Poiseuille flow) together with a sufficiently strong external electric field in the flow gradient direction, Quincke rotation arises in the same direction as the external flow vorticity and thereby effectively decreases the apparent viscosity of the suspension. This effect, which is easy to interpret theoretically [34,36,37], has been observed in a number of experiments in both Couette and pressure-driven flow setups [29][30][31][32][33]. An increase in the effective electric conductivity of the suspension has also been observed [38,39].…”

Section: Introductionsupporting

confidence: 54%

“…Equation (12) for the dipole moment P differs slightly from the dipole evolution equation appearing in previous studies of Quincke rotation [34,35], through the presence of the term involving × ∇φ e (0). This discrepancy is easily resolved by realizing that the dipole P appearing in Eq.…”

Section: Governing Equations and Moment Equationsmentioning

confidence: 91%

“…Quincke electrorotation in large-scale suspensions has interesting consequences for the effective rheology of the suspensions [29][30][31][32][33][34][35]. When an external shear flow is applied (for instance in a Couette device or in pressure-driven Poiseuille flow) together with a sufficiently strong external electric field in the flow gradient direction, Quincke rotation arises in the same direction as the external flow vorticity and thereby effectively decreases the apparent viscosity of the suspension.…”

Section: Introductionmentioning

confidence: 99%

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Electrohydrodynamic interaction of spherical particles under Quincke rotation

Das

Saintillan

2013

Phys. Rev. E

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Weakly conducting dielectric particles suspended in a dielectric liquid of higher conductivity can undergo a transition to spontaneous sustained rotation when placed in a sufficiently strong dc electric field. This phenomenon of Quincke rotation has interesting implications for the rheology of these suspensions, whose effective viscosity can be controlled and reduced by application of an external field. While previous models based on the rotation of isolated particles have provided accurate estimates for this viscosity reduction in dilute suspensions, discrepancies have been reported in more concentrated systems where particle-particle interactions are likely significant. Motivated by this observation, we extend the classic description of Quincke rotation based on the Taylor-Melcher leaky dielectric model to account for pair electrohydrodynamic interactions between two identical spheres using the method of reflections. A coupled system of evolution equations for the dipole moments and angular velocities of the spheres is derived that accounts for electric dipole-dipole interactions and hydrodynamic rotlet interactions up to order O(R(-5)), where R is the separation distance between the spheres. A linear stability analysis of this system shows that interactions modify the value of the critical electric field for the onset of Quincke rotation: both electric and hydrodynamic interactions can either stabilize or destabilize the system depending on the orientation of the spheres, but the leading effect of interactions on the onset of rotation is hydrodynamic. We also analyze the dynamics in the nonlinear regime by performing numerical simulations of the governing equations. In the case of a pair of spheres that are fixed in space, we find that particle rotations always synchronize in magnitude at long times, though the directions of rotation of the spheres need not be the same. The steady-state angular velocity magnitude depends on the configuration of the spheres and electric field strength and agrees very well with an asymptotic estimate derived for corotating spheres. In the case of freely-suspended spheres, dipolar interactions are observed to lead to a number of distinct behaviors depending on the initial relative configuration of the spheres and on any infinitesimal initial perturbation introduced in the system: in some cases the spheres slowly separate in space while steadily rotating, while in other cases they pair up and either corotate or counterrotate depending on their orientation relative to the field.

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Section: Introductionsupporting

confidence: 54%

Section: Governing Equations and Moment Equationsmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

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Electrohydrodynamic interaction of spherical particles under Quincke rotation

Das

Saintillan

2013

Phys. Rev. E

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“…From these results and Eqs. (19) and (20), we numerically obtained G M = 1.9 × 10 −2 Pa and τ = 0.98 s, and then we numerically solved Eqs. (2) and (3) with Eq.…”

Section: Analysis Of Experimental Resultsmentioning

confidence: 99%

“…Therefore, in the case of negative viscosity, the flow is amplified by negative resistance, even in the absence of external stress, resulting in spontaneous flow. Numerous experimental [2][3][4][5][6][7][8][9] and theoretical [10][11][12][13][14][15][16][17][18][19][20] studies have attempted to observe negative viscosity, mainly in magnetic fluids [7,8,16,17], electrorheological suspension [9,[18][19][20], and active suspensions of bacteria [2][3][4][5][6][10][11][12][13][14][15][21][22][23]. Recently, active suspensions exhibit liquid crystalline order at high concentrations, have attracted much attention [13,15,[21][22][23], and are theoretically predicted to show intriguing nonlinear rheological properties [13,…”

Section: Introductionmentioning

confidence: 99%

Negative viscosity of liquid crystals in the presence of turbulence: Conductivity dependence, phase diagram, and self-oscillation

et al. 2020

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Recently, we reported the discovery of enormous negative viscosity of a nematic liquid crystal in the presence of turbulence induced by ac electric fields, which enabled us to observe unique phenomena related to the negative viscosity, such as spontaneous shear flow, hysteresis in flow curves, and self-oscillation [Orihara et al., Phys. Rev. E 99, 012701 (2019)]. In the present paper, we report the rheological properties of another nematic liquid crystal, which is a homologue of the previous one. The properties of the present liquid crystal are strongly dependent on electrical conductivity. Three samples with different conductivities were prepared by changing the amount of an ionic dopant. It was found that the lowest-conductivity sample without dopant shows no negative viscosity whereas the other ion-doped samples exhibit negative viscosity with strong dependence on the frequency of the ac electric field, consistent with microscopic observations. Phase diagrams of the negative-and positive-viscosity states in the amplitude and frequency plane are constructed to show the conductivity effect. Furthermore, we propose a model to reproduce another type of self-oscillation found in the present study.

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