LIQUID CRYSTAL ELECTRO-OSMOSIS

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1 LIQUID CRYSTAL ELECTRO-OSMOSIS Chris Conklin and Jorge Viñals School of Physics and Astronomy University of Minnesota Acknowledgments: Chenhui Peng and Oleg Lavrentovich (LCI, Kent State). Carme Calderer (U. of M.), Dmitry Golovaty (Akron).

PATTERNED DIRECTOR IN THIN CELL Benchmark Director Configurations Thin cell with director configuration photo patterned on cell bounding walls.

2 PATTERNED DIRECTOR IN THIN CELL Benchmark Director Configurations Thin cell with director configuration photo patterned on cell bounding walls. Assume nematic director ˆn(x) in the fluid layer remains fixed, parallel to bounding plates, and along the photo patterned orientation. Consider parameters of experiments by Peng and Lavrentovich. Flow induced by a uniform, oscillatory applied electric field.

3 TWO CONFIGURATIONS OF INTEREST Periodic nematic configuration

4 TWO CONFIGURATIONS OF INTEREST Periodic nematic configuration Isolated disclinations

5 CHARGE SEPARATION MOBILITY ANISOTROPY Dissolved ions always present in LC samples. Concentration in experiments known. Anisotropic ionic mobility relative to director µ ij = µ δ ij + µ n i n j, with µ = µ µ > 0, Body force µ µ 0.3 < 1 µ n xn y ɛe 2 µ + µny 2

6 CHARGE SEPARATION MOBILITY ANISOTROPY Dissolved ions always present in LC samples. Concentration in experiments known. Anisotropic ionic mobility relative to director µ ij = µ δ ij + µ n i n j, with µ = µ µ > 0, Body force µ µ 0.3 < 1 µ n xn y ɛe 2 µ + µny 2

7 CHARGE SEPARATION PERMITTIVITY ANISOTROPY Same anisotropy of dielectric constant tensor, ɛ ij = ɛ δ ij + ɛ n i n j, with ɛ = ɛ ɛ positive or negative. Charge separation may be of opposite sign to mobility anisotropy. Both anisotropies can counteract each other.

8 CHARGE SEPARATION PERMITTIVITY ANISOTROPY Same anisotropy of dielectric constant tensor, ɛ ij = ɛ δ ij + ɛ n i n j, with ɛ = ɛ ɛ positive or negative. Charge separation may be of opposite sign to mobility anisotropy. Both anisotropies can counteract each other.

9 TRANSPORT MODEL Standard nematodynamics in d = 2 with fixed director. Leslie-Ericksen stress, σ D ij = α 1n i n j n k n l D kl + α 2N i n j + α 3n i N j + α 4D ij + α 5n j D ik n k + α 6n i D jk n k N i = ṅ i Ω ij n j, D ij = 1 2 ( iv j + j v i ), Ω ij = 1 2 ( iv j j v i ) Stokes Flow (Re ), 0 = [ p1 + σ D ij ], v = 0 Electrostatic equilibrium ɛ 0 (ɛe) = k=1,2 ez kc k. Ionic species transport, c k t + (vc k) = (D k c k c k z k µ k E). with the Einstein relation D k = k B T ez k µ k.

10 BENCHMARK: PERIODIC ANCHORING Uniform system along the imposed field direction x. Variables only depend on y. No advection, v c k = 0. To first order in the anisotropy, the equation for c 1 + c 2 decouples. Consider only ρ = e c = e(c 1 c 2). Characteristic times (separation and diffusion), τ ρ = ɛ (c 1 + c 2)eµ 0.02s, τ D = (Dq 2 ) 1 70s t c }{{} Saturation due to oscillation = y [ D yy y c }{{} Saturation due to diffusion (µ 2 ) yx (c 1 + c 2 )E x }{{} Driving term (µ 2 ) yy (c 1 + c 2 )E y }{{} Saturation due to transverse charge separation ]

11 BENCHMARK: PERIODIC ANCHORING ( ρ(y, t) = σ σ + ɛ ) [ ] σ cos(ωt δ) sin(2qy) ɛ 0ɛE 0 ɛ y 2 σyy 2 + (ωɛ 0ɛ yy ) 2 tan δ = ωɛ0ɛyy σ yy Body force ρ(y, t)e x(t). Large frequency ω σ yy /ɛ 0ɛ yy 40Hz. Charge and field out of phase by π/2. No average flow. Small frequency, nonzero average flow of scale ( ɛ = 0), [v x] ɛe 2 0 ηq σ yx σ yy Miesowicz viscosities can be measured from v x(y = 0) and v x(y = π/2q).

In the one constant approximation, a disclination is given by ρ 1(r, t) = ˆn(r) = (cos

12 PATTERNED ISOLATED DISCLINATIONS Groups of disclinations offer the possibility of flow control with the imposed A/C field. In the one constant approximation, a disclination is given by ρ 1(r, t) = ˆn(r) = (cos θ(r), sin θ(r)) m=1/2 θ(r) = m tan 1 y x. π 2 Dɛ0ɛ [L0(r/ε) I0(r/ε)] 2mɛE0 cos(ωt) ε = ε σ ρ 1(r 0) 2mɛE 0 ( r ε π ) 2 ε ρ 1(r ) 2mεE0 r

13 PATTERNED ISOLATED DISCLINATIONS m = 1 ρ 1 (r) = 1 ε ( K1 (r/ ε) ε/r ) cos φ 2mɛ 0ɛE 0 cos(ωt) ε ρ 1 (r 0) 0, ρ 1 (r ) 2mɛ 0ɛE 0 cos φ cos ωt r

14 PATTERNED ISOLATED DISCLINATIONS m = -1/2

15 DISCLINATION TRIPLET Push fluid outward along the line joining the defects. [Peng et al., PRE 92, (2015)]

16 TRANSVERSE FIELD MOBILITY Spherical particle and hyperbolic hedgehog motion under an A/C field. Assume a combination of m = +1 and m = 1 point defects, and E perpendicular to defect dipole. [Lazo et al., Nat. Commun. 5, 5033 (2014)]

JournalName. Electrokinetic flows in liquid crystal thin films with fixed anchoring. Christopher Conklin and Jorge Viñals

JournalName. Electrokinetic flows in liquid crystal thin films with fixed anchoring. Christopher Conklin and Jorge Viñals JournalName Electrokinetic flows in liquid crystal thin films with fixed anchoring Christopher Conklin and Jorge Viñals We study ionic and mass transport in a liquid crystalline fluid film in its nematic