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Electrically driven nematic flow in microfluidic capillary with radial temperature gradient

A. V. Zakharov, P. V. Maslennikov, and S. V. Pasechnik
Phys. Rev. E 103, 012702 – Published 13 January 2021
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  • INTRODUCTION
  • FORMULATION OF THE BASIC EQUATIONS FOR…
  • NUMERICAL RESULTS
  • CONCLUSION
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    An electrically driven fluid pumping principle and a mechanism of kinklike distortion of the director field n̂ in the microsized nematic volume has been described. It is shown that the interactions, on the one hand, between the electric field E and the gradient of the director's field ∇n̂, and, on the other hand, between the ∇n̂ and the temperature gradient ∇T arising in a homogeneously aligned liquid crystal microfluidic channel, confined between two infinitely long horizontal coaxial cylinders, may excite the kinklike distortion wave spreading along normal to both cylindrical boundaries. Calculations show that the resemblance to the kinklike distortion wave depends on the value of radially applied electric field E and the curvature of these boundaries. Calculations also show that there exists a range of parameter values (voltage and curvature of the inner cylinder) producing a nonstandard pumping regime with maximum flow near the hot cylinder in the horizontal direction.

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    • Received 7 September 2020
    • Revised 24 November 2020
    • Accepted 1 January 2021

    DOI:https://doi.org/10.1103/PhysRevE.103.012702

    ©2021 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    EntropyTemperature
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    A. V. Zakharov*

    • Saint Petersburg Institute for Machine Sciences, The Russian Academy of Sciences, Saint Petersburg 199178, Russia

    P. V. Maslennikov†

    • Immanuel Kant Baltic Federal University, Kaliningrad 236040, Str. Universitetskaya 2, Russia

    S. V. Pasechnik‡

    • Russian Technological University (MIREA), Moscow 119454, Russia

    • *Author to whom correspondence should be addressed: alexandre.zakharov@yahoo.ca; homepage: www.ipme.ru
    • †pashamaslennikov@mail.ru
    • ‡s-p-a-s-m@mail.ru

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    Vol. 103, Iss. 1 — January 2021

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    Images

    • Figure 1
      Figure 1

      Geometry of a homogeneously aligned liquid crystal (LC) capillary. The z axis and the unit vector êz are taken as being parallel to coaxial cylinders which are kept at different temperatures, with the outer one Tr=R2=T2 hotter than the inner one Tr=R1=T1 (T2>T1). The cylinder LC cavity d=R2−R1 confined between two infinitely long horizontal coaxial cylinders is subjected to both radially applied temperature gradient ∇T and electric field E=E(r)êr.

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    • Figure 2
      Figure 2

      Plot of the evolution of the director's field component nr(r,τi), for different times τi=0.01i (i=1,...,7) [τ7=τR(tR∼50ms)], to its equilibrium distribution nreq(r,τ7)≡nreq(r) across the microsized HALC cavity a≤r≤a+1, under the effect of the electric field U0=6 and the temperature difference ▵χ=0.0162, both for the cases P=0 (a) and P≠0 (b), respectively. Here, κ=5.

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    • Figure 3
      Figure 3

      Plot of the evolution of the director's field component nr(r,τi), for different times τi=0.0005i (i=1,...,10) (τ10=τR)(tR∼50μs), to its equilibrium distribution nreq(r,τ10)≡nreq(r) across the microsized HALC cavity a≤r≤a+1, under the effect of the electric field U0=14 and the temperature difference ▵χ=0.0162. Here, κ=5.

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    • Figure 4
      Figure 4

      Same as described in the caption of Fig. 2, but a plot of the evolution of the electric field U0E(r,τi) to its equilibrium distribution U0Eeq(r,τ7)≡U0Eeq(r) across the microsized HALC cavity a≤r≤a+1, both for the cases P=0 (a) and P≠0 (b), respectively. Here, U0=6.

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    • Figure 5
      Figure 5

      Same as described in the caption Fig. 3, but a plot of the evolution of the electric field U0E(r,τi) to its equilibrium distribution U0Eeq(r,τ10)≡U0Eeq(r) across the microsized HALC cavity a≤r≤a+1, both for the cases P=0 (a) and P≠0 (b), respectively. Here, U0=14 and κ=1.

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    • Figure 6
      Figure 6

      Plot of the evolution of the velocity field u(r,τi) for different times τi=0.01i (i=1,...,7) [τ7=τR(tR∼50ms)], to its equilibrium distribution ueq(r,τ7)≡ueq(r) across the microsized HALC cavity a≤r≤a+1, both for the cases P=0 (a) and P≠0 (b), respectively. Here, U0=6 and κ=5.

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    • Figure 7
      Figure 7

      Results of calculations of the space and time evolution for the dimensionless velocity field u(r,τi) (a) and the dimensionless hydrodynamic pressure Q(r,τi) (b), for different times τ1=0.001(∼0.7ms), τ2=0.025(∼17.5ms), τ3=0.04(∼28ms), τ4=0.05(∼35ms), τ5=0.06(∼42ms), and [τ6=τR=0.15(tR∼0.1s)], to their equilibrium distributions ueq(r,τ6)≡ueq(r) and Qeq(r,τR)≡Qeq(r) across the microsized HALC cavity a≤r≤a+1, under the effect of the electric field U0=3.5 and the temperature difference ▵χ=0.0162. Here, P≠0 and κ=1.

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    • Figure 8
      Figure 8

      Radial equilibrium distribution of the dimensionless velocity field ueq(r) across the microsized HALC cavity a≤r≤a+1, for different values of the radially applied electric field: U0=1.0 (curve 1), U0=1.1 (curve 2), U0=1.5 (curve 3), U0=2.0 (curve 4), and U0=3.0 (curve 5), respectively, for the case P≠0. Here, κ=1 (a) and κ=0.1 (b), respectively.

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    • Figure 9
      Figure 9

      (a) Dependence of umax(U0)≡umaxeq(U0) vs U0 for two sizes of the HALC cavity: κ=1 (curve 1) and κ=0.1 (curve 2), respectively, and for the case P≠0, whereas the curve 3 shows the effect of U0 on the maximum steady flow velocity, which is borrowed from Ref. [6] [see Fig. 8]. (b) Effect of curvature κ and the flexoelectric coupling on the maximum values of steady flow velocities |umax(κ)|. Results were obtained for U0=6, Δ=0.0162, and for the models of P=0 (curve 1) and P≠0 (curve 2), respectively.

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    • Figure 10
      Figure 10

      Same as described in the caption of Fig. 2, but a plot of the evolution of the temperature field χ(r,τi)=T(r,τi)/TNI, for different times τi=0.01i (i=1,...,7) [τ7=τR(tR∼50ms)], to its equilibrium distribution χeq(r,τ7)≡χeq(r) across the microsized HALC cavity a≤r≤a+1, both for the cases P=0 (a) and P≠0 (b), respectively. Here, U0=6.

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    • Figure 11
      Figure 11

      Plot of the evolution of the wall horizontal pozition rw(τ) (a) and velocity uw(τ) (b) vs τ across the HALC cavity a≤r≤a+1, for the case P≠0 and under the effect of U0=6 and Δχ=0.0162. Results were obtained for κ=8 (curves 1), 4 (curves 2), and 2 (curves 3), respectively.

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