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  • Open Access

Pumping and Mixing in Active Pores

G. C. Antunes, P. Malgaretti, J. Harting, and S. Dietrich
Phys. Rev. Lett. 129, 188003 – Published 25 October 2022
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    Abstract

    We show both numerically and analytically that a chemically patterned active pore can act as a micro- or nanopump for fluids, even if it is fore-aft symmetric. This is possible due to a spontaneous symmetry breaking which occurs when advection rather than diffusion is the dominant mechanism of solute transport. We further demonstrate that, for pumping and tuning the flow rate, a combination of geometrical and chemical inhomogeneities is required. For certain parameter values, the flow is unsteady, and persistent oscillations with a tunable frequency appear. Finally, we find that the flow exhibits convection rolls and hence promotes mixing in the low Reynolds number regime.

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    • Received 18 March 2022
    • Accepted 14 September 2022

    DOI:https://doi.org/10.1103/PhysRevLett.129.188003

    Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

    Published by the American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Applications of soft matterConfinementDiffusiophoresisTransport phenomena
    1. Physical Systems
    Living matter & active matter
    1. Techniques
    Lattice-Boltzmann methods
    Polymers & Soft Matter

    Authors & Affiliations

    G. C. Antunes1,2,3,*, P. Malgaretti1,2,3,†, J. Harting3,4, and S. Dietrich1,2

    • 1Max–Planck–Institut für Intelligente Systeme, Heisenbergstraße 3, 70569 Stuttgart, Germany
    • 2IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
    • 3Helmholtz-Institut Erlangen-Nürnberg für Erneuerbare Energien (IEK–11), Forschungszentrum Jülich, Cauerstraße 1, 91058 Erlangen, Germany
    • 4Department Chemie—und Bioingenieurwesen und Department Physik, Friedrich-Alexander-Universität Erlangen-Nürnberg, Fürther Straße 248, 90429 Nürnberg, Germany

    • *g.antunes@fz-juelich.de
    • †p.malgaretti@fz-juelich.de

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    Issue

    Vol. 129, Iss. 18 — 28 October 2022

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    • Figure 1
      Figure 1

      Longitudinal section of the axially symmetric and partially active pore with length 2L and variable radius R(z). The decomposition of a chemical species to produce solute occurs solely in the catalytically active part of the inner pore wall with length 2Lacov (black). Convection rolls (dark blue arrows) appear due to diffusioosmosis and eventually may lead to the onset of a net nonzero flow rate Q˜.

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    • Figure 2
      Figure 2

      Panels (a) and (b), snapshots of the steady-state velocity profile in the plane x=0 for Pe=2.0 and 2.4, respectively. (c) Flow rate Q˜ as a function of time, with acov=0.45. The parameters are Rmax/(2L)=1, ντf/(2L)2=1, βU0=4×10−4, l/(2L)=0.1, ξ(2L)2τf=1.5×107, and χτf=9.6. In lattice units: L=20, η=1/6, U0=4×10−4, l=4, ξ=1, χ=10−3, β=1, and θ=π/6. The simulation box is of size 80×80×40.

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    • Figure 3
      Figure 3

      Time-averaged flow rate ⟨Q˜⟩. Open (solid) symbols mark systems which converge to a steady state (limit cycle). ⟨Q˜⟩ (a) as function of Pe for θ=π/6 and for acov={0.45 (squares), 0.55 (inverted triangles), 0.65 (diamonds)}; (b) as function of acov for θ=π/6 and for Pe={2.4 (inverted triangles), 5.3 (squares), 8.0 (triangles)}; (c) as function of θ, for {Pe,acov}=[{5.3,0.45} (triangles), {8.0,0.45} (inverted triangles), {8.0,0.55} (squares)]. For further parameters see the caption of Fig. 2. In panel (c), the size of the simulation box is adjusted so as to keep the volume of the pore constant. The dashed lines are guides to the eye.

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    • Figure 4
      Figure 4

      In panels (a) and (b) Q˜ and J [thick lines (orange, blue), and grey thin lines, respectively] normalized by their maximum value. In (a) {acov,Pe}={0.55,4.6} and in (b) {acov,Pe}={0.55,7.0}. (c) Power spectrum SQ˜Q˜ of Q˜(t) [from panels (a) and (b)]. (d) Period of oscillations Tmax in units of τf. (e) Amplitude of the oscillations ΔQ˜. For (d) and (e), the data are shown as function of acov for Pe={5.3 (squares), 7.9 (triangles)}. For further parameters see the caption of Fig. 2.

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    • Figure 5
      Figure 5

      Classification of the asymptotic dynamics into nonpumping states (crosss), steady pumping states (circles), and oscillating states (filled circles). Overlapping symbols indicate bistability (see Supplemental Material). The purple line is a semianalytic prediction for the onset of pumping. (Concerning the parameter set, see the caption of Fig. 2.)

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