Research ArticleCHEMICAL PHYSICS

A novel physical mechanism of liquid flow slippage on a solid surface

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Science Advances  27 Mar 2020:
Vol. 6, no. 13, eaaz0504
DOI: 10.1126/sciadv.aaz0504
  • Fig. 1 Density fluctuation near the wall at a quiescent condition and under shear.

    (A) The amplitude of density fluctuation near the boundary wall at γ̇=0. The red dashed line represents the thermal equilibrium value theoretically estimated for a bulk system without boundary walls. The inset shows the average density profile near the boundary wall. (B) Dependence of the normalized amplitude of density fluctuation on the distance to the boundary wall in the one-dimensional model B system. The results are for the case of the contact angle θ = 90°. The dashed curves are the theoretical prediction, Eq. 3. (C) Contact-angle dependence of the amplitude of density fluctuation near the boundary wall for γ̇=0.01. (D) Shear rate dependence of the amplitude of density fluctuation near the boundary wall for θ = 90°. Data are obtained in the metastable liquid state under steady shear.

  • Fig. 2 Bubble formation on the wall induced by shear flow.

    (A) Temporal growth of density fluctuation on the boundary wall for θ = 90°. Data are obtained by averaging more than eight datasets simulated with different thermal noises. The solid curves represent the fitting results by using Eq. 4. (B) Amplification factor ω(γ̇) of density fluctuation. (C) Dependence of the characteristic shear rates γ̇ on the contact angle θ. The purple squares are obtained by the relation ω(γ̇c)=0 in (B). The purple dashed line represents the critical shear rate for the onset of instability of bulk liquid obtained from simulations in a system without walls (i.e., under a periodic boundary condition). We note that the theoretical values of the critical shear rate γ̇c predicted by Furukawa and Tanaka (31) and Steinberg et al. (35) are 0.0093 and 0.226, respectively. The upper white region corresponds to the unstable region under shear with walls. The orange and green regions correspond to two types of metastability, characterized by intermittent and steady behaviors, respectively (see below for the estimation of the black dashed line). (D) Time evolution of the slip length for an intermittent case (γ̇=0.010 and θ = 27.6°). Here, the time axis is t = tt0, where t0 is arbitrarily chosen in the time trajectory, in which the slip length is fluctuating. Thus, this figure shows only a part of the fluctuating trajectory. The state at t = t0 in the figure is the gas-liquid coexisting state, but later, the gas phase is torn by the Taylor mechanism and eventually dissolved into the liquid phase. The insets are the corresponding snapshots of the density distribution. The brighter regions have lower density.

  • Fig. 3 Bubble formation on the walls in a metastable state under shear flow.

    (A) A bubble formation process for γ̇=0.063 and θ = 135°: the metastable liquid (t = 1000) (left), immediately after bubble formation (t = 70,500) (middle), and a long time after the bubble formation (t = 82,500) (right). (B) Incubation time versus contact angle θ. Each point is obtained by averaging more than eight datasets, which are simulated with different sets of thermal noises. The black dashed curve represents the spinodal line, which is obtained from the purple square points in (C). Although in the spinodal region the system is thermodynamically unstable, there is apparently a finite incubation time in our criteria to detect the gas phase generation time. (C) Shear rate dependence of the incubation time for various contact angles. The dashed curves are guides to the eye. Data are obtained by using the same procedures discussed in the main text.

  • Fig. 4 Time evolution of a gas-phase droplet under shear flow.

    (A) The results are for γ̇=0.00010 and θ = 27.6°. The fluctuation in the background is due to thermal noise (see movie S1). (B) The results are for γ̇=0.00016 and θ = 90.0° (see movie S2). (C) The results are for γ̇=0.0040 and θ = 90.0° (see movie S3). (D) The results are for γ̇=0.0016 and θ = 150.8° (see movie S4). (E) The results are for γ̇=0.0040 and θ = 150.8° (see movie S5). (F) Dependence of the critical shear rate for detachment of the gas phase on the wall on the contact angle. The green filled circles indicate the shear rate above which the gas phase is peeled off from the wall while keeping a spherical shape. The purple squares indicate the shear rate above which the SD of the wall coverage fluctuation exceeds 0.03. The critical shear rate is not sensitive to this choice of the threshold coverage.

  • Fig. 5 Apparent slip of fluid under shear.

    (A) An example of the y dependence of the averaged shear velocity vx(y) ≡ 〈vx(x, y, t0)x〉 after gas-bubble growth in the steady state for γ̇=0.0010 and θ = 135°. The green and purple symbols are for the initial densities of ψ0 = 0.46 and ψ0 = 0.48, respectively. The small averaged viscosities of the gas phase formed on the wall lead to finite slip lengths indicated by the double-headed arrows. The insets show snapshots of the density distribution for ψ0 = 0.46 and 0.48. (B) Dependence of the time-averaged apparent slip length on the contact angle θ ≥ 90.0° for the shear rate γ̇ and the initial densities of ψ0 = 0.46, 0.47, and 0.48. The dashed arrows indicate the theoretically predicted slip lengths for θ = 180.0°, which are estimated from the thickness of the gas layers on the basis of the thermodynamic lever’s rule and the balance of the shear stress. (C) Time dependence of the slip length for spinodal states. The results are shown for (γ̇,θ)=(0.0398,27.6), (0.0398, 90.0°), and (0.0100, 169.4°). (D) Snapshots of density distribution for spinodal states. These figures correspond to the results in (C).

  • Table 1 Simulation unit time τ for phenyl ether oligomer (5P4E) and metallic glass (Vitreloy-1).

    Simulation unit time τ for phenyl ether oligomer (5P4E) and metallic glass (Vitreloy-1).. The pressure dependence of viscosity for 5P4E and Vitreloy-1 are calculated by the empirical formula in (29) and (54), respectively. We assume the particle volume v0 ∼ 10−29m3.

    T [C]p [GPa]η [Pa·s]γ̇c [s−1]τ[s]
    5P4E50.0312 × 1037 × 1038 × 10−6
    200.0973 × 1034 × 1031 × 10−5
    200.1108 × 1031 × 1034 × 10−5
    400.2602 × 10659 × 10−3
    600.3909 × 10614 × 10−2
    Metallic glass (Vitreloy-1)4201 atm2 × 1083 × 10−12 × 10−2
    4001 atm2 × 1093 × 10−22 × 10−1
    3801 atm2 × 10102 × 10−33
    3601 atm4 × 10118 × 10−57 × 101

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/6/13/eaaz0504/DC1

    Supplementary Text

    Fig. S1. The van der Waals equation of state used in the main text.

    Fig. S2. Normalized density dependence of the viscosity coefficient.

    Fig. S3. Shear rate dependence of the incubation time for viscosity functions.

    Movie S1. Time evolution of a gas-phase droplet under shear flow (ShearRate = 0.0001_theta = 27.6).

    Movie S2. Time evolution of a gas-phase droplet under shear flow (ShearRate = 0.0016_theta = 90.0).

    Movie S3. Time evolution of a gas-phase droplet under shear flow (ShearRate = 0.0040_theta = 90.0).

    Movie S4. Time evolution of a gas-phase droplet under shear flow (ShearRate = 0.0016_theta = 150.8).

    Movie S5. Time evolution of a gas-phase droplet under shear flow (ShearRate = 0.0040_theta = 150.8).

    Reference (69)

  • Supplementary Materials

    The PDF file includes:

    • Supplementary Text
    • Fig. S1. The van der Waals equation of state used in the main text.
    • Fig. S2. Normalized density dependence of the viscosity coefficient.
    • Fig. S3. Shear rate dependence of the incubation time for viscosity functions.
    • Reference (69)

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    Other Supplementary Material for this manuscript includes the following:

    • Movie S1 (.mp4 format). Time evolution of a gas-phase droplet under shear flow (ShearRate = 0.0001_theta = 27.6).
    • Movie S2 (.mp4 format). Time evolution of a gas-phase droplet under shear flow (ShearRate = 0.0016_theta = 90.0).
    • Movie S3 (.mp4 format). Time evolution of a gas-phase droplet under shear flow (ShearRate = 0.0040_theta = 90.0).
    • Movie S4 (.mp4 format). Time evolution of a gas-phase droplet under shear flow (ShearRate = 0.0016_theta = 150.8).
    • Movie S5 (.mp4 format). Time evolution of a gas-phase droplet under shear flow (ShearRate = 0.0040_theta = 150.8).

    Files in this Data Supplement:

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