Spreading of complex fluids with a soft blade

Marion Krapez, Anaïs Gauthier, Jean-Baptiste Boitte, Odile Aubrun, Jean-François Joanny, and Annie Colin

Phys. Rev. Fluids 7, 084002 – Published 18 August 2022

Abstract

The spreading of complex fluids is not only a part of our everyday life but also a central process in industry to produce functional thin films or protective coatings. Here we consider the spreading of polymer solutions with an elastic blade that deforms during the coating (similarly to a brush or a finger). By using complex fluids with well-chosen rheological properties, we disentangle the effects of shear viscosity, shear thinning, and normal stresses. We reveal two counterintuitive results: First, the mechanical work needed to spread a given volume of a shear-thinning fluid is higher than for the same volume of an equivalent Newtonian fluid at constant spreading velocity. Second, the first normal stress difference, which usually leads to remarkable behaviors such as the swelling of jets or the rise of the fluid on a rotating rod, has strikingly negligible effect here.

Received 15 December 2021
Accepted 8 August 2022

DOI:https://doi.org/10.1103/PhysRevFluids.7.084002

Physics Subject Headings (PhySH)

Applications of soft matter

Complex fluids Polymer thin films

Polymers & Soft Matter

Authors & Affiliations

Marion Krapez¹, Anaïs Gauthier ¹, Jean-Baptiste Boitte², Odile Aubrun², Jean-François Joanny ^3,4, and Annie Colin ¹

¹MIE–Chemistry, Biology and Innovation (CBI) UMR8231, ESPCI Paris, CNRS, PSL Research University, 75794 Paris, France
²Centre de recherche de l'Oréal, 94550 Chevilly-Larue, France
³Physico Chimie Curie, Institut Curie, PSL University, 75005 Paris, France
⁴Collège de France, 75005 Paris, France

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Issue

Vol. 7, Iss. 8 — August 2022

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Images

Figure 1
Rheological curves of silicone oil with viscosity $η = 480$ mPa s, xanthan gum at $0.9 %$ and HPAM solutions with concentrations $0.1 %$ , $0.3 %,$ and $0.5 %$ . (a) Viscosity $η$ as a function of the shear rate $\dot{γ}$ . (b) First normal stress difference $N_{1}$ as a function of $\dot{γ}$ . The pictures show the swelling of a jet of HPAM at $0.5 %$ (green) compared to xanthane at $0.9 %$ (blue) from a capillary tube of outside diameter 0.65 mm and at a flow rate of $0.5 {ml s}^{- 1}$ .
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Figure 2
(a) Schematic representation of the soft blade coating experiment. (b) Map of the central part of the film for xanthane $0.9 %$ during the spreading, as a function of the width $z$ and time $t$ . The color code varies from $e ≃ 0$ (red) up to $e = 250 μ m$ (yellow). The first peak is an artifact and is not taken into consideration. The white line shows the mean thickness $e (t)$ over the film width as a function of time.
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Figure 3
(a) Evolution of the fluid thickness $e$ with the wetting length $l_{w}$ for two complex fluids (xanthan 0.9% in blue, HPAM 0.3% in green, and HPAM 0.1% in light green) and a Newtonian fluid (silicone oil, $η = 480 mPa s$ in red). The markers correspond to the experimental data measured for different initial fluid volumes. The continuous lines show the scaling law [Eq. (1)] with prefactors 0.17 (for silicone oil) and 0.06 (for xanthan and HPAM) corresponding to the best fits. The dashed lines are the numerical solutions. (b) Comparison of xanthan 0.9% and HPAM 0.5% (dark green). The blue symbols correspond to the same experiments in (a) and (b).
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Figure 4
Evolution of the fluid thickness $e$ with the wetting length $l_{w}$ for two different velocities and for a solutions of xanthan (and 0.9%). The continuous lines show the scaling law [Eq. (1)] with prefactors of 0.06 corresponding to the best fits.
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Figure 5
(a) Deposition time $t_{d}$ as a function of the deposited volume $Ω_{d}$ for xanthan at 0.9% (dark blue) and Newtonian fluids with viscosity from top to bottom: 1000 mPa s (green), 500 mPa s (yellow), 300 mPa s (pink), and 150 mPa s (cyan). For $Ω_{0} = 0.40 {cm}^{3}$ , $t_{d} = 6$ s for the xanthan solution. (b) Work of the viscous forces during the spreading of volume $Ω_{d}$ for the fluids of Fig. 5 and 50 mPa s (red). The xanthan fluid dissipates more energy than the Newtonian fluid at $η = 300$ mPa s. (c) Evolution of the thickness of the deposit as a function of the deposited length for silicone oil of 480 mPa s (red) and xanthan at 0.9%. Dots are experiments, and lines computations without fitting parameters. The experiments are carried with a velocity equals $1 cm s^{- 1}$ . (d) Shape of deposit for xanthan and Newtonian fluids of viscosity: 500, 300, and 150 mPa s.
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Figure 6
(a) Soft blade coating experimental setup, notations, and axes convention. (b) Schematic representation of the Newtonian and shear-thinning areas in the liquid.
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