Neutron radiography of an anisotropic drainage flow

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Neutron radiography of an anisotropic drainage flow

Artem Skrypnik, Katie Cole, Tobias Lappan, Pablo R. Brito-Parada, Stephen J. Neethling, Pavel Trtik, Kerstin Eckert, and Sascha Heitkam

Phys. Rev. E 109, 014609 – Published 16 January 2024

Abstract

Liquid drainage through foam is dominated by gravity, capillary, and viscous forces. The liquid is conducted by an isotropic network of Plateau borders; however, imposed stress changes the alignment of the foam's structural elements. Previous numerical simulations predicted that a vertical drainage flow will be deflected horizontally if the foam is sheared. We investigated this phenomenon by measuring the distribution of the liquid fraction within a foam formed in a flat rectangular cell. The foam was subjected to shear stress under a forced liquid supply from the top of the cell. Neutron radiographies of unchanged and sheared foam were analyzed to extract measurements of the liquid fraction. Deflections in the distribution of the drainage liquid were detected and found to be positively correlated with increasing foam shear.

Received 5 May 2023
Accepted 8 November 2023

DOI:https://doi.org/10.1103/PhysRevE.109.014609

Physics Subject Headings (PhySH)

Surface & interfacial phenomena Transport phenomena

Foams

Rheology

Neutron imaging

Polymers & Soft MatterFluid Dynamics

Authors & Affiliations

Artem Skrypnik ^1,*, Katie Cole ², Tobias Lappan ³, Pablo R. Brito-Parada⁴, Stephen J. Neethling ⁴, Pavel Trtik⁵, Kerstin Eckert ^1,3, and Sascha Heitkam^1,3,†

¹Institute of Process Engineering and Environmental Technology, TU Dresden, 01062 Dresden, Germany
²Department of Physics, University of Cape Town, 7700 Cape Town, South Africa
³Institute of Fluid Dynamics, Helmholtz-Zentrum Dresden-Rossendorf, 01328 Dresden, Germany
⁴Department of Earth Science and Engineering, Imperial College London, SW7 2AZ London, United Kingdom
⁵Laboratory for Neutron Scattering and Imaging, Paul Scherrer Institut, 5232 Villigen, Switzerland

^*artem.skrypnik@tu-dresden.de
^†sascha.heitkam@tu-dresen.de

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Issue

Vol. 109, Iss. 1 — January 2024

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Images

Figure 1
The arrangement of the measurement setup (a) and a schematic of the foam cell with its component parts (b): 1, the bubble generator; 2, the peristaltic pump; 3, shearing plates, inclined by angle $θ$ ; 4, the drainage liquid source; 5, the air pump; 6, blackbody mesh.
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Figure 2
[(a)–(d)] Schematic of the sequence of the experimental procedure. The line of sight is in the direction of the neutron beam.
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Figure 3
Schematic sequence of the method to determine the local texture and stress tensors. The digital image of the foam structure (a) is postprocessed to extract the structural elements of foam—Plateau borders and bubbles (b)—within the region of interest (ROI). For an interrogation window (IW), vectors $\vec{l}$ connecting the bubble centers (c) were used to calculate a texture tensor $M$ [Eq. (3)], while the stress tensor $σ$ [Eq. (4)] was determined with the vectors $\vec{m}$ representing Plateau borders. The semiaxes of the ellipse (c) are proportional to the eigenvectors of the texture tensor $M$ , and the color of the filled rectangle (d) corresponds to the sign of the normal stress difference (see key at bottom of figure).
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Figure 4
An example of the process for determining liquid fraction deflection from image analysis: A Gaussian model [Eq. (8)] was fitted to a column-averaged liquid fraction distribution at three heights (dashed rectangles) of the 2D liquid fraction distribution (a). The corresponding Gaussian fits (the values are scaled) are depicted as solid lines in (a), and one is shown explicitly in (b) for line 1. The related absolute deflections $Δ x_{i}$ of the peak positions, relative to the initial drainage point $x_{0}$ [cyan line in (a)], and corresponding vertical distances $Δ y_{i}$ were then used to estimate the relative deflections $Δ$ [Eq. (10)] as a function of the applied strain $ɛ$ (c). The 2D liquid profile corresponds to the bubble diameter of $D_{32} = 2.8$ mm and drainage flow rate $Q_{w} = 107 mL / \min$ .
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Figure 5
The effect of the liquid fraction on the deflection $δ$ of a draining liquid and imposed strain $ɛ$ : (a) $Q_{w} = 32 mL / \min$ , (b) $Q_{w} = 53 mL / \min$ , and (c) $Q_{w} = 107 mL / \min$ , with constant bubble size $D_{32} = 4.7 mm$ .
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Figure 6
Estimated texture tensor $M$ maps for different magnitudes of the global strain $ɛ$ , which are colored according to the sign of the normal stress difference $σ_{x x} - σ_{y y}$ (foam bubble size $D_{32} = 4.7 mm$ , and drainage flow rate $Q_{w} = 32 mL / \min$ ).
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