Morphology of contorted fluid structures

Dumouchel, Christophe; Thiesset, Fabien; Ménard, Thibaut

doi:10.1016/j.ijmultiphaseflow.2022.104055

Cited by 7 publications

(2 citation statements)

References 40 publications

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“…The reach of the surface plays an important role here since it is the scale which separates the zones in scale space where depends only on integral geometric measures (, , ) and the range of scales for which two-point statistics become a morphological descriptor (Torquato 2002) for which both the geometry and the additional information about the medial axis is required for the structure to be characterized. For scales larger than the reach, the separation cannot be interpreted as the size of the structure under consideration (as it will be seen later, the correlation tends to 0 when the scale is similar to the size of the structure), but should rather be referred to as the morphological parameter as it is generally done in morphological analysis using, for example, integral geometrical measures (the Minkowski functional) of parallel sets (Arns, Knackstedt & Mecke 2004; Dumouchel, Thiesset & Ménard 2022).…”

Section: Analytical Considerationsmentioning

confidence: 99%

Structure of iso-scalar sets

et al. 2022

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An analytical framework is proposed to explore the structure and kinematics of iso-scalar fields. It is based on a two-point statistical analysis of the phase indicator field which is used to track a given iso-scalar volume. The displacement speed of the iso-surface, i.e. the interface velocity relative to the fluid velocity, is explicitly accounted for, thereby generalizing previous two-point equations dedicated to the phase indicator in two-phase flows. Although this framework applies to many transported quantities, we here focus on passive scalar mixing. Particular attention is paid to the effect of Reynolds (the Taylor based Reynolds number is varied from 88 to 530) and Schmidt numbers (in the range 0.1 to 1), together with the influence of flow and scalar forcing. It is first found that diffusion in the iso-surface tangential direction is predominant, emphasizing the primordial influence of curvature on the displacement speed. Second, the appropriate normalizing scales for the two-point statistics at either large, intermediate and small scales are revealed and appear to be related to the radius of gyration, the surface density and the standard deviation of mean curvature, respectively. Third, the onset of an intermediate ‘scaling range’ for the two-point statistics of the phase indicator at sufficiently large Reynolds numbers is observed. The scaling exponent complies with a fractal dimension of 8/3. A scaling range is also observed for the transfer of iso-scalar fields in scale space whose exponent can be estimated by simple scaling arguments and a recent closure of the Corrsin equation. Fourth, the effects of Reynolds and Schmidt numbers together with flow or scalar forcing on the different terms of the two-point budget are highlighted.

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Section: Analytical Considerationsmentioning

confidence: 99%

Structure of iso-scalar sets

et al. 2022

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“…Similarly to the number of droplets in a flow, the Euler characteristic of an interface is an integer-valued topological invariant, and any change in its value requires a splitting or merging of interfaces. Despite its physical significance, the Euler characteristic has only recently been applied to multiphase flows: Dumouchel, Thiesset & Ménard (2022) linked the Euler characteristic to the Gaussian curvature of the droplets and used it to parametrize the morphology of liquid droplets undergoing breakup. The Euler characteristic is commonly used in characterizing the sintering of metal powders (DeHoff, Aigeltinger & Craig 1972;Mendoza et al 2006), classifying lung tissues (Boehm et al 2008) and correcting MRI scans of the human brain (Yotter et al 2011).…”

Section: Introductionmentioning

confidence: 99%

Morphology of clean and surfactant-laden droplets in homogeneous isotropic turbulence

Cannon,

Soligo,

Rosti

2024

J. Fluid Mech.

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We perform direct numerical simulations of surfactant-laden droplets in homogeneous isotropic turbulence with Taylor Reynolds number $Re_\lambda \approx 180$ . The droplets are modelled using the volume-of-fluid method, and the soluble surfactant is transported using an advection–diffusion equation. Effects of surfactant on the droplet and local flow statistics are well approximated using a lower, averaged value of surface tension, thus allowing us to extend the framework developed by Hinze (AIChE J., vol. 1, no. 3, 1955, pp. 289–295) and Kolmogorov (Dokl. Akad. Navk. SSSR, vol. 66, 1949, pp. 825–828) for surfactant-free bubbles to surfactant-laden droplets. We find that surfactant-induced tangential stresses play a minor role in this set-up, thus allowing us to extend the Kolmogorov–Hinze framework to surfactant-laden droplets. The Kolmogorov–Hinze scale $d_H$ is indeed found to be a pivotal length scale in the droplets’ dynamics, separating the coalescence-dominated (droplets smaller than $d_H$ ) and the breakage-dominated (droplets larger than $d_H$ ) regimes in the droplet size distribution. We find that droplets smaller than $d_H$ have a rather compact, regular, spheroid-like shape, whereas droplets larger than $d_H$ have long, convoluted, filamentous shapes with a diameter equal to $d_H$ . This results in very different scaling laws for the interfacial area of the droplet. The normalized area, $A/d_H^2$ , of droplets smaller than $d_H$ is proportional to $(d/d_H)^2$ , while the area of droplets larger than $d_H$ is proportional to $(d/d_H)^3$ , where $d$ is the droplet characteristic size. We further characterize the large filamentous droplets by computing the number of handles (loops of the dispersed phase extending into the carrier phase) and voids (regions of the carrier fluid completely enclosed by the dispersed phase) for each droplet. The number of handles per unit length of filament scales inversely with surface tension. The number of voids is proportional to the droplet size and independent of surface tension. Handles are indeed an unstable feature of the interface and are destroyed by the restoring effect of surface tension, whereas voids can move freely in the interior of the droplets, unaffected by surface tension.

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