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REVIEW 4 major objections 5 minor 38 references

How interfacial tension enhances drag in turbulent Taylor-Couette flow with neutrally buoyant and equally viscous droplets

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Droplet drag in Taylor–Couette flow traced to interfacial tension on stretched droplet fore heads.

desk verdict Solid simulation study with an exact flux decomposition and a plausible, clearly-stated fore-head/rear-end mechanism; the high-volume-fraction causal chain rests on unverified droplet statistics, so review but with careful attention to the coalescence caveats. read the letter →

arxiv 2411.13115 v1 pith:SCVDO63Q submitted 2024-11-20 physics.flu-dyn

Jinghong Su , Yi-bao Zhang , Cheng Wang , Lei Yi , Fan Xu , Yaning Fan , Junwu Wang , Chao Sun This is my paper · ORCID
classification physics.flu-dyn
keywords Taylor-Couetteflowturbulentdragenhancementinterfacialtensiondropletdeformationmulti-markerVOFmethodliquid-liquidtwo-phaseangularvelocityfluxvolume-of-fluid
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper uses direct numerical simulations of liquid-liquid Taylor-Couette turbulence to identify why dispersed droplets raise the drag of the flow when they have the same density and viscosity as the carrier liquid. At Reynolds number 5200 and droplet volume fractions up to 40%, the torque on the inner cylinder rises with droplet fraction, matching earlier experiments. The paper argues that the extra drag comes from interfacial tension, not from turbulent or viscous stresses averaged over the gap: the interfacial contribution to the angular velocity flux grows with droplet fraction while the other two contributions do not. Near the inner cylinder, shear stretches droplets, and interfacial tension on the fore head (the side closer to the cylinder) pulls against the flow, so the droplet phase moves slower than the surrounding fluid and brakes it. That braking disrupts high-speed streaks, promotes low-speed streaks, and raises the viscous stress at the wall.

What carries the argument

The load-bearing tool is the angular velocity flux decomposition $J^{\omega} = J_T^{\omega}(r) + J_V^{\omega}(r) + J_\sigma^{\omega}(r) = \mathrm{const.}$, which splits the conserved flux into turbulent, viscous, and interfacial-tension transport. The interfacial term is $J_\sigma^{\omega}(r) = -\int_{r_i}^r \langle r^2 f_\sigma^{\theta} \rangle\,dr$, so it directly converts the azimuthal component of interfacial tension into a drag contribution. The causal mechanism is the fore-head/rear-end asymmetry: near the inner cylinder, shear stretches droplets, and interfacial tension on the fore head acts against the flow while that on the rear end acts with it; the fore-head effect dominates, producing a net hindering force that slows the continuous phase and raises wall viscous stress.

What would settle it

A direct test would be to run the same geometry and parameters with interfacial tension switched off ($\sigma = 0$) while keeping droplets deformable by another mechanism; if drag enhancement persists, the claim that interfacial tension is the source fails. Alternatively, tracking individual droplets near the inner cylinder and measuring the azimuthal interfacial tension summed over fore heads should give a net against-flow value that grows with volume fraction; observing zero or positive fore-head forces would falsify the mechanism.

Watch

Extended reading notes

Core claim

The central claim is that the droplet-induced drag enhancement in this system originates from the contribution of interfacial tension, specifically the hindering of the continuous phase by the fore head of stretched droplets. In a Taylor-Couette cell at Re=5200 with neutrally buoyant, equally viscous droplets at volume fractions 0-40%, the torque required to drive the inner cylinder increases with the volume fraction, in line with experiment. Decomposing the conserved angular velocity flux into turbulent, viscous, and interfacial-tension parts shows that the interfacial part grows monotonically with volume fraction, while the radial averages of the other two stay essentially unchanged. Within the viscous and buffer layers near the inner cylinder, shear deforms droplets in the streamwise direction so that the rear end lags behind the fore head; interfacial tension then acts against the flow on the fore head and with the flow on the rear end, with the fore-head effect dominant. This braking effect lowers the angular velocity near the wall, disrupts high-speed streaks, increases the occurrence of low-speed streaks, and thereby raises viscous stress and drag.

Load-bearing premise

The load-bearing assumption is that the modified multi-marker VOF method with marker-group volume fraction 5% produces droplet sizes, deformation, and coalescence behavior representative of the real experiments at all volume fractions up to 40%; the paper itself notes that numerical coalescence remains and that no resolution test was run at 40%.

Editorial extensions

If this is right

  • If the central claim is correct, models of turbulent two-phase drag must include interfacial tension in the near-wall region, and omitting it will underpredict drag at moderate volume fractions.
  • The linear wall law $u^+ = y^+$ breaks down in the viscous sublayer of two-phase flow, because interfacial tension acts as an additional near-wall stress rather than a simple roughness effect.
  • Drag enhancement should grow with droplet volume fraction at fixed Reynolds and Weber numbers, consistent with experiments up to about 30% volume fraction, with the deviation at 40% attributed to residual numerical coalescence.
  • The mechanism explains why deformable droplets enhance drag less than rigid particles: deformability lets droplets adjust shape and exert a weaker hindering effect on the surrounding flow.
  • In industrial Euler-Lagrange type predictions, the boundary-layer interfacial tension contribution must be added to correctly capture the torque increase reported here.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A testable extension is to vary the Weber number at fixed Reynolds number: the fore-head braking effect should weaken as interfacial tension becomes weaker relative to inertia, giving a shear-thinning trend in effective viscosity.
  • If the mechanism is general, the same fore-head braking should appear in other wall-bounded shear flows with deformable droplets, including turbulent channel and pipe flows, not only Taylor-Couette geometry.
  • Comparing droplets with progressively higher surface tension against rigid-particle suspensions could sharpen the claim that deformability is what caps the drag enhancement.
  • Direct experimental measurement of droplet interface curvature near the wall could reveal the sign of the azimuthal interfacial tension on fore heads and rear ends, providing a non-simulation check on the proposed causal chain.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper studies turbulent Taylor–Couette flow laden with neutrally buoyant, equally viscous droplets at volume fractions up to 40%, using a modified multi-marker volume-of-fluid method with the dispersed phase split into marker groups of 5% volume fraction each. The main claim is that the observed drag enhancement originates from interfacial tension: an exact decomposition of the angular velocity flux shows that the interfacial-tension contribution J_sigma grows with phi while the turbulent and viscous contributions do not, and near-wall diagnostics indicate that stretched droplets near the inner cylinder exert a fore-head interfacial-tension force opposing the flow, which slows the continuous phase, disrupts high-speed streaks, and raises wall viscous stress. The paper reports agreement with previous experiments on global torque and presents supporting statistics: radial profiles of J_sigma, joint PDFs of viscous stress and angular velocity, phase-resolved angular velocity PDFs, and per-droplet fore-head/rear-end interfacial tension PDFs.

Significance. If the proposed mechanism is correct, it offers a concrete physical picture for droplet-induced drag enhancement in turbulent emulsions, connecting interfacial tension in the viscous sublayer to streak modification and wall stress. The work combines an exact flux budget with multiple independent diagnostics and includes open-source code, a comparison against experiments, and a spurious-current assessment, which are strengths. The significance is moderate: it is a mechanism-focused numerical study at a single Reynolds and Weber number, and its broader reach depends on the fidelity of the simulated droplet population at high volume fractions.

major comments (4)
  1. [Appendix B, Fig. 10] The manuscript states that the modified multi-marker VOF method 'does not completely resolve the issue of numerical coalescence' and that at phi=40% the simulated droplet-size PDF deviates from experimental results. Because the causal mechanism in §3 is explicitly deformation- and size-dependent (fore-head versus rear-end interfacial tension on stretched droplets), the mechanism is least verified exactly in the regime where the drag enhancement is largest. The standard-VOF comparison in Fig. 11 shows quantitatively different droplet and continuous phase velocity PDFs at phi=40%, confirming that the numerical method affects the droplet statistics on which the mechanism rests. The authors should either provide evidence that the remaining numerical coalescence does not change the sign or magnitude of the fore-head PDF in Fig. 5(b), or explicitly restrict the mechanism claim to volume fractions where the droplet size distribution is validated.
  2. [Appendix A] The resolution test is conducted only for phi=0 and phi=10%, and the paper acknowledges that a resolution test at phi=40% is impractical. The proposed mechanism depends on interface curvature, droplet deformation, and interfacial tension in the viscous sublayer; the Kolmogorov-scale grid estimate does not address interface-resolution requirements such as curvature accuracy and parasitic currents at high phi. A resolution study at an intermediate high volume fraction, or at least a quantitative estimate of how the fore-head interfacial tension statistics change with grid refinement, is needed to support the deformation-based mechanism at the volume fractions where it is invoked.
  3. [§2, choice of phi_mvf] The marker-group volume fraction phi_mvf=5% is a free parameter that controls the maximum droplet size and the degree of numerical coalescence, and no sensitivity study with respect to this parameter is reported. Since the fore-head/rear-end mechanism depends on droplet size and deformation, and since the choice is justified only by reproduction of the global drag from experiments, the robustness of the mechanism to different phi_mvf values should be demonstrated to rule out a method-induced artifact.
  4. [§3, discussion near Fig. 5] The fore-head/rear-end division by the droplet center of mass is acknowledged by the authors as 'somewhat idealized.' The proposed causal chain relies on this division being physically meaningful, but the paper does not test whether the result is sensitive to the definition of the dividing surface, for example by using a different split criterion or by weighting droplets by their deformation. Such a sensitivity check would strengthen the causal interpretation beyond the exact flux budget.
minor comments (5)
  1. [§1 and Appendix B] The phrase 'fore head' is written inconsistently with the standard 'forehead' and appears without hyphen in most places; please unify the spelling.
  2. [§2, notation near Eq. (3.1)] The operator 'Í' used for radial averaging is nonstandard and not defined in the main text; please define it explicitly at first use.
  3. [Fig. 5(b) caption] The normalization of the PDFs by the absolute value of the total azimuthal interfacial tension experienced by all droplets in the range y+<24 should be stated more clearly in the caption, since the PDFs are not conventional probability densities.
  4. [§2, text after Fig. 2] The sentence 'The datasets agree well with each other at phi ⩽ 30%, with a minor deviation observed at phi=40%' should be supported by an explicit error metric, as the deviation at 40% is later used to qualify the method's fidelity.
  5. [Appendix C] The statement that |u|_max/u_i < 0.02 is acceptable would be more informative with a comparison to the typical turbulent velocity fluctuations in the simulations, rather than only to the inner-cylinder velocity.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the interfacial-tension mechanism is diagnosed from the simulated surface-tension force, not imposed by the calibration of phi_mvf.

full rationale

The only potentially self-referential element is the choice of marker-group volume fraction phi_mvf=5%, which the paper states 'faithfully reproduces the global drag of the system reported in our previous experimental study (Yi et al. 2021)' in Section 2. This is a calibration of one numerical parameter to a global benchmark, not a fit of the mechanism. The central claim that drag enhancement originates from interfacial tension is obtained from the exact angular-velocity-flux decomposition in Eq. (3.1), where J_sigma(r) is computed directly from the simulated azimuthal surface-tension force via J_sigma(r) = -∫_{r_i}^{r} <r^2 f_sigma^theta> dr. Nothing in that budget is set equal to the experimental drag increment; the turbulent and viscous contributions are independently measured and shown not to grow with phi. The causal story is supported by separate diagnostics: the fore-head/rear-end PDFs of summed interfacial tension (Fig. 5b), the negative joint PDF between angular velocity and viscous stress (Fig. 3c), the droplet/continuous phase velocity PDFs (Fig. 4), and the standard-VOF comparison in Appendix B. The acknowledged limitations—numerical coalescence at 30-40% (Appendix B) and the absence of a resolution test at phi=40% (Appendix A)—are validity and verification concerns about the droplet population, not circular reductions of the conclusion to its inputs. The paper therefore has no significant circularity.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central claim rests on standard CFD machinery plus several domain assumptions about domain size, stationarity, and the physical meaningfulness of the fore head and rear end split. The only hand-calibrated number is the marker-group volume fraction, chosen to match the authors' own experimental drag data.

free parameters (2)
  • Marker-group volume fraction phi_mvf = 5%
    Chosen by hand to limit numerical coalescence while keeping computational cost feasible; the paper states this choice 'faithfully reproduces the global drag' from Yi et al. (2021), so it is calibrated against experimental data.
  • Domain size parameters = azimuthal angle pi/3, axial aspect ratio 2pi/3
    Chosen to minimize computational cost and validated in prior work; the 6-fold rotational symmetry may truncate large-scale streaks that the mechanism invokes.
assumptions (5)
  • standard math The Navier-Stokes equations with a continuum surface force model govern the two-phase flow (Eqs. 2.1-2.4).
    Unproved background; standard fluid mechanics.
  • domain assumption A 6-fold rotational symmetry and axial aspect ratio 2pi/3 adequately represent the full Taylor-Couette annulus.
    Invoked in Section 2; validated against prior single-phase and multiphase simulations, but limits the range of structures captured.
  • domain assumption The droplet population reaches a statistically stationary state with breakup-coalescence balance.
    Supported by interfacial surface area time series in Fig. 1(a) inset; required for time-averaged statistics.
  • ad hoc to paper The division of a droplet into fore head and rear end at its center of mass is physically meaningful for the mechanism.
    Acknowledged in Section 3 as 'somewhat idealized'; the entire causal argument relies on this split.
  • standard math The angular velocity flux decomposition (Eq. 3.1) is exact and the radial average of the three contributions is the appropriate diagnostic.
    Follows from the Navier-Stokes equations; the interpretive step is the claim that the interfacial contribution 'originates' the drag increase.

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Pith. "Pith review of How interfacial tension enhances drag in turbulent Taylor-Couette flow with neutrally buoyant and equally viscous droplets." pith.science (2026). https://pith.science/paper/SCVDO63Q

@misc{pith2026241113115,
  author       = {Pith},
  title        = {Pith review of: How interfacial tension enhances drag in turbulent Taylor-Couette flow with neutrally buoyant and equally viscous droplets},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SCVDO63Q}},
  note         = {Machine review of arXiv:2411.13115}
}
abstract

The presence of dispersed-phase droplets can result in a notable increase in the system's drag. However, our understanding of the mechanism underlying this phenomenon remains limited. In this study, we use three-dimensional direct numerical simulations with a modified multi-marker volume-of-fluid method to investigate liquid-liquid two-phase turbulence in a Taylor-Couette geometry. The dispersed phase has the same density and viscosity as the continuous phase. The Reynolds number $Re\equiv r_i\omega_i d/\nu$ is fixed at 5200, the volume fraction of the dispersed phase is up to $40\%$, and the Weber number $We\equiv \rho u^2_\tau d/\sigma$ is around 8. It is found that the increase in the system's drag originates from the contribution of interfacial tension. Specifically, droplets experience significant deformation and stretching in the streamwise direction due to shear near the inner cylinder. Consequently, the rear end of the droplets lags behind the fore head. This causes opposing interfacial tension effects on the fore head and rear end of the droplets. For the fore head of the droplets, the effect of interfacial tension appears to act against the flow direction. For the rear end, the effect appears to act in the flow direction. The increase in the system's drag is primarily attributed to the effect of interfacial tension on the fore head of the droplets which leads to the hindering effect of the droplets on the surrounding continuous phase. This hindering effect disrupts the formation of high-speed streaks, favoring the formation of low-speed ones, which are generally associated with higher viscous stress and drag of the system. This study provides new insights into the mechanism of drag enhancement reported in our previous experiments.

Figures

Figures reproduced from arXiv: 2411.13115 by the authors.

Figure 1
Figure 1. (a) The torque 𝑇 needed to drive the IC rotating at a constant rate 𝜔𝑖 . 𝑇 is normalized by the single-phase torque 𝑇𝜙=0. The simulated results are compared with experimental results from our previous work (Yi et al. 2021). The inset shows the interfacial surface area 𝑆/𝑆𝑐𝑦𝑙 as a function of time 𝑡/𝑡0 at various droplet volume fraction 𝜙, where 𝑆𝑐𝑦𝑙 is the surface area of the IC and 𝑡0 is the large eddy turnover tim… view at source ↗
Figure 2
Figure 2. (a) Angular velocity flux and its three contributions as a function of the radial position for the case with 𝜙 = 20%. The radial position (𝑟 − 𝑟𝑖)/𝑑 = 0 corresponds to the IC and (𝑟 − 𝑟𝑖)/𝑑 = 1.0 corresponds to the OC. (b) Viscous stress [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Contour plots of (a) the instantaneous angular velocity and (b) viscous stress on the cylinder surface with radius (𝑟𝑐𝑢𝑡 −𝑟𝑖)/𝑑 = 0.0105 for two-phase turbulence with 𝜙 = 40%. (𝑟𝑐𝑢𝑡 −𝑟𝑖)/𝑑 = 0.0105 corresponds to 𝑦 + = 3.45. (c) Joint probability density function between the angular velocity and the viscous stress for 𝜙 = 40%. (d) Probability density functions of 𝜏𝑉 for different droplet volume fractions. In (c) and… view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: Contour plots of the instantaneous angular velocity 𝜔/𝜔𝑖 on a cylinder surface with (𝑟𝑐𝑢𝑡 − 𝑟𝑖)/𝑑 = 0.02 for (a) single-phase turbulence with 𝜙 = 0 and (b) two-phase turbulence with 𝜙 = 40%. The droplet interfaces (𝛼 = 0.5, solid lines) are also superimposed in (b). (c…
Figure 5
Figure 5. Figure 5: (a) Contour plot of the instantaneous angular velocity in the 𝑟 −𝜃 plane for 𝜙 = 40% case. Droplet interfaces (𝛼 = 0.5) are represented by the solid lines. The inset is an enlarged view of the main figure marked by the red rectangle. The droplet in the inset is divided…
Figure 6
Figure 6. Figure 6: A sketch of how the interfacial tension works in a TC system. the role of interfacial tension contribution 𝐽 𝜔 𝜎 (𝑟) to the total angular velocity flux, which is plotted in figure 7(a) for various volume fractions. Although the above discussion focuses on the region ne…
Figure 7
Figure 7. Figure 7: (a) Interfacial tension contribution 𝐽 𝜔 𝜎 (𝑟) as a function of radial position at various droplet volume fractions. The inset shows the azimuthal component of the interfacial tension in the near wall region and the negative value indicates that the effect of interfaci…
Figure 8
Figure 8. Figure 8: (a) Mean azimuthal velocity profiles near the IC. 𝑢 + = (𝑢𝑖 − ⟨𝑢 𝜃 ⟩)/𝑢𝜏 is the velocity difference from the IC normalized by the friction velocity. The dashed lines show the linear relation 𝑢 + = 𝑦 + and the logarithmic law 𝑢 + = (1/𝜅)ln𝑦 + + 𝐵 with the typical values…
Figure 9
Figure 9. Figure 9: Radial dependence of 𝑁𝑢𝜔 for two different grid resolutions. An error bar indicating a 1% error is provided for reference and both the cases for 𝜙 = 0 and 𝜙 = 10% lie within the error bar. Experimental results Numerical results 0.0 0.5 1.0 1.5 2.0 2.5 3.0 10 -2 10 -1 1…
Figure 10
Figure 10. Figure 10: The PDF of the droplet diameter 𝐷 with respect to the average diameter 𝐷𝑚 for two-phase turbulence with 𝜙 = 40%. The solid lines denote the fitting results with a log-normal distribution function. The simulated results are compared with experimental results from our p…
Figure 11
Figure 11. Figure 11: Angular velocity probability density functions for the droplet and continuous phases at the radius cut (𝑟𝑐𝑢𝑡 − 𝑟𝑖)/𝑑 = 0.02 obtained using (a) the standard VOF method and (b) the modified multi-marker VOF method. The inset shows the average angular velocity of the dro…
Figure 12
Figure 12. Figure 12: Spurious currents for two static drops in a TC system with the two cylinders fixed. (a) Contour of the velocity magnitude. (b) The maximum velocity magnitude, |𝑢|𝑚𝑎𝑥, as a function of time. |𝑢|𝑚𝑎𝑥 is normalized by the velocity of the inner cylinder 𝑢𝑖 considered in ou…

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Works this paper leans on

38 extracted references · 38 canonical work pages

  1. [1]

    Assen, Martin PA, Ng, Chong Shen, Will, Jelle B, Stevens, Richard JAM, Lohse, Detlef & Verzicco, Roberto 2022 Strong alignment of prolate ellipsoids in Taylor–Couette flow. J. Fluid Mech. 935, A7

    work page 2022

  2. [2]

    Huisman, Sander G 2021 Catastrophic phase inversion in high-Reynolds-number turbulent Taylor– Couette flow. Phys. Rev. Lett. 126 (6), 064501. Balc´azar, N ´estor, Lehmkuhl, Oriol, Rigola, Joaquim & Oliva, Assensi 2015 A multiple marker level-set method for simulation of deformable fluid particles. Int. J. Multiphase Flow 74, 125–142

    work page 2021

  3. [3]

    Fluid Mech

    Barcilon, AJMFR, Brindley, J, Lessen, M & Mobbs, FR 1979 Marginal instability in Taylor–Couette flows at a very high Taylor number.J. Fluid Mech. 94 (3), 453–463

    work page 1979

  4. [4]

    Fluid Mech

    Brauckmann, Hannes J & Eckhardt, Bruno 2013 Direct numerical simulations of local and global torque in Taylor–Couette flow up to Re= 30 000.J. Fluid Mech. 718, 398–427

    work page 2013

  5. [5]

    Chen, Songtao, Zhao, Weiwen & Wan, Decheng 2022 Turbulent structures and characteristics of flows past a vertical surface-piercing finite circular cylinder. Phys. Fluids 34 (1), 015115

    work page 2022

  6. [6]

    Coyajee, Emil & Boersma, Bendiks Jan 2009 Numerical simulation of drop impact on a liquid–liquid interface with a multiple marker front-capturing method. J. Comput. Phys. 228 (12), 4444–4467

    work page 2009

  7. [7]

    Crialesi-Esposito, Marco, Rosti, Marco Edoardo, Chibbaro, Sergio & Brandt, Luca 2022 Modulation of homogeneous and isotropic turbulence in emulsions. J. Fluid Mech. 940, A19

    work page 2022

  8. [8]

    Fluid Mech

    Dong, S 2007 Direct numerical simulation of turbulent Taylor–Couette flow.J. Fluid Mech. 587, 373–393

    work page 2007

Show all 38 references
  1. [9]

    Eckhardt, Bruno, Grossmann, Siegfried & Lohse, Detlef 2007 Torque scaling in turbulent Taylor– Couette flow between independently rotating cylinders. J. Fluid Mech. 581, 221–250

    2007

  2. [10]

    Elghobashi, Said 2019 Direct numerical simulation of turbulent flows laden with droplets or bubbles. Annu. Rev. Fluid Mech. 51, 217–244

    2019

  3. [11]

    Loeben, Germany: Holzmann CFD

    Holzmann, Tobias 2016 Mathematics, numerics, derivations and openfoam ®. Loeben, Germany: Holzmann CFD

    2016

  4. [12]

    Sun, Chao 2013 Logarithmic boundary layers in strong Taylor–Couette turbulence.Phys. Rev. Lett. 110 (26), 264501

    2013

  5. [13]

    Innocenti, Alessio, Jaccod, Alice, Popinet, St ´ephane & Chibbaro, Sergio 2021 Direct numerical simulation of bubble-induced turbulence. J. Fluid Mech. 918, A23

    2021

  6. [14]

    Energy Fuels 26 (7), 4017–4026

    Kilpatrick, Peter K 2012 Water-in-crude oil emulsion stabilization: review and unanswered questions. Energy Fuels 26 (7), 4017–4026

    2012

  7. [15]

    Maxey, Martin R 2017 Droplets in turbulence: a new perspective. J. Fluid Mech. 816, 1–4

    2017

  8. [16]

    Mcclements, David Julian 2007 Critical review of techniques and methodologies for characterization of emulsion stability. Crit. Rev. Food Sci. Nutr.47 (7), 611–649

    2007

  9. [17]

    Mukherjee, Siddhartha, Safdari, Arman, Shardt, Orest, Kenjere ˇs, Sa ˇsa & Van den Akker, Harry EA 2019 Droplet–turbulence interactions and quasi-equilibrium dynamics in turbulent emulsions. J. Fluid Mech. 878, 221–276

    2019

  10. [18]

    Nemati, Hassan, Breugem, Wim-Paul, Kwakkel, Marcel & Boersma, Bendiks Jan 2021 Direct numerical simulation of turbulent bubbly down flow using an efficient CLSVOF method. Int. J. Multiphase Flow 135, 103500

    2021

  11. [19]

    Ni, Rui 2024 Deformation and breakup of bubbles and drops in turbulence. Annu. Rev. Fluid Mech. 56, 319–347

    2024

  12. [20]

    Fluid Mech.719, 14–46

    Ostilla, Rodolfo, Stevens, Richard JAM, Grossmann, Siegfried, Verzicco, Roberto & Lohse, Detlef 2013 Optimal Taylor–Couette flow: direct numerical simulations.J. Fluid Mech.719, 14–46

    2013

  13. [21]

    Picano, Francesco, Breugem, Wim-Paul & Brandt, Luca 2015 Turbulent channel flow of dense suspensions of neutrally buoyant spheres. J. Fluid Mech. 764, 463–487

    2015

  14. [22]

    Popinet, St´ephane 2018 Numerical models of surface tension. Annu. Rev. Fluid Mech. 50 (1), 49–75

    2018

  15. [23]

    Rosti, Marco E, Brandt, Luca & Mitra, Dhrubaditya 2018 Rheology of suspensions of viscoelastic spheres: Deformability as an effective volume fraction. Phys. Rev. Fluids 3 (1), 012301

    2018

  16. [24]

    Rosti, Marco E, Ge, Zhouyang, Jain, Suhas S, Dodd, Michael S & Brandt, Luca 2019 Droplets in homogeneous shear turbulence. J. Fluid Mech. 876, 962–984

    2019

  17. [25]

    PhD thesis, Imperial College London (University of London)

    Rusche, Henrik 2003 Computational fluid dynamics of dispersed two-phase flows at high phase fractions. PhD thesis, Imperial College London (University of London)

    2003

  18. [26]

    Scarbolo, Luca & Soldati, Alfredo 2015 Wall drag modification by large deformable droplets in turbulent channel flow. Comput. Fluids 113, 87–92

    2015

  19. [27]

    Scheufler, Henning & Roenby, Johan 2019 Accurate and efficient surface reconstruction from volume fraction data on general meshes. J. Comput. Phys. 383, 1–23

    2019

  20. [28]

    Spandan, Vamsi, Verzicco, Roberto & Lohse, Detlef 2018 Physical mechanisms governing drag reduction in turbulent Taylor–Couette flow with finite-size deformable bubbles. J. Fluid Mech. 849, R3. 20 J Su, Y Zhang, C Wang, L Yi, F Xu, Y Fan, J Wang, and C Sun

    2018

  21. [29]

    Spernath, Aviram & Aserin, Abraham 2006 Microemulsions as carriers for drugs and nutraceuticals. Adv. Colloid Interface Sci. 128, 47–64

    2006

  22. [30]

    Su, Jinghong, Wang, Cheng, Zhang, Yi-bao, Xu, Fan, Wang, Junwu & Sun, Chao 2024a Turbulence modulation in liquid-liquid two-phase Taylor-Couette turbulence, arXiv: 2407.00992

    arXiv

  23. [31]

    Thomas, S, Esmaeeli, A & Tryggvason, G 2010 Multiscale computations of thin films in multiphase flows. Int. J. Multiphase Flow 36 (1), 71–77. de Vita, Francesco, Rosti, Marco Edoardo, Caserta, Sergio & Brandt, Luca2019 On the effect of coalescence on the rheology of emulsions....

    2010

  24. [32]

    Fluid Mech.952, A39

    Wang, Cheng, Yi, Lei, Jiang, Linfeng & Sun, Chao 2022 Turbulence drag modulation by dispersed droplets in Taylor–Couette flow: the effects of the dispersed phase viscosity.J. Fluid Mech.952, A39

    2022

  25. [33]

    Wang, Guiquan, Abbas, Micheline & Climent, ´Eric 2017 Modulation of large-scale structures by neutrally buoyant and inertial finite-size particles in turbulent Couette flow. Phys. Rev. Fluids 2 (8), 084302

    2017

  26. [34]

    Wang, Lijuan, Li, Xuefeng, Zhang, Gaoyong, Dong, Jinfeng & Eastoe, Julian 2007 Oil-in-water nanoemulsions for pesticide formulations. J. Colloid Interface Sci. 314 (1), 230–235

    2007

  27. [35]

    Xu, Fan, Su, Jinghong, Lan, Bin, Zhao, Peng, He, Yurong, Sun, Chao & Wang, Junwu 2023 Direct numerical simulation of Taylor–Couette flow with vertical asymmetric rough walls. J. Fluid Mech. 975, A30

    2023

  28. [36]

    Xu, Fan, Zhao, Peng, Sun, Chao, He, Yurong & Wang, Junwu 2022 Direct numerical simulation of Taylor-Couette flow: Regime-dependent role of axial walls.Chem. Eng. Sci. 263, 118075

    2022

  29. [37]

    Yi, Lei, Toschi, Federico & Sun, Chao 2021 Global and local statistics in turbulent emulsions. J. Fluid Mech. 912, A13

    2021

  30. [38]

    Yi, Lei, Wang, Cheng, van Vuren, Thomas, Lohse, Detlef, Risso, Fr´ed´eric, Toschi, Federico & Sun, Chao 2022 Physical mechanisms for droplet size and effective viscosity asymmetries in turbulent emulsions. J. Fluid Mech. 951, A39

    2022

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.