Pith. sign in

REVIEW 3 major objections 4 minor 54 references

Membrane Heterogeneity Driven Dynamics of Multicomponent Vesicles in Shear Flow

T0 review · 3 major / 4 minor · reviewed 2026-08-04 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The paper claims that membrane surface-tension contrast alone—without viscosity mismatch or asymmetric phase placement—can drive vesicles to swing and tumble under shear, and that bending-rigidity contrast organizes a phase diagram with thr

desk verdict Solid 3D phase-field study with a genuinely new surface-tension contrast mechanism, but the unstated inextensibility relaxation parameter and single-shot phase diagrams mean the headline claims need a sensitivity pass before I'd trust them. read the letter →

arxiv 2509.08295 v1 pith:LQBBPQ3V submitted 2025-09-10 cond-mat.soft physics.bio-phphysics.flu-dyn

Shuqi Tang , Steven M. Wise , John Lowengrub , Zhenlin Guo This is my paper · ORCID
classification cond-mat.softphysics.bio-phphysics.flu-dyn
keywords multicomponentvesiclesshearflowphase-fieldmodelsurfacetensioncontrastbendingrigidityvesicledynamicslipiddomainsphasediagram
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

The authors build a thermodynamically consistent phase-field model coupling vesicle-fluid flow, membrane shape, and lateral phase separation into co-existing liquid-ordered and liquid-disordered domains, and validate it against experiments on lipid-domain coarsening and on two-phase vesicles in shear. Using this model, they claim that surface tension heterogeneity (the ld phase having lower surface tension) can by itself produce swinging and tumbling—two motions previously attributed to viscosity contrast or asymmetric phase distributions. They also map a phase diagram for bending-rigidity contrast and capillary number, identifying six regimes, three of which (lateral ring banding, lateral broken-ring banding, vertical broken-ring banding) are new. If true, the result turns membrane surface-tension contrast into a controllable design knob for vesicle-based carriers in flow.

What carries the argument

A phase-field model with two order parameters: φ marks the vesicle membrane as a diffuse interface, and c_Γ marks the lateral lo/ld composition; the diffuse-domain method extends surface equations into the bulk. The model is derived from a free energy (bending, surface, line, area-penalty) via energy variation, giving thermodynamically consistent forces and fluxes, with local inextensibility enforced by a Lagrange multiplier. The regime map is organized by dimensionless contrasts κ_B = κ_B^ld/κ_B^lo, σ_S = σ_S^ld/σ_S^lo, and the bending capillary number Ca = μ_out U L²/κ_B^lo. The surface-tension mechanism works by lowering the energetic cost of deforming ld domains, anchoring them at the ti

What would settle it

Run the same parameters but replace the symmetric tip domains with a random or single off-center ld domain, or change the reduced volume to v=0.8; if surface-tension-driven swinging/tumbling disappears or the six-regime taxonomy collapses into different states, the mechanism is not generic. Alternatively, a microfluidic experiment on a giant unilamellar vesicle with matched bending rigidities but σ_S<1 should show the predicted tumbling at Ca≈1; failure to observe it would contradict the claim.

Watch

Extended reading notes

Core claim

The central discovery is twofold. First, for a prolate vesicle with reduced volume v≈0.91 and two symmetric ld domains pre-placed at the tips, lowering the ld/lo surface-tension ratio σS below 1 at fixed bending contrast κ_B=0.65 causes the vesicle to enter two new regimes: small-amplitude swinging (VII) and rigid-body-like tumbling (VIII), with no viscosity contrast and no asymmetric domain placement. Second, varying the bending-rigidity contrast κ_B and the bending capillary number Ca sweeps out six banding/treading regimes, including three not previously reported: lateral ring banding (I), lateral broken-ring banding (II), and vertical broken-ring banding (IV); within vertical ring bandin

Load-bearing premise

The whole regime map—including the claim that surface tension contrast alone triggers swinging and tumbling—is computed from a single initial condition: a prolate vesicle with reduced volume v≈0.91 and two symmetric ld domains placed at the tips; if the regimes depend sensitively on that geometry or on the diffuse-interface form of the surface-tension energy, the general claim would not follow.

Editorial extensions

If this is right

  • Surface-tension contrast should be treated as a first-order control parameter for vesicle motion in flow, alongside viscosity contrast and bending contrast.
  • The three new banding regimes (I, II, IV) expand the known dynamical repertoire and should be observable in experiments with tunable lipid compositions.
  • The identified 'Low-Rigidity Full-Dynamics Belt' and 'Low-Capillary Full-Dynamics Belt' mark parameter windows where all six regimes coexist, useful for designing vesicle-based carriers.
  • Subdividing vertical ring banding into temporary, cyclic, and stable rings implies the ring is a metastable structure governed by bending contrast and shear strength.
  • The model's agreement with experiments on phase separation and shear dynamics offers a validated 3D framework for predicting multicomponent vesicle behavior under flow.

Reading between the lines

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

  • If the surface-tension-only swinging and tumbling mechanism holds generally, it suggests vesicles could be steered by locally modulating tension (e.g., via drugs, light, or other stimuli) rather than by controlling viscosity; a testable extension is to scan reduced volume v and initial domain arrangement to check the robustness of regimes VII and VIII.
  • The surface-tension-driven swinging bears a formal resemblance to thermocapillary or surfactant-driven migration of droplets; the same diffuse-domain machinery might translate to droplets with heterogeneous surface tension.
  • The regime taxonomy depends on the diffuse-interface representation of surface tension (through the regularized delta function and the specific surface energy); a sharp-interface benchmark or a convergence study in the interfacial thickness ε_ϕ would clarify whether the new regimes are physical or artifacts of the model's regularization.
  • Because the phase diagram was computed from a single initial condition (prolate vesicle with v≈0.91 and symmetric tip domains), the regime boundaries are likely to shift with vesicle deflation and domain placement; mapping those shifts would produce a more complete design chart.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. This paper proposes a thermodynamically consistent phase-field model for multicomponent vesicles in shear flow, coupling a bulk Navier–Stokes/Cahn–Hilliard system with a diffuse-domain surface Cahn–Hilliard equation for lipid phases. The membrane energy includes bending, surface tension, line tension, and surface-area penalty terms, and local inextensibility is imposed through a harmonic-relaxation Lagrange multiplier. The model is validated against GUV phase-separation experiments [5] and shear-flow experiments [33], including a quantitative comparison of inclination-angle oscillations. The authors then present phase diagrams in the (bending-rigidity contrast, capillary number) and (surface-tension contrast, capillary number) planes, reporting three new bending-driven regimes (lateral ring banding, lateral broken-ring banding, vertical broken-ring banding) and a new surface-tension-driven swinging/tumbling mechanism that operates without viscosity contrast or asymmetric phase distributions.

Significance. If the reported results are robust, the paper offers a useful 3D computational framework for multicomponent vesicles and identifies a previously unrecognized control knob—membrane surface-tension heterogeneity—for vesicle dynamics in shear. The model derivation is a genuine strength: Appendix B supplies a free-energy dissipation identity (B.25) with explicit nonnegative dissipation terms, and the validation against experiments gives nontrivial support for the model's physical content. The inclination-angle comparison in Fig. 12 is particularly valuable. However, the central new claims—the three new bending regimes and the surface-tension-driven swinging/tumbling mechanism—are supported only by simulations whose inextensibility regularization parameter is never reported and for which no mesh or ξ-convergence study is shown, and the phase diagrams are built on a single initial geometry/phase configuration. These gaps must be addressed before the paper's headline conclusions can be considered established.

major comments (3)
  1. [§4.2, Eq. (20), Table 1, Appendix C Step 4] The inextensibility relaxation parameter ξ is listed in Table 1 but never assigned a value in any numerical setup, including the phase-diagram runs of §4.1–4.2. Eq. (20) enforces P:∇u=0 only in the limit ξ→0; for finite ξ the membrane is extensible, and the surface-energy term ∫σ_S(c_Γ)ζ(ϕ)dV can then do mechanical work that would be forbidden for a strictly inextensible vesicle. The §3.2 validation sets σ_S=1 and therefore does not test the heterogeneous-surface-tension term. Without a reported ξ, a ξ→0 (or sufficiently small) convergence study, and a spatial-resolution check for the swinging/tumbling regimes (VII) and (VIII), the headline surface-tension mechanism cannot be distinguished from a regularization artifact. This is load-bearing for the paper's central claim.
  2. [§4.1, §4.2, Figs. 13 and 16] The phase diagrams and the regime taxonomy are generated from a single initial condition: a prolate vesicle with reduced volume v≈0.91, two symmetric ld domains pre-positioned at the tips, and area fraction a_ld=0.4 (§4.1; §4.2 states 'The numerical setup follows Section 4.1'). No sensitivity study is reported with respect to initial vesicle aspect ratio, initial domain placement or area fraction, or stochastic phase-field noise. Since the claim is that surface-tension heterogeneity (and bending heterogeneity) generically drives these regimes, the authors should show representative checks that the regimes and their boundaries are not artifacts of this one prepared initial state. A single 128^3 point-sampled run per parameter pair is also insufficient to establish convergence of the regime boundaries.
  3. [§3.1, §3.2, and Abstract] The abstract and conclusion describe the model as 'quantitatively validated,' but the validation is partly calibrated: in §3.1 the lipid mobility ratio Cn_Γ/Pe_Γ=0.12 and the interface thickness ε_c=0.02 are fitted/adjusted to the experimental data, and in §3.2 ε_c and ε_ϕ are 'fitted to experimental GUVs.' This is not a fatal flaw, but the claim of parameter-free quantitative prediction should be softened, and the fitting ranges and the sensitivity of the validation to those fitted values should be stated explicitly.
minor comments (4)
  1. [Eqs. (25)–(26), Table 1] Notation is inconsistent: the dimensionless surface-tension strength appears as Cs in Eq. (26) and as Cs_Γ in Table 1 and Eq. (C.29). Section 3.2 also uses 'Cs=27' without the subscript. Please unify.
  2. [§4.2, paragraph after Fig. 16] The text says that as σ_S decreases to 0.85, ld domains form a complete ring and its periodic rupture/reconnection 'result[s] in regime (VIII).' But regime (VIII) is later defined as tumbling with ld domains 'stably anchored at high-curvature tips.' This apparent contradiction should be clarified, since the description sounds like regime (VII) swinging.
  3. [§2.3 and Appendix B] The line-tension delta function is written as ζ(c_Γ) in Eq. (16), but the variational derivatives in Appendix B and the chemical potential (26) use expressions involving η_c f'(c_Γ)/ε_c − η_c ε_c Δc_Γ. The relationship between δ(c_Γ) and ζ(c_Γ) should be stated precisely, and the signs in the line-tension contributions to ω_c should be checked against the energy (13).
  4. [Appendix C, Step 4] The local inextensibility correction in Eq. (C.41) uses ∇·u^n in the constraint, while the velocity field has already been updated to u^{n+1} in Step 3. The temporal staggering is likely intentional, but it should be stated explicitly, along with the order of accuracy implied for the constraint.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the model is derived from an explicit free energy, validated against external experiments, and the new dynamical regimes are outputs of parameter sweeps rather than fitted inputs.

full rationale

The paper's central derivation chain is self-contained. The governing equations (17)-(26) are obtained from an explicit free energy functional (Eq. 13) via an energy-variation procedure (Appendix B), and the thermodynamic consistency identity (B.25) is derived rather than assumed. The new dynamical regimes, including surface-tension-driven swinging (VII) and tumbling (VIII), are computed from the PDE system by varying the stated dimensionless parameters (sigma_S, Ca, kappa_B) while holding viscosity contrast at unity and using a symmetric initial condition (two symmetric ld domains at the tips, v=0.91, a_ld=0.4). These regimes are not fitted to the target phenomenon: they appear only when sigma_S<1 in the simulations, and the phase diagrams are outputs of the numerical model, not inputs. The experimental validation in Section 3 uses fitted interfacial thicknesses and line tension values, but it is presented as reproduction/validation, not as a prediction of the new regimes, and the new regime diagrams are not constructed from those fitted quantities. Self-citations in the paper are limited to numerical methods (diffuse-domain discretization and multigrid solver) and do not carry the physical argument. No uniqueness theorem is imported from the authors' prior work, and no known result is merely renamed. The reviewer-raised concerns about the unspecified inextensibility relaxation parameter xi and the single initial condition are robustness or correctness issues, not definitional circularity: there is no equation or fitted parameter that makes the predicted swinging/tumbling equivalent to the model inputs by construction. Therefore the circularity score is 0.

Assumptions & free parameters 6 free parameters · 7 assumptions · 0 invented entities

The central claim rests on a free-energy phase-field model whose surface-tension term, diffuse-domain extension, penalty area constraint, and single initial condition are adopted as modeling inputs. Several validation parameters are fitted to the experimental datasets used as benchmarks. The new regimes are simulation outputs of this model, so their strength is conditional on these assumptions and on the chosen initial geometry.

free parameters (6)
  • epsilon_c (membrane-component interface thickness) = 0.02 (Sec 3.1), 0.05 (Sec 3.2)
    Section 3.1: 'epsilon_c = 0.02, fitted to match experimental GUVs.' Section 3.2: 'Interfacial thickness parameters ... are fitted to experimental GUVs.' The resulting domain coarsening and regime transitions depend on this diffuse-interface width.
  • lipid mobility ratio CnGamma/PeGamma = 0.12
    Section 3.1: 'The lipid mobility is adjusted such that CnGamma/PeGamma = 0.12.' It controls the coarsening rate compared with experimental domain counts and perimeters.
  • line tension (Cahn number) in shear validation = sigma_L = 0.1, 1, 4 pN, CnGamma = 0.2, 2, 8
    Section 3.2: 'The line tension sigma_L is varied as 0.1, 1, and 4 pN to reproduce the three dynamical regimes observed experimentally.' This makes the shear-flow validation partly a calibration to the target outcomes.
  • epsilon_phi (membrane diffuse-interface thickness) in shear runs = 0.05
    Section 3.2: 'Interfacial thickness parameters epsilon_c = 0.05 for membrane components and epsilon_phi = 0.05 for the membrane are fitted to experimental GUVs.' The diffuse membrane width affects all force terms and the phase diagram.
  • surface area penalty coefficient M_S = 2000
    Set in Sections 3.2 and 4.1. The penalty controls how strictly area conservation is imposed; weak penalization can allow area drift that affects regime boundaries.
  • surface-tension strength CsGamma and Peclet numbers in phase-diagram runs = CsGamma = 10, PeGamma = 1, Pe = 1000, CnGamma = 0.05
    Section 4.1: 'dimensionless parameters are specified as follows ... CsGamma = 10, ... PeGamma = 1.' These are chosen by hand for the phase diagrams; the surface-tension-driven regimes are mapped at CsGamma = 10, and the Pe values set how fast domains relax.
assumptions (7)
  • standard math The phase-field omega_phi approximates mean curvature and the regularized delta approximates the sharp membrane in the zero-thickness limit
    Used throughout Sections 2.3 and Appendix A; relies on asymptotic convergence results [39, 41-47].
  • domain assumption Normal extension of cGamma off the membrane, n(n dot grad cGamma) = 0, and tangential flux n dot qc = 0
    Appendix A, equations (A.2)-(A.3), are required to convert the surface Cahn-Hilliard equation into the diffuse-domain equation (A.9).
  • domain assumption Zero spontaneous curvature and neglected Gaussian curvature in bending energy
    Section 2.3: 'zero spontaneous curvature is assumed and the contribution from Gaussian curvature is neglected.' This affects which shapes and banding patterns are stable.
  • domain assumption Inner and outer fluids have equal density and, in the heterogeneity studies, equal viscosity
    Section 3.2 sets rho_in = rho_out and mu_in = mu_out; Sections 4.1 and 4.2 follow that setup and claim surface-tension-induced tumbling and swinging with no viscosity contrast. The claim is conditional on viscosity contrast being absent.
  • ad hoc to paper A single initial geometry is used for the phase diagrams: prolate vesicle about v=0.91 with two symmetric ld domains at the tips, ald=0.4
    Section 4.1: 'two symmetric ld-phase domains (red) are pre-positioned at the vesicle tips along the x-axis, with an initial area fraction ald = 0.4'; Section 4.2 says the setup follows Section 4.1. The regime taxonomy and the new mechanism are derived from this one initial condition.
  • domain assumption The prescribed local surface tension energy sigma_S(cGamma) zeta(phi) is a valid representation of membrane surface-tension heterogeneity
    Section 2.3 adds this term to the free energy rather than deriving it from a sharp-interface limit; the new swinging/tumbling mechanism depends on this energy form.
  • domain assumption Boundary conditions are no-flux for phase fields, Dirichlet shear velocity at top and bottom, and periodic in x and y
    Sections 2.1 and 3.2; the finite-domain and periodicity choices can affect long-time vesicle orientation and regime classification.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Membrane Heterogeneity Driven Dynamics of Multicomponent Vesicles in Shear Flow." pith.science (2026). https://pith.science/paper/LQBBPQ3V

@misc{pith2026250908295,
  author       = {Pith},
  title        = {Pith review of: Membrane Heterogeneity Driven Dynamics of Multicomponent Vesicles in Shear Flow},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LQBBPQ3V}},
  note         = {Machine review of arXiv:2509.08295}
}
read the original abstract

Despite their significance in biology and materials science, the dynamics of multicomponent vesicles under shear flow remain poorly understood because of their nonlinear and strongly coupled nature, especially regarding the role of membrane heterogeneity in driving nonequilibrium behavior. Here we present a thermodynamically consistent phase-field model, which is validated against experiments, for the quantitative investigation of these dynamics. While prior research has primarily focused on viscosity or bending rigidity contrasts, we demonstrate that surface tension heterogeneity can also trigger swinging and tumbling in vesicles under shear. Additionally, our systematic phase diagram reveals three previously unreported dynamical regimes arising from the interplay between bending rigidity heterogeneity and shear flow. Overall, our model provides a robust framework for understanding multicomponent vesicle dynamics, with findings offering new physical insights and design principles for tunable vesicle-based carriers.

Figures

Figures reproduced from arXiv: 2509.08295 by the authors.

Figure 1
Figure 1. (a) A multicomponent vesicle with lipid components ( [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Phase separation on GUVs at ald = 0.3: experimental snapshots (top) from [5] and numerical results (bottom), showing lo domains (blue) forming within the ld phase (red). To further validate the accuracy of our model, we compare the time evolution of the number of ld domains predicted by our numerical simulations with the experimental measurements reported in [5]. As shown in figure 4, for both area fractions under i… view at source ↗
Figure 3
Figure 3. Phase separation on GUVs at ald = 0.7: experimental snapshots (top) from [5] and numerical results (bottom), showing ld domains (red) forming within the lo phase (blue) [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (14 more)
Figure 4
Figure 4. Figure 4: Time evolution of number of lipid rafts for [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: Time evolution of the total perimeter of lipid domains at [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: Experimental images (left) from [5] and numerical results (right) showing the time evolution of lo domains (blue) within the ld phase (red). The simulation is initialized with 12 symmetrically placed lo domains and an area fraction alo = 0.64. In our simulations, the c…
Figure 7
Figure 7. Figure 7: Experimental images (left) from [5] and numerical results (right) with front and rear views over time, showing a combination of lo phase (blue) and ld phase (red). The simulation is initialized with 6 symmetrically placed lo domains and an area fraction alo = 0.65 [PI…
Figure 8
Figure 8. Figure 8: Geometric parameters used to characterize vesicle dynamics under shear flow: the principal axes of the vesicle [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]
Figure 9
Figure 9. Figure 9: Experimental images (top) from [33] and numerical results (bottom) showing tank treading and swinging at [PITH_FULL_IMAGE:figures/full_fig_p010_9.png]
Figure 10
Figure 10. Figure 10: Experimental images (top) from [33] and numerical results (bottom) showing strong deformation during tank treading and swinging at CnΓ = 2, for a vesicle with reduced volume v = 0.8, flattening parameter f = 0.65, and area fraction ald = 0.6 [PITH_FULL_IMAGE:figures/…
Figure 11
Figure 11. Figure 11: Experimental images (top) from [33] and numerical results (bottom) showing the tumbling at CnΓ = 8, for a vesicle with reduced volume v = 0.7, flattening parameter f = 0.75, and area fraction ald = 0.5. not only the accuracy and robustness of the model but also its pr…
Figure 12
Figure 12. Figure 12: Time evolution of inclination angle θ for a vesicle with reduced volume v = 0.95, flattening parameter f = 0.3, and area fraction ald = 0.7 at CnΓ = 0.2, comparing numerical results (solid line) with experimental data (circles) from [33]. 4 Numerical experiments In th…
Figure 13
Figure 13. Figure 13: Phase diagram of vesicle dynamics under shear flow as a function of bending rigidity contrast [PITH_FULL_IMAGE:figures/full_fig_p013_13.png]
Figure 14
Figure 14. Figure 14: (a) Time evolution of six vesicle dynamic regimes [PITH_FULL_IMAGE:figures/full_fig_p015_14.png]
Figure 15
Figure 15. Figure 15: (a) Time evolution of sub-regimes (Va)–(Vc) within regime (V) at κB = 0.45 with varying Ca. (b) Corresponding evolution of bending and line energies. Key time points: t1 = 8.2, t2 = 11.6, t3 = 14.3, t4 = 20.5, t5 = 25.7, t6 = 28.9, t7 = 43.6, t8 = 62, t9 = 66. In addi…
Figure 16
Figure 16. Figure 16: (a) Phase diagram of vesicle dynamics under shear flow as a function of surface tension contrast [PITH_FULL_IMAGE:figures/full_fig_p017_16.png]
Figure 17
Figure 17. Figure 17: (a) Time evolution of vesicle dynamic regimes [PITH_FULL_IMAGE:figures/full_fig_p018_17.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

54 extracted references · 54 canonical work pages

  1. [5]

    Lipid domain coarsening and fluidity in multicompo- nent lipid vesicles: A continuum based model and its experimental validation.Biochim

    Y Wang, Y Palzhanov, A Quaini, M Olshanskii, and S Majd. Lipid domain coarsening and fluidity in multicompo- nent lipid vesicles: A continuum based model and its experimental validation.Biochim. Biophys. Acta Biomembr ., 1864(7):183898, 2022

    work page 2022

  2. [33]

    When giant vesicles mimic red blood cell dynamics: swinging of two-phase vesicles in shear flow.Phys

    Simon Tusch, Etienne Loiseau, Al-Hair Al-Halifa, Kamel Khelloufi, Emmanuèle Helfer, and Annie Viallat. When giant vesicles mimic red blood cell dynamics: swinging of two-phase vesicles in shear flow.Phys. Rev. Fluids, 3(12):123605, 2018

    work page 2018

  3. [1]

    Hess, and Watt W

    Tobias Baumgart, Samuel T. Hess, and Watt W. Webb. Imaging coexisting fluid domains in biomembrane models coupling curvature and line tension.Nature, 425(6960):821–824, 2003

    work page 2003

  4. [2]

    Veatch and Sarah L

    Sarah L. Veatch and Sarah L. Keller. Separation of Liquid Phases in Giant Vesicles of Ternary Mixtures of Phospholipids and Cholesterol.Biophysical J., 85(5):3074–3083, 2003

    work page 2003

  5. [3]

    Veatch and Sarah L

    Sarah L. Veatch and Sarah L. Keller. Miscibility Phase Diagrams of Giant Vesicles Containing Sphingomyelin. Phys. Rev. Lett., 94(14):148101, 2005

    work page 2005

  6. [4]

    Lipid rafts as a membrane-organizing principle.Science, 327(5961):46–50, 2010

    Daniel Lingwood and Kai Simons. Lipid rafts as a membrane-organizing principle.Science, 327(5961):46–50, 2010

    work page 2010

  7. [6]

    Baumgart, S

    T. Baumgart, S. Das, W.W. Webb, and J.T. Jenkins. Membrane Elasticity in Giant Vesicles with Fluid Phase Coexistence.Biophysical J., 89(2):1067–1080, 2005

    work page 2005

  8. [7]

    Shape Deformation of Ternary Vesicles Coupled with Phase Separation.Phys

    Miho Yanagisawa, Masayuki Imai, and Takashi Taniguchi. Shape Deformation of Ternary Vesicles Coupled with Phase Separation.Phys. Rev. Lett., 100(14):148102, 2008

    work page 2008

Show all 54 references
  1. [8]

    Functional rafts in cell membranes.Nature, 387(6633):569–572, 1997

    Kai Simons and Elina Ikonen. Functional rafts in cell membranes.Nature, 387(6633):569–572, 1997

    1997

  2. [9]

    Lipid rafts and signal transduction.Nat

    Kai Simons and Derek Toomre. Lipid rafts and signal transduction.Nat. Rev. Mol. Cell. Biol., 1(1):31–39, 2000

    2000

  3. [10]

    Physics of cell adhesion: some lessons from cell-mimetic systems.Soft Matter, 10(11):1644, 2014

    Erich Sackmann and Ana-Sunˇcana Smith. Physics of cell adhesion: some lessons from cell-mimetic systems.Soft Matter, 10(11):1644, 2014

    2014

  4. [11]

    Kai Simons and Winchil L.C. Vaz. Model systems, lipid rafts, and cell membranes.Annu. Rev. Biophys. Biomol. Struct., 33(1):269–295, 2004

    2004

  5. [12]

    Maxfield

    Sushmita Mukherjee and Frederick R. Maxfield. Membrane domains.Annu. Rev. Biophys. Biomol. Struct., 20(1):839–866, 2004

    2004

  6. [13]

    Law, and Oscar Ces

    Yuval Elani, Robert V . Law, and Oscar Ces. Vesicle-based artificial cells as chemical microreactors with spatially segregated reaction pathways.Nat. Commun., 5(1):5305, 2014

    2014

  7. [14]

    Allen and Pieter R

    Theresa M. Allen and Pieter R. Cullis. Drug delivery systems: Entering the mainstream.Science, 303(5665):1818– 1822, 2004

    2004

  8. [15]

    Extracellular vesicles as a next- generation drug delivery platform.Nat

    Inge Katrin Herrmann, Matthew John Andrew Wood, and Gregor Fuhrmann. Extracellular vesicles as a next- generation drug delivery platform.Nat. Nanotechnol., 16(7):748–759, 2021

    2021

  9. [16]

    Liposomes under shear: Structure, dynamics, and drug delivery applications

    Selcan Karaz and Erkan Senses. Liposomes under shear: Structure, dynamics, and drug delivery applications. Adv. Nanobiomed Res., 3(4):2200101, 2023

    2023

  10. [17]

    Kooijmans, Olivier G

    Sander A.A. Kooijmans, Olivier G. De Jong, and Raymond M. Schiffelers. Exploring interactions between extracellular vesicles and cells for innovative drug delivery system design.Adv. Drug Deliv. Rev., 173:252–278, 2021

    2021

  11. [18]

    Keller and Richard Skalak

    Stuart R. Keller and Richard Skalak. Motion of a tank-treading ellipsoidal particle in a shear flow.J. Fluid Mech., 120:27–47, 1982

    1982

  12. [19]

    Vacillating breathing and tumbling of vesicles under shear flow.Phys

    Chaouqi Misbah. Vacillating breathing and tumbling of vesicles under shear flow.Phys. Rev. Lett., 96(2):028104, 2006

    2006

  13. [20]

    Vlahovska and Ruben Serral Gracia

    Petia M. Vlahovska and Ruben Serral Gracia. Dynamics of a viscous vesicle in linear flows.Phys. Rev. E, 75(1):016313, 2007. 23 APREPRINT- SEPTEMBER11, 2025

    2007

  14. [21]

    Swinging and tumbling of fluid vesicles in shear flow.Phys

    Hiroshi Noguchi and Gerhard Gompper. Swinging and tumbling of fluid vesicles in shear flow.Phys. Rev. Lett., 98(12):128103, 2007

    2007

  15. [22]

    Transition to tumbling and two regimes of tumbling motion of a vesicle in shear flow.Phys

    Vasiliy Kantsler and Victor Steinberg. Transition to tumbling and two regimes of tumbling motion of a vesicle in shear flow.Phys. Rev. Lett., 96(3):036001, 2006

    2006

  16. [23]

    Abkarian and A

    M. Abkarian and A. Viallat. Dynamics of vesicles in a wall-bounded shear flow.Biophysical J., 89(2):1055–1066, 2005

    2005

  17. [24]

    Deschamps, V

    J. Deschamps, V . Kantsler, and V . Steinberg. Phase diagram of single vesicle dynamical states in shear flow.Phys. Rev. Lett., 102(11):118105, 2009

    2009

  18. [25]

    Dynamics and rheology of a dilute suspension of vesicles: higher order theory.Phys

    Gerrit Danker, Thierry Biben, Thomas Podgorski, Claude Verdier, and Chaouqi Misbah. Dynamics and rheology of a dilute suspension of vesicles: higher order theory.Phys. Rev. E, 76(4):041905, 2007

    2007

  19. [26]

    Lebedev, K.S

    V .V . Lebedev, K.S. Turitsyn, and S.S. Vergeles. Nearly spherical vesicles in an external flow.New J. Phys., 10(4):043044, 2008

    2008

  20. [27]

    Spagnolie

    Prerna Gera, David Salac, and Saverio E. Spagnolie. Swinging and tumbling of multicomponent vesicles in flow. J. Fluid Mech., 935:A39, 2022

    2022

  21. [28]

    Lowengrub, J.J

    J.S. Lowengrub, J.J. Xu, and A. V oigt. Surface phase separation and flow in a simple model of multicomponent drops and vesicles.Fluid Dyn. Mater . Proc., 3(1):1–20, 2007

    2007

  22. [29]

    Lowengrub

    Jin Sun Sohn, Yu-Hau Tseng, Shuwang Li, Axel V oigt, and John S. Lowengrub. Dynamics of multicomponent vesicles in a viscous fluid.J. Comput. Phys., 229(1):119–144, 2010

    2010

  23. [30]

    Marple, Jun Allard, Shuwang Li, Shravan Veerapaneni, and John Lowengrub

    Kai Liu, Gary R. Marple, Jun Allard, Shuwang Li, Shravan Veerapaneni, and John Lowengrub. Dynamics of a multicomponent vesicle in shear flow.Soft Matter, 13(19):3521–3531, 2017

    2017

  24. [31]

    Three-dimensional multicomponent vesicles: dynamics and influence of material properties.Soft Matter, 14(37):7690–7705, 2018

    Prerna Gera and David Salac. Three-dimensional multicomponent vesicles: dynamics and influence of material properties.Soft Matter, 14(37):7690–7705, 2018

    2018

  25. [32]

    Modeling of multicomponent three-dimensional vesicles.Comput

    Prerna Gera and David Salac. Modeling of multicomponent three-dimensional vesicles.Comput. Fluids, 172:362– 383, 2018

    2018

  26. [34]

    Shape dynamics of nearly spherical, multicomponent vesicles under shear flow

    Anirudh Venkatesh and Vivek Narsimhan. Shape dynamics of nearly spherical, multicomponent vesicles under shear flow. 2024

    2024

  27. [35]

    Two-phase fluid deformable surfaces with constant enclosed volume and phase-dependent bending and Gaussian rigidity.Comput

    Jan Magnus Sischka and Axel V oigt. Two-phase fluid deformable surfaces with constant enclosed volume and phase-dependent bending and Gaussian rigidity.Comput. Methods Appl. Mech. Eng., 445:118166, 2025

    2025

  28. [36]

    Diffuse interface models of locally inextensible vesicles in a viscous fluid.J

    Sebastian Aland, Sabine Egerer, John Lowengrub, and Axel V oigt. Diffuse interface models of locally inextensible vesicles in a viscous fluid.J. Comput. Phys., 277:32–47, 2014

    2014

  29. [37]

    Experimental validation of a phase-field model to predict coarsening dynamics of lipid domains in multicomponent membranes

    Alexander Zhiliakov, Yifei Wang, Annalisa Quaini, Maxim Olshanskii, and Sheereen Majd. Experimental validation of a phase-field model to predict coarsening dynamics of lipid domains in multicomponent membranes. Biochim. Biophys. Acta Biomembr ., 1863(1):183446, 2021

    2021

  30. [38]

    A diffuse-interface approach for modeling transport, diffusion and adsorption/desorption of material quantities on a deformable interface.Commun

    Knut Erik Teigen, Xiangrong Li, John Lowengrub, Fan Wang, and Axel V oigt. A diffuse-interface approach for modeling transport, diffusion and adsorption/desorption of material quantities on a deformable interface.Commun. Math. Sci., 4(7):1009, 2009

    2009

  31. [39]

    Solving pdes in complex geometries: a diffuse domain approach

    X Li, John Lowengrub, A Rätz, and A V oigt. Solving pdes in complex geometries: a diffuse domain approach. Commun. Math. Sci., 7(1):81, 2009

    2009

  32. [40]

    PDE’s on surfaces — a diffuse interface approach.Commun

    Andreas Rätz and Axel V oigt. PDE’s on surfaces — a diffuse interface approach.Commun. Math. Sci., 4(3):575– 590, 2006

    2006

  33. [41]

    Thornton

    Hui-Chia Yu, Hsun-Yi Chen, and K. Thornton. Extended Smoothed Boundary Method for Solving Partial Differential Equations with General Boundary Conditions on Complex Boundaries.Model Simul. Mat. Sci. Eng., 20(7):075008, 2012

    2012

  34. [42]

    A diffuse domain method for two-phase flows with large density ratio in complex geometries.J

    Zhenlin Guo, Fei Yu, Ping Lin, Steven Wise, and John Lowengrub. A diffuse domain method for two-phase flows with large density ratio in complex geometries.J. Fluid Mech., 907:A38, 2021

    2021

  35. [43]

    Nonlinear coupling effects of the thermocapillarity and insoluble surfactants to droplet migration under Poiseuille flow.Phys

    Zhenlin Guo. Nonlinear coupling effects of the thermocapillarity and insoluble surfactants to droplet migration under Poiseuille flow.Phys. Rev. Fluids, 8(2):024001, 2023. 24 APREPRINT- SEPTEMBER11, 2025

    2023

  36. [44]

    Analysis of the diffuse-domain method for solving PDEs in complex geometries.Commun

    Karl Yngve Lervåg and John Lowengrub. Analysis of the diffuse-domain method for solving PDEs in complex geometries.Commun. Math. Sci., 13(6):1473–1500, 2015

    2015

  37. [45]

    Chadwick, James A

    Alexander F. Chadwick, James A. Stewart, Raúl A. Enrique, Sicen Du, and Katsuyo Thornton. Numerical Modeling of Localized Corrosion Using Phase-Field and Smoothed Boundary Methods.J. Electrochem Soc., 165(10):C633–C646, 2018

    2018

  38. [46]

    S. O. Poulsen and P. W. V oorhees. Smoothed boundary method for diffusion-related partial differential equations in complex geometries.Int. J. Comp. Meth-Sing, 15(03):1850014, 2018

    2018

  39. [47]

    Higher-order accurate diffuse-domain methods for partial differential equations with Dirichlet boundary conditions in complex, evolving geometries.J

    Fei Yu, Zhenlin Guo, and John Lowengrub. Higher-order accurate diffuse-domain methods for partial differential equations with Dirichlet boundary conditions in complex, evolving geometries.J. Comput. Phys., 406:109174, 2020

    2020

  40. [48]

    Z. Guo, P. Lin, J. Lowengrub, and S.M. Wise. Mass conservative and energy stable finite difference methods for the quasi-incompressible Navier–Stokes–Cahn–Hilliard system: Primitive variable and projection-type schemes. Comput. Methods Appl. Mech. Eng., 326:144–174, 2017

    2017

  41. [49]

    R. A. Van Santen. The Ostwald step rule.J. Phys. Chem., 88(24):5768–5769, 1984

    1984

  42. [50]

    Insights into phase transition kinetics from colloid science

    Valerie J Anderson and Henk NW Lekkerkerker. Insights into phase transition kinetics from colloid science. Nature, 416(6883):811–815, 2002

    2002

  43. [51]

    Cytoarchitecture and physical properties of cytoplasm: volume, viscosity, diffusion, intracellular surface area.Int

    Katherine Luby-Phelps. Cytoarchitecture and physical properties of cytoplasm: volume, viscosity, diffusion, intracellular surface area.Int. Rev. Cytol., 192:189–221, 1999

    1999

  44. [52]

    A diffuse-interface method for two-phase flows with soluble surfactants.J

    Knut Erik Teigen, Peng Song, John Lowengrub, and Axel V oigt. A diffuse-interface method for two-phase flows with soluble surfactants.J. Comput. Phys., 230(2):375–393, 2011

    2011

  45. [53]

    James and John Lowengrub

    Ashley J. James and John Lowengrub. A surfactant-conserving volume-of-fluid method for interfacial flows with insoluble surfactant.J. Comput. Phys., 201(2):685–722, 2004

    2004

  46. [54]

    Numerical simulation of endocytosis: Viscous flow driven by membranes with non-uniformly distributed curvature-inducing molecules.J

    John Lowengrub, Jun Allard, and Sebastian Aland. Numerical simulation of endocytosis: Viscous flow driven by membranes with non-uniformly distributed curvature-inducing molecules.J. Comput. Phys., 309:112–128, 2016. 25

    2016

Pith tools

Reviewed August 4, 2026 · model on record in the stance chip above.