Dynamical behavior of compound vesicles in wall-bounded shear flow

TL;DR

The paper addresses how compound vesicles, consisting of an inner vesicle inside an outer vesicle, dynamically respond to wall-bounded shear flow. It uses a two-dimensional mesoscale hydrodynamic approach combining molecular dynamics with multi-particle collision dynamics to include thermal fluctuations and to vary parameters such as $\Lambda$, $S$, $\phi$, and $\Delta_{int}$. It reveals a rich set of dynamical states—TT, TR, TU, UND—with inner–outer coupling; thermal fluctuations drive trembling and swinging; the UND state shows outer vesicle buckling and four-lobed shapes whose features depend on relative sizes and swelling degrees. The results quantitatively reproduce experimental trends and extend understanding of multi-compartment vesicle dynamics, with potential implications for biomimetic systems like leukocytes and vesosomes in microfluidic environments.

Abstract

We report a numerical study addressing the dynamics of compound vesicles confined in a channel under shear flow. The system comprises a smaller vesicle embedded within a larger one and can be used to mimic, for example, leukocytes or nucleate cells. A two-dimensional model, which combines molecular dynamics and mesoscopic hydrodynamics including thermal fluctuations, is adopted to perform an extended investigation. We are able to vary independently the swelling degree and the relative size of vesicles, the viscosities of fluids internal and external to vesicles, and the Capillary number, so to observe a rich dynamical phenomenology which goes well beyond what observed for single vesicles, matching quantitatively with experimental findings. Tank-treading, tumbling, and trembling motions are enriched by dynamical states where inner and outer vesicles can perform different motions. We show that thermal fluctuations are crucial during trembling and swinging dynamics, as observed in experiments. Undulating motion of the external vesicle, characterized by periodic oscillation of the inclination and buckling of the membrane, is observed at high filling fractions. This latter state exhibits features that are shown to depend on the relative size, the swelling degree of both vesicles as well as on thermal noise lacking in previous analytical and numerical studies.

Figures (10)

• Figure 1: Schematic layout of the simulated system.
• Figure 2: (a) Dependence of the average inclination angle on $\Lambda$ for the external (red triangles) and internal (green squares) tank-treading vesicles compared with data of single tank-treading vesicles (black circles) lamu22. The full line is the fit to the data of single vesicles and the dashed line is the same fit line shifted up. The data shown are obtained from different compound vesicles with $0.16 \leq \Delta_{ext} \leq 1.23$, $0.16 \leq \Delta_{int} \leq 0.74$, and $0.4 \leq \phi \leq 0.8$. In the case of single vesicles it is $0.16 \leq \Delta \leq 1.23$. (b) Dependence of the average tank-treading frequency on $\Lambda$ for the external (red triangles) and internal (green squares) vesicles compared with data of single vesicles (black circles)
• Figure 3: (a) Comparison of the spectra, averaged in time, of amplitudes of shapes for a single vesicle with $\Delta=0.74$ (black circles) and a compound one with $\Delta_{ext}=\Delta_{int}=0.74$, $\phi=0.6$ (red triangles). Both single vesicle and compound one are in tank-treading motion at $(\Lambda, S)=(0.61, 229)$. Corresponding typical configurations are shown in panels (b) and (c), respectively.
• Figure 4: (a) Time evolution of the inclination angles $\theta_{ext}$ (red continuous line) and $\theta_{int}$ (green dashed line) of a compound vesicle with $\Delta_{ext}=\Delta_{int}=0.16$, $\phi=0.2$ at $(\Lambda, S)=(1.94, 1058)$ showing trembling (external vesicle) and swinging (internal vesicle) motion. (b) Time evolution of the asphericities $A_{ext}$ (red continuous line) and $A_{int}$ (green dashed line) corresponding to the case in panel (a).
• Figure 5: (a) Time evolution of the inclination angles $\theta_{ext}$ (red continuous line) and $\theta_{int}$ (green dashed line) of a compound vesicle with $\Delta_{ext}=1.23$, $\Delta_{int}=0.74$, $\phi=0.2$ at $(\Lambda, S)=(5.38, 138)$ in desynchronized tumbling motion. (b) Time dependence of $\Delta \theta=\theta_{int}-\theta_{ext}$ corresponding to the data in panel (a). (c) Time evolution of the inclination angles $\theta_{ext}$ (red continuous line) and $\theta_{int}$ (green dashed line) of a compound vesicle with $\Delta_{ext}=\Delta_{int}=0.74$, $\phi=0.6$ at $(\Lambda, S)=(4.18, 23)$ in synchronized tumbling motion.