# A Note on Vestigial Osmotic Pressure

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## Abstract

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## 1. Introduction

## 2. Osmotic Pressure Equilibrium

## 3. Results and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) A schematic depiction of the “parent”, a single spherical vesicle with the fixed radius ${R}_{0}$, area ${A}_{0}$, and volume ${V}_{0}$ (the parent state), converting to (

**b**) the “progeny” spherical vesicle with the fixed radius ${R}_{1}$, area ${A}_{1}$, and volume ${V}_{1}$, including n daughter spherical vesicles with the fixed radius ${R}_{d}$, area ${A}_{d}$, and volume ${V}_{d}$ (the progeny state).

**Figure 2.**The final vesicle size ${R}_{1}$ as a function of the initial size ${R}_{0}$. The light yellow color indicates a stable regime for $\Delta \mathcal{F}<0$. The blue solid line, the red dashed line, and the green dash-dotted line corresponds to ${\gamma}_{sp}=7.05\times {10}^{-6}\phantom{\rule{3.33333pt}{0ex}}\mathrm{mN}/\mathrm{m}$, $7.01\times {10}^{-6}\phantom{\rule{3.33333pt}{0ex}}\mathrm{mN}/\mathrm{m}$, and $6.97\times {10}^{-6}\phantom{\rule{3.33333pt}{0ex}}\mathrm{mN}/\mathrm{m}$, respectively, within the spontaneous tension range in Table 1 of [7].

**Figure 3.**The number of daughter vesicles as a function of the initial size ${R}_{0}$. The black dots with the error bars are calculated from the experimental data of [3]. The light yellow color indicates the stable regime for $\Delta \mathcal{F}<0$. The blue solid line, the red dashed line, and the green dash-dotted line corresponds to ${\gamma}_{sp}=7.05\times {10}^{-6}\phantom{\rule{3.33333pt}{0ex}}\mathrm{mN}/\mathrm{m}$, $7.01\times {10}^{-6}\phantom{\rule{3.33333pt}{0ex}}\mathrm{mN}/\mathrm{m}$, and $6.97\times {10}^{-6}\phantom{\rule{3.33333pt}{0ex}}\mathrm{mN}/\mathrm{m}$, respectively, within the spontaneous tension range in Table 1 of [7].

**Figure 4.**Vestigial osmotic pressure as a function of the initial size ${R}_{0}$. The vestigial osmotic pressure, according to the experiments in [2], was estimated to be $0.4$ mPa, which is marked by a magenta arrow. The light yellow color indicates a stable regime for $\Delta \mathcal{F}<0$. The blue solid line, the red dashed line, and the green dash-dotted line corresponds to ${\gamma}_{sp}=7.05\times {10}^{-6}\phantom{\rule{3.33333pt}{0ex}}\mathrm{mN}/\mathrm{m}$, $7.01\times {10}^{-6}\phantom{\rule{3.33333pt}{0ex}}\mathrm{mN}/\mathrm{m}$, and $6.97\times {10}^{-6}\phantom{\rule{3.33333pt}{0ex}}\mathrm{mN}/\mathrm{m}$, respectively, within the spontaneous tension range in Table 1 of [7].

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**MDPI and ACS Style**

Wu, H.; Ou-Yang, Z.-C.; Podgornik, R.
A Note on Vestigial Osmotic Pressure. *Membranes* **2023**, *13*, 332.
https://doi.org/10.3390/membranes13030332

**AMA Style**

Wu H, Ou-Yang Z-C, Podgornik R.
A Note on Vestigial Osmotic Pressure. *Membranes*. 2023; 13(3):332.
https://doi.org/10.3390/membranes13030332

**Chicago/Turabian Style**

Wu, Hao, Zhong-Can Ou-Yang, and Rudolf Podgornik.
2023. "A Note on Vestigial Osmotic Pressure" *Membranes* 13, no. 3: 332.
https://doi.org/10.3390/membranes13030332