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Activity-induced propulsion of a vesicle

Published online by Cambridge University Press:  23 May 2022

Zhiwei Peng Open the ORCID record for Zhiwei Peng [Opens in a new window] ,
Tingtao Zhou Open the ORCID record for Tingtao Zhou [Opens in a new window]  and
John F. Brady Open the ORCID record for John F. Brady [Opens in a new window]
Zhiwei Peng
Affiliation:
Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, USA
Tingtao Zhou
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA
John F. Brady*
Affiliation:
Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, USA Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA
*
†Email address for correspondence: jfbrady@caltech.edu
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Abstract

Modern biomedical applications such as targeted drug delivery require a delivery system capable of enhanced transport beyond that of passive Brownian diffusion. In this work, an osmotic mechanism for the propulsion of a vesicle immersed in a viscous fluid is proposed. By maintaining a steady-state solute gradient inside the vesicle, a seepage flow of the solvent (e.g. water) across the semipermeable membrane is generated, which in turn propels the vesicle. We develop a theoretical model for this vesicle–solute system in which the seepage flow is described by a Darcy flow. Using the reciprocal theorem for Stokes flow, it is shown that the seepage velocity at the exterior surface of the vesicle generates a thrust force that is balanced by the hydrodynamic drag such that there is no net force on the vesicle. We characterize the motility of the vesicle in relation to the concentration distribution of the solute confined inside the vesicle. Any osmotic solute is able to propel the vesicle so long as a concentration gradient is present. In the present work, we propose active Brownian particles (ABPs) as a solute. To maintain a symmetry-breaking concentration gradient, we consider ABPs with spatially varying swim speed, and ABPs with constant properties but under the influence of an orienting field. In particular, it is shown that at high activity, the vesicle velocity is $\boldsymbol {U}\sim [K_\perp /(\eta _e\ell _m) ]\int \varPi _0^{swim} \boldsymbol {n}\,{\rm d}\varOmega$, where $\varPi _0^{swim}$ is the swim pressure just outside the thin accumulation boundary layer on the vesicle interior surface, $\boldsymbol {n}$ is the unit normal vector of the vesicle boundary, $K_\perp$ is the membrane permeability, $\eta _e$ is the viscosity of the solvent, and $\ell _m$ is the membrane thickness.

JFM classification

Complex Fluids: Active matter Complex Fluids: Colloids Complex Fluids: Suspensions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 942 , 10 July 2022 , A32
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

REFERENCES

Arlt, J., Martinez, V.A., Dawson, A., Pilizota, T. & Poon, W.C.K. 2018 Painting with light-powered bacteria. Nat. Commun. 9 (1), 768.CrossRefGoogle ScholarPubMed
Arlt, J., Martinez, V.A., Dawson, A., Pilizota, T. & Poon, W.C.K. 2019 Dynamics-dependent density distribution in active suspensions. Nat. Commun. 10 (1), 2321.CrossRefGoogle ScholarPubMed
Beavers, G.S. & Joseph, D.D. 1967 Boundary conditions at a naturally permeable wall. J. Fluid Mech. 30 (1), 197–207.CrossRefGoogle Scholar
Blake, J.R. 1971 A spherical envelope approach to ciliary propulsion. J. Fluid Mech. 46 (1), 199–208.CrossRefGoogle Scholar
Brenner, H. 1964 The Stokes resistance of a slightly deformed sphere. Chem. Engng Sci. 19 (8), 519–539.CrossRefGoogle Scholar
Bunea, A.-I. & Taboryski, R. 2020 Recent advances in microswimmers for biomedical applications. Micromachines 11 (12), 1048.CrossRefGoogle ScholarPubMed
Burkholder, E.W. & Brady, J.F. 2020 Nonlinear microrheology of active Brownian suspensions. Soft Matt. 16, 1034–1046.CrossRefGoogle ScholarPubMed
Chaubal, C.V. & Leal, L.G. 1998 A closure approximation for liquid-crystalline polymer models based on parametric density estimation. J. Rheol. 42 (1), 177–201.CrossRefGoogle Scholar
Delong, S., Balboa Usabiaga, F. & Donev, A. 2015 Brownian dynamics of confined rigid bodies. J. Chem. Phys. 143 (14), 144107.CrossRefGoogle ScholarPubMed
Dulaney, A.R. & Brady, J.F. 2020 Waves in active matter: the transition from ballistic to diffusive behavior. Phys. Rev. E 101, 052609.CrossRefGoogle ScholarPubMed
Durlofsky, L. & Brady, J.F. 1987 Analysis of the Brinkman equation as a model for flow in porous media. Phys. Fluids 30 (11), 3329–3341.CrossRefGoogle Scholar
Elfring, G.J. 2015 A note on the reciprocal theorem for the swimming of simple bodies. Phys. Fluids 27 (2), 023101.CrossRefGoogle Scholar
Erkoc, P., Yasa, I.C., Ceylan, H., Yasa, O., Alapan, Y. & Sitti, M. 2019 Mobile microrobots for active therapeutic delivery. Adv. Ther. 2 (1), 1800064.CrossRefGoogle Scholar
Felfoul, O., et al. 2016 Magneto-aerotactic bacteria deliver drug-containing nanoliposomes to tumour hypoxic regions. Nat. Nanotechnol. 11 (11), 941–947.CrossRefGoogle ScholarPubMed
Frangipane, G., Dell'Arciprete, D., Petracchini, S., Maggi, C., Saglimbeni, F., Bianchi, S., Vizsnyiczai, G., Bernardini, M.L. & Di Leonardo, R. 2018 Dynamic density shaping of photokinetic E. coli. eLife 7, e36608.CrossRefGoogle ScholarPubMed
Gao, X., Yang, L., Petros, J.A., Marshall, F.F., Simons, J.W. & Nie, S. 2005 In vivo molecular and cellular imaging with quantum dots. Curr. Opin. Biotech. 16 (1), 63–72.CrossRefGoogle ScholarPubMed
Guazzelli, E. & Morris, J.F. 2011 A Physical Introduction to Suspension Dynamics, vol. 45. Cambridge University Press.CrossRefGoogle Scholar
Heyes, D.M. & Melrose, J.R. 1993 Brownian dynamics simulations of model hard-sphere suspensions. J. Non-Newtonian Fluid Mech. 46 (1), 1–28.CrossRefGoogle Scholar
Huang, Z., Omori, T. & Ishikawa, T. 2020 Active droplet driven by a collective motion of enclosed microswimmers. Phys. Rev. E 102, 022603.CrossRefGoogle ScholarPubMed
Jackson, L.A., et al. 2020 An mRNA vaccine against SARS-CoV-2 – preliminary report. N. Engl. J. Med. 383 (20), 1920–1931.CrossRefGoogle ScholarPubMed
Jones, I.P. 1973 Low Reynolds number flow past a porous spherical shell. Proc. Camb. Phil. Soc. 73 (1), 231–238.CrossRefGoogle Scholar
Kaiser, A., Peshkov, A., Sokolov, A., ten Hagen, B., Löwen, H. & Aranson, I.S. 2014 Transport powered by bacterial turbulence. Phys. Rev. Lett. 112, 158101.CrossRefGoogle ScholarPubMed
Leal, L.G. 2007 Advanced Transport Phenomena: Fluid Mechanics and Convective Transport Processes, vol. 7. Cambridge University Press.CrossRefGoogle Scholar
Lebedev, V.V., Turitsyn, K.S. & Vergeles, S.S. 2007 Dynamics of nearly spherical vesicles in an external flow. Phys. Rev. Lett. 99, 218101.CrossRefGoogle Scholar
Lighthill, M.J. 1952 On the squirming motion of nearly spherical deformable bodies through liquids at very small Reynolds numbers. Commun. Pure Appl. Maths 5 (2), 109–118.CrossRefGoogle Scholar
Marchetti, M.C., Joanny, J.F., Ramaswamy, S., Liverpool, T.B., Prost, J., Rao, M. & Simha, R.A. 2013 Hydrodynamics of soft active matter. Rev. Mod. Phys. 85, 1143–1189.CrossRefGoogle Scholar
Marshall, K.J. & Brady, J.F. 2021 The hydrodynamics of an active squirming particle inside of a porous container. J. Fluid Mech. 919, A31.CrossRefGoogle Scholar
Masoud, H. & Stone, H.A. 2019 The reciprocal theorem in fluid dynamics and transport phenomena. J. Fluid Mech. 879, P1.CrossRefGoogle Scholar
Medina-Sánchez, M., Xu, H. & Schmidt, O.G. 2018 Micro- and nano-motors: the new generation of drug carriers. Ther. Deliv. 9 (4), 303–316.CrossRefGoogle ScholarPubMed
Park, B.-W., Zhuang, J., Yasa, O. & Sitti, M. 2017 Multifunctional bacteria-driven microswimmers for targeted active drug delivery. ACS Nano 11 (9), 8910–8923.CrossRefGoogle ScholarPubMed
Pattni, B.S., Chupin, V.V. & Torchilin, V.P. 2015 New developments in liposomal drug delivery. Chem. Rev. 115 (19), 10938–10966.CrossRefGoogle ScholarPubMed
Peng, Z. & Brady, J.F. 2020 Upstream swimming and Taylor dispersion of active Brownian particles. Phys. Rev. Fluids 5, 073102.CrossRefGoogle Scholar
Rao, J., Dragulescu-Andrasi, A. & Yao, H. 2007 Fluorescence imaging in vivo: recent advances. Curr. Opin. Biotech. 18 (1), 17–25.CrossRefGoogle ScholarPubMed
Row, H. & Brady, J.F. 2020 Reverse osmotic effect in active matter. Phys. Rev. E 101, 062604.CrossRefGoogle ScholarPubMed
Saffman, P.G. 1971 On the boundary condition at the surface of a porous medium. Stud. Appl. Maths 50 (2), 93–101.CrossRefGoogle Scholar
Saintillan, D. & Shelley, M.J. 2015 Theory of Active Suspensions, 319–355. Springer.Google Scholar
Schnitzer, M.J. 1993 Theory of continuum random walks and application to chemotaxis. Phys. Rev. E 48, 2553–2568.CrossRefGoogle ScholarPubMed
Singh, A.V., Ansari, M.H.D., Laux, P. & Luch, A. 2019 Micro-nanorobots: important considerations when developing novel drug delivery platforms. Expert Opin. Drug Del. 16 (11), 1259–1275.CrossRefGoogle ScholarPubMed
Singh, A.V., Hosseinidoust, Z., Park, B.-W., Yasa, O. & Sitti, M. 2017 Microemulsion-based soft bacteria-driven microswimmers for active cargo delivery. ACS Nano 11 (10), 9759–9769.CrossRefGoogle ScholarPubMed
Sokolov, A., Apodaca, M.M., Grzybowski, B.A. & Aranson, I.S. 2010 Swimming bacteria power microscopic gears. Proc. Natl Acad. Sci. USA 107 (3), 969–974.CrossRefGoogle ScholarPubMed
Spagnolie, S.E. & Lauga, E. 2010 Jet propulsion without inertia. Phys. Fluids 22 (8), 081902.CrossRefGoogle Scholar
Stone, H.A. & Samuel, A.D.T. 1996 Propulsion of microorganisms by surface distortions. Phys. Rev. Lett. 77, 4102–4104.CrossRefGoogle ScholarPubMed
Stroka, K.M., Jiang, H., Chen, S.-H., Tong, Z., Wirtz, D., Sun, S.X. & Konstantopoulos, K. 2014 Water permeation drives tumor cell migration in confined microenvironments. Cell 157 (3), 611–623.CrossRefGoogle ScholarPubMed
Tailleur, J. & Cates, M.E. 2008 Statistical mechanics of interacting run-and-tumble bacteria. Phys. Rev. Lett. 100, 218103.CrossRefGoogle ScholarPubMed
Takatori, S.C. & Brady, J.F. 2014 Swim stress, motion, and deformation of active matter: effect of an external field. Soft Matt. 10, 9433–9445.CrossRefGoogle ScholarPubMed
Takatori, S.C., De Dier, R., Vermant, J. & Brady, J.F. 2016 Acoustic trapping of active matter. Nat. Commun. 7 (1), 10694.CrossRefGoogle ScholarPubMed
Takatori, S.C. & Sahu, A. 2020 Active contact forces drive nonequilibrium fluctuations in membrane vesicles. Phys. Rev. Lett. 124, 158102.CrossRefGoogle ScholarPubMed
Takatori, S.C., Yan, W. & Brady, J.F. 2014 Swim pressure: stress generation in active matter. Phys. Rev. Lett. 113, 028103.CrossRefGoogle ScholarPubMed
Torchilin, V.P. 2012 Multifunctional nanocarriers. Adv. Drug Deliver. Rev. 64, 302–315.CrossRefGoogle Scholar
Trantidou, T., Dekker, L., Polizzi, K., Ces, O. & Elani, Y. 2018 Functionalizing cell-mimetic giant vesicles with encapsulated bacterial biosensors. Interface Focus 8 (5), 20180024.CrossRefGoogle ScholarPubMed
Trefethen, L.N. 2000 Spectral Methods in MATLAB. Society for Industrial and Applied Mathematics.CrossRefGoogle Scholar
Vlahovska, P.M. & Gracia, R.S. 2007 Dynamics of a viscous vesicle in linear flows. Phys. Rev. E 75, 016313.CrossRefGoogle ScholarPubMed
Vutukuri, H.R., Hoore, M., Abaurrea-Velasco, C., van Buren, L., Dutto, A., Auth, T., Fedosov, D.A., Gompper, G. & Vermant, J. 2020 Active particles induce large shape deformations in giant lipid vesicles. Nature 586 (7827), 52–56.CrossRefGoogle ScholarPubMed
Weady, S., Shelley, M.J. & Stein, D.B. 2022 A fast Chebyshev method for the Bingham closure with application to active nematic suspensions. J. Comput. Phys. 457, 110937.CrossRefGoogle Scholar
West, J.L. & Halas, N.J. 2003 Engineered nanomaterials for biophotonics applications: improving sensing, imaging, and therapeutics. Annu. Rev. Biomed. Engng 5 (1), 285–292.CrossRefGoogle ScholarPubMed
Yan, W. & Brady, J.F. 2015 The force on a boundary in active matter. J. Fluid Mech. 785, R1.CrossRefGoogle Scholar
Yan, W. & Brady, J.F. 2018 The curved kinetic boundary layer of active matter. Soft Matt. 14, 279–290.CrossRefGoogle ScholarPubMed
Ye, H. & Curcuru, A. 2015 Vesicle biomechanics in a time-varying magnetic field. BMC Biophys. 8 (1), 2.CrossRefGoogle Scholar
Zampogna, G.A. & Gallaire, F. 2020 Effective stress jump across membranes. J. Fluid Mech. 892, A9.CrossRefGoogle Scholar