Publication Cover
LHB
Hydroscience Journal
Volume 108, 2022 - Issue 1
779
Views
1
CrossRef citations to date
0
Altmetric
Research Article

Stokeslet parallèle entre deux disques rigides antidérapants positionnés de manière coaxiale : une approche aux équations intégrales duales

Parallel Stokeslet between two coaxially positioned rigid no-slip disks: A dual integral equation approach

ORCID Icon
Article: 2016023 | Published online: 16 Mar 2022

Références

  • Abramowitz, M., & Stegun, I. A. (1965). Handbook of mathematical functions with formulas, graphs, and mathematical table ( National Bureau of Standards Applied Mathematics Series 55). US Department of Commerce.
  • Batchelor, G. K. (2000). An introduction to fluid dynamics. Cambridge University Press.
  • Bechinger, C., Di Leonardo, R., Löwen, H., Reichhardt, C., Volpe, G., & Volpe, G. (2016). Active particles in complex and crowded environments. Reviews of Modern Physics, 88(4), 1. https://doi.org/10.1103/RevModPhys.88.045006.
  • Becker, R., Braack, M., Meidner, D., Richter, T., & Vexler, B. (2020). The finite element toolkit Gascoigne3d. http://www.gascoigne.de.
  • Becker, R., & Braack, M. (2001). A finite element pressure gradient stabilization for the Stokes equations based on local projections. Calcolo, 38(4), 173–21. https://doi.org/10.1007/s10092-001-8180-4.
  • Benesch, T., Yiacoumi, S., & Tsouris, C. (2003). Brownian motion in confinement. Physical Review E, 68(2), 021401. https://doi.org/10.1103/PhysRevE.68.021401.
  • Bertin, V. (2021). Écoulements au voisinage d’interfaces molles: les rôles de l’élasticité, la capillarité & les fluctuations [Ph.D. thesis]. Univ. Bordeaux.
  • Bertin, V., Amarouchene, Y., Raphael, E., & Salez, T. (2021). Soft-lubrication interactions between a rigid sphere and an elastic wall. Journal of Fluid Mechanics, 933, A23. https://doi.org/10.1017/jfm.2021.1063.
  • Bevan, M. A., & Prieve, D. C. (2000). Hindered diffusion of colloidal particles very near to a wall: Revisited. The Journal of Chemical Physics, 113(3), 1228–1236. https://doi.org/10.1063/1.481900.
  • Bhattacharya, S., & Blawzdziewicz, J. (2002). Image system for Stokes-flow singularity between two parallel planar walls. Journal of Mathematical Physics, 43(11), 5720–5731. https://doi.org/10.1063/1.1508812.
  • Bickel, T. (2006). Brownian motion near a liquid-like membrane. European Physical Journal E, 20(4), 379–385. https://doi.org/10.1140/epje/i2006-10026-0.
  • Bickel, T. (2007). Hindered mobility of a particle near a soft interface. Physical Review E, 75(4), 041403. https://doi.org/10.1103/PhysRevE.75.041403.
  • Bickel, T. (2014). Probing nanoscale deformations of a fluctuating interface. Europhysics Letters, 106(1), 16004. https://doi.org/10.1209/0295-5075/106/16004.
  • Blake, J. R. (1971). A note on the image system for a Stokeslet in a no-slip boundary. Mathematical Proceedings of the Cambridge Philosophical Society, 70(2), 303. https://doi.org/10.1017/S0305004100049902.
  • Blawzdziewicz, J., Cristini, V., & Loewenberg, M. (1999). Stokes flow in the presence of a planar interface covered with incompressible surfactant. Physics of Fluids, 11(2), 251–258. https://doi.org/10.1063/1.869875.
  • Blawzdziewicz, J., Wajnryb, E., & Loewenberg, M. (1999). Hydrodynamic interactions and collision efficiencies of spherical drops covered with an incompressible surfactant film. Journal of Fluid Mechanics, 395, 29–59. https://doi.org/10.1017/S002211209900590X.
  • Cates, M. E., & Tailleur, J. (2015). Motility-induced phase separation. Annual Review of Condensed Matter Physics, 6(1), 219–244. https://doi.org/10.1146/annurev-conmatphys-031214-014710.
  • Copson, E. T. (1961). On certain dual integral equations. The Glasgow Mathematical Journal, 5(1), 21. https://doi.org/10.1017/S2040618500034249.
  • Daddi-Moussa-Ider, A., & Gekle, S. (2016). Hydrodynamic interaction between particles near elastic interfaces. The Journal of Chemical Physics, 145(1), 014905. https://doi.org/10.1063/1.4955099.
  • Daddi-Moussa-Ider, A., & Gekle, S. (2018). Brownian motion near an elastic cell membrane: A theoretical study. European Physical Journal E, 41(2), 1–13. https://doi.org/10.1140/epje/i2018-11627-6.
  • Daddi-Moussa-Ider, A., Guckenberger, A., & Gekle, S. (2016a). Long-lived anomalous thermal diffusion induced by elastic cell membranes on nearby particles. Physical Review E, 93(1), 012612. https://doi.org/10.1103/PhysRevE.93.012612.
  • Daddi-Moussa-Ider, A., Guckenberger, A., & Gekle, S. (2016b). Particle mobility between two planar elastic membranes: Brownian motion and membrane deformation. Physics of Fluids, 28(7), 071903. https://doi.org/10.1063/1.4955013.
  • Daddi-Moussa-Ider, A., Kaoui, B., & Löwen, H. (2019). Axisymmetric flow due to a Stokeslet near a finite-sized elastic membrane. Journal of the Physical Society of Japan, 88(5), 054401. https://doi.org/10.7566/JPSJ.88.054401.
  • Daddi-Moussa-Ider, A., Lisicki, M., Gekle, S., Menzel, A. M., & Löwen, H. (2018). Hydrodynamic coupling and rotational mobilities nearby planar elastic membranes. The Journal of Chemical Physics, 149(1), 014901. https://doi.org/10.1063/1.5032304.
  • Daddi-Moussa-Ider, A., Lisicki, M., Hoell, C., & Löwen, H. (2018). Swimming trajectories of a three-sphere microswimmer near a wall. The Journal of Chemical Physics, 148(13), 134904. https://doi.org/10.1063/1.5021027.
  • Daddi-Moussa-Ider, A., Lisicki, M., Löwen, H., & Menzel, A. M. (2020). Dynamics of a microswimmer–microplatelet composite. Physics of Fluids, 32(2), 021902. https://doi.org/10.1063/1.5142054.
  • Daddi-Moussa-Ider, A., Lisicki, M., Mathijssen, A. J. T. M., Hoell, C., Goh, S., B-lawzdziewicz, J., Menzel, A. M., & Löwen, H. (2018). State diagram of a three-sphere microswimmer in a channel. Journal of Physics: Condensed Matter, 30, 254004. https://doi.org/10.1088/1361-648X/aac470.
  • Daddi-Moussa-Ider, A., Lisicki, M., & Mathijssen, A. J. T. M. (2020). Tuning the upstream swimming of microrobots by shape and cargo size. Physical Review Applied, 14(2), 024071. https://doi.org/10.1103/PhysRevApplied.14.024071.
  • Daddi-Moussa-Ider, A., Löwen, H., & Liebchen, B. (2021). Hydrodynamics can determine the optimal route for microswimmer navigation. Communications Physics, 4(1), 1–11. https://doi.org/10.1038/s42005-021-00522-6.
  • Daddi-Moussa-Ider, A., Rallabandi, B., Gekle, S., & Stone, H. A. (2018). Reciprocal theorem for the prediction of the normal force induced on a particle translating parallel to an elastic membrane. Physical Review Fluids, 3(8), 084101. https://doi.org/10.1103/PhysRevFluids.3.084101.
  • Daddi-Moussa-Ider, A., Sprenger, A. R., Amarouchene, Y., Salez, T., Schönecker, C., Richter, T., Löwen, H., & Menzel, A. M. (2020). Axisymmetric Stokes flow due to a point-force singularity acting between two coaxially positioned rigid no-slip disks. Journal of Fluid Mechanics, 904, A34. https://doi.org/10.1017/jfm.2020.706.
  • Daddi-Moussa-Ider, A., Sprenger, A. R., Richter, T., Löwen, H., & Menzel, A. M. (2021). Steady azimuthal flow field induced by a rotating sphere near a rigid disk or inside a gap between two coaxially positioned rigid disks. Physics of Fluids, 33(8), 082011. https://doi.org/10.1063/5.0062688.
  • Daddi-Moussa-Ider, A., Vilfan, A., & Golestanian, R. (2021). Diffusiophoretic propulsion of an isotropic active colloidal particle near a finite-sized disk embedded in a planar fluid-fluid interface. arXiv:2109.14437.
  • Daddi-Moussa-Ider, A. (2020). Asymmetric Stokes flow induced by a transverse point force acting near a finite-sized elastic membrane. Journal of the Physical Society of Japan, 89(12), 124401. https://doi.org/10.7566/JPSJ.89.124401.
  • Dahan, M., Levi, S., Luccardini, C., Rostaing, P., Riveau, B., & Triller, A. (2003). Diffusion dynamics of glycine receptors revealed by single-quantum dot tracking. Science, 302(5644), 442–445. https://doi.org/10.1126/science.1088525.
  • Deamer, D., Akeson, M., & Branton, D. (2016). Three decades of nanopore sequencing. Nature Biotechnology, 34(5), 518–524. https://doi.org/10.1038/nbt.3423.
  • Doostmohammadi, A., Ignés-Mullol, J., Yeomans, J. M., & Sagués, F. (2018). Active nematics. Nature Communications, 9(1), 1–13. https://doi.org/10.1038/s41467-018-05666-8.
  • Driscoll, M., & Delmotte, B. (2019). Leveraging collective effects in externally driven colloidal suspensions: Experiments and simulations. Current Opinion in Colloid & Interface Science, 40, 42–57. https://doi.org/10.1016/j.cocis.2018.10.002.
  • Dufresne, E. R., Altman, D., & Grier, D. G. (2001). Brownian dynamics of a sphere between parallel walls. Europhysics Letters, 53(2), 264. https://doi.org/10.1209/epl/i2001-00147-6.
  • Elgeti, J., Winkler, R. G., & Gompper, G. (2015). Physics of microswimmers – Single particle motion and collective behavior: A review. Reports on Progress in Physics, 78(5), 056601. https://doi.org/10.1088/0034-4885/78/5/056601.
  • Failer, L., & Richter, T. (2020). A parallel Newton multigrid framework for monolithic fluid-structure interactions. Journal on Scientific Computing, 82(2). https://doi.org/10.1007/s10915-019-01113-y.
  • Faucheux, L. P., & Libchaber, A. J. (1994). Confined Brownian motion. Physical Review E, 49(6), 5158–5163. https://doi.org/10.1103/PhysRevE.49.5158.
  • Faxén, H. (1921). Einwirkung der Gefȧsswände auf den Widerstand gegen die Bewegung einer kleinen Kugel in einer zähen Flüssigkeit [Ph.D. thesis]. Uppsala University.
  • Felderhof, B. U. (2012). Hydrodynamic force on a particle oscillating in a viscous fluid near a wall with dynamic partial-slip boundary condition. Physical Review E, 85(4), 046303. https://doi.org/10.1103/PhysRevE.85.046303.
  • François, N., Amarouchene, Y., Lounis, B., & Kellay, H. (2009). Polymer conformations and hysteretic stresses in nonstationary flows of polymer solutions. Europhysics Letters, 86(3), 34002. https://doi.org/10.1209/0295-5075/86/34002.
  • François, N., Lasne, D., Amarouchene, Y., Lounis, B., & Kellay, H. (2008). Drag enhancement with polymers. Physical Review Letters, 100(1), 018302. https://doi.org/10.1103/PhysRevLett.100.018302.
  • Franosch, T., Grimm, M., Belushkin, M., Mor, F. M., Foffi, G., Forró, L., & Jeney, S. (2011). Resonances arising from hydrodynamic memory in Brownian motion. Nature, 478(7367), 85–88. https://doi.org/10.1038/nature10498.
  • Fulford, G., & Blake, J. (1983). On the motion of a slender body near an interface between two immiscible liquids at very low reynolds numbers. Journal of Fluid Mechanics, 127(–1), 203–217. https://doi.org/10.1017/S0022112083002694.
  • Ganatos, P., Weinbaum, S., & Pfeffer, R. (1980). A strong interaction theory for the creeping motion of a sphere between plane parallel boundaries. part 1. perpendicular motion. Journal of Fluid Mechanics, 99(4), 739–753. https://doi.org/10.1017/S0022112080000870.
  • Gentile, F. S., De Santo, I., D’Avino, G., Rossi, L., Romeo, G., Greco, F., Netti, P. A., & Maffettone, P. L. (2015). Hindered Brownian diffusion in a square-shaped geometry. Journal of Colloid and Interface Science, 447, 25–32. https://doi.org/10.1016/j.jcis.2015.01.055.
  • Golub, G. H., & Welsch, J. H. (1969). Calculation of Gauss quadrature rules. Mathematics of Computation, 23(106), 221–230. https://doi.org/10.1090/S0025-5718-69-99647-1.
  • Gompper, G., Winkler, R. G., Speck, T., Solon, A., Nardini, C., Peruani, F., Löwen, H., Golestanian, R., Kaupp, U. B., Alvarez, L., Kiørboe, T. (2020). The 2020 motile active matter roadmap. Journal of Physics: Condensed Matter, 32(19), 193001. https://doi.org/10.1088/1361-648X/ab6348.
  • Graham, M. D. (2011). Fluid dynamics of dissolved polymer molecules in confined geometries. Annual Review of Fluid Mechanics, 43(1), 273–298. https://doi.org/10.1146/annurev-fluid-121108-145523.
  • Guazzelli, E., & Morris, J. F. (2011). A physical introduction to suspension dynamics (Vol. 45). Cambridge University Press.
  • Happel, J., & Brenner, H. (1983). Low Reynolds number hydrodynamics (Vol. 1965). The Hague: Springer Netherlands, Martinus Nijhoff Publishers.
  • Hoell, C., Löwen, H., Menzel, A. M., & Daddi-Moussa-Ider, A. (2019). Creeping motion of a solid particle inside a spherical elastic cavity: II. Asymmetric motion. European Physical Journal E, 42(7), 89. https://doi.org/10.1140/epje/i2019-11853-4.
  • Holmqvist, P., Dhont, J. K. G., & Lang, P. R. (2007). Colloidal dynamics near a wall studied by evanescent wave light scattering: Experimental and theoretical improvements and methodological limitations. The Journal of Chemical Physics, 126(4), 044707. https://doi.org/10.1063/1.2431175.
  • Hsu, R., & Ganatos, P. (1989). The motion of a rigid body in viscous fluid bounded by a plane wall. Journal of Fluid Mechanics, 207, 29–72. https://doi.org/10.1017/S0022112089002491.
  • Illien, P., Golestanian, R., & Sen, A. (2017). ‘Fuelled’ motion: Phoretic motility and collective behaviour of active colloids. Chemical Society Reviews, 46, 5508–5518. https://doi.org/10.1039/C7CS00087A.
  • Kan, C. -W., Fredlake, C. P., Doherty, E. A., & Barron, A. E. (2004). DNA sequencing and genotyping in miniaturized electrophoresis systems. Electrophoresis, 25(21–22), 3564–3588. https://doi.org/10.1002/elps.200406161.
  • Kim, M. -U., & Chung, W. -K. (1985). Axisymmetric slow viscous flow due to the motion of two equal coaxial disks. Journal of the Physical Society of Japan, 54(8), 2874–2882. https://doi.org/10.1143/JPSJ.54.2874.
  • Kim, M. -U. (1983). Axisymmetric Stokes flow due to a point force near a circular disk. Journal of the Physical Society of Japan, 52(2), 449–455. https://doi.org/10.1143/JPSJ.52.449.
  • Kim, S., & Karrila, S. J. (2013). Microhydrodynamics: Principles and selected applications. Courier Corporation.
  • Kurzthaler, C., Zhu, L., Pahlavan, A. A., & Stone, H. A. (2020). Particle motion nearby rough surfaces. Physical Review Fluids, 5(8), 082101. https://doi.org/10.1103/PhysRevFluids.5.082101.
  • Lauga, E., & Powers, T. R. (2009). The hydrodynamics of swimming microorganisms. Reports on Progress in Physics, 72(9), 096601. https://doi.org/10.1088/0034-4885/72/9/096601.
  • Lauga, E., & Squires, T. M. (2005). Brownian motion near a partial-slip boundary: A local probe of the no-slip condition. Physics of Fluids, 17(10), 103102. https://doi.org/10.1063/1.2083748.
  • Lauga, E. (2016). Bacterial hydrodynamics. Annual Review of Fluid Mechanics, 48(1), 105–130. https://doi.org/10.1146/annurev-fluid-122414-034606.
  • Lauga, E. (2020). The fluid dynamics of cell motility (Vol. 62). Cambridge University Press.
  • Laumann, M., Schmidt, W., Farutin, A., Kienle, D., Förster, S., Misbah, C., & Zimmermann, W. (2019). Emerging attractor in wavy poiseuille flows triggers sorting of biological cells. Physical Review Letters, 122(12), 128002. https://doi.org/10.1103/PhysRevLett.122.128002.
  • Lee, Y. K., Porter, C., Diamond, S. L., Crocker, J. C., & Sinno, T. (2018). Deposition of sticky spheres in channel flow: Modeling of surface coverage evolution requires accurate sphere-sphere collision hydrodynamics. Journal of Colloid and Interface Science, 530, 383–393. https://doi.org/10.1016/j.jcis.2018.06.097.
  • Lin, B., Yu, J., & Rice, S. A. (2000). Direct measurements of constrained Brownian motion of an isolated sphere between two walls. Physical Review E, 62(3), 3909–3919. https://doi.org/10.1103/PhysRevE.62.3909.
  • Liron, N., & Mochon, S. (1976). Stokes flow for a stokeslet between two parallel flat plates. The Journal of Engineering Mathematics, 10(4), 287–303. https://doi.org/10.1007/BF01535565.
  • Lisicki, M. (2015). Evanescent wave dynamic light scattering by optically anisotropic Brownian particles [Ph.D. thesis]. University of Warsaw.
  • Lisicki, M., Cichocki, B., Dhont, J. K. G., & Lang, P. R. (2012). One-particle correlation function in evanescent wave dynamic light scattering. The Journal of Chemical Physics, 136(20), 204704. https://doi.org/10.1063/1.4720069.
  • Lisicki, M., Cichocki, B., Rogers, S. A., Dhont, J. K. G., & Lang, P. R. (2014). Translational and rotational near-wall diffusion of spherical colloids studied by evanescent wave scattering. Soft Matter, 10(24), 4312–4323. https://doi.org/10.1039/c4sm00148f.
  • Lobry, L., & Ostrowsky, N. (1996). Diffusion of Brownian particles trapped between two walls: Theory and dynamic-light-scattering measurements. Physical Review B, 53(18), 12050–12056. https://doi.org/10.1103/PhysRevB.53.12050.
  • Lushi, E., Wioland, H., & Goldstein, R. E. (2014). Fluid flows created by swimming bacteria drive self-organization in confined suspensions. Proceedings of the National Academy of Sciences, 111(27), 9733–9738. https://doi.org/10.1073/pnas.1405698111.
  • Marchetti, M. C., Joanny, J. -F., Ramaswamy, S., Liverpool, T. B., Prost, J., Rao, M., & Simha, R. A. (2013). Hydrodynamics of soft active matter. Reviews of Modern Physics, 85(3), 1143. https://doi.org/10.1103/RevModPhys.85.1143.
  • Martínez-Pedrero, F., & Tierno, P. (2018). Advances in colloidal manipulation and transport via hydrodynamic interactions. Journal of Colloid and Interface Science, 519, 296–311. https://doi.org/10.1016/j.jcis.2018.02.062.
  • Mathijssen, A. J. T. M., Culver, J., Bhamla, M. S., & Prakash, M. (2019). Collective intercellular communication through ultra-fast hydrodynamic trigger waves. Nature, 571(7766), 560–564. https://doi.org/10.1038/s41586-019-1387-9.
  • Mathijssen, A. J. T. M., Doostmohammadi, A., Yeomans, J. M., & Shendruk, T. N. (2016). Hydrodynamics of micro-swimmers in films. Journal of Fluid Mechanics, 806, 35–70. https://doi.org/10.1017/jfm.2016.479.
  • Menzel, A. M. (2015). Tuned, driven, and active soft matter. Physics Reports, 554, 1–45. https://doi.org/10.1016/j.physrep.2014.10.001
  • Miyazaki, T. (1984). The effect of a circular disk on the motion of a small particle in a viscous fluid. Journal of the Physical Society of Japan, 53(3), 1017–1025. https://doi.org/10.1143/JPSJ.53.1017.
  • Needleman, D., & Dogic, Z. (2017). Active matter at the interface between materials science and cell biology. Nature Reviews Materials, 2(9), 1–14. https://doi.org/10.1038/natrevmats.2017.48.
  • Nilsson, J., Evander, M., Hammarström, B., & Laurell, T. (2009). Review of cell and particle trapping in microfluidic systems. Analytica Chimica Acta, 649(2), 141–157. https://doi.org/10.1016/j.aca.2009.07.017.
  • Oseen, C. W. (1928). Neuere Methoden und Ergebnisse in der Hydrodynamik. Leipzig, Germany: Akademische Verlagsgesellschaft mbH.
  • Ostrowski, A. M. (2016). Solution of equations and systems of equations: Pure and applied mathematics: A series of monographs and textbooks (Vol. 9). Elsevier.
  • Padding, J. T., & Briels, W. J. (2010). Translational and rotational friction on a colloidal rod near a wall. The Journal of Chemical Physics, 132(5), 054511. https://doi.org/10.1063/1.3308649.
  • Pagonabarraga, I., Hagen, M. H. J., Lowe, C. P., & Frenkel, D. (1998). Algebraic decay of velocity fluctuations near a wall. Physical Review E, 58(6), 7288–7295. https://doi.org/10.1103/PhysRevE.58.7288.
  • Piessens, R. (2000). The Hankel transform (2nd ed., Vol. 2). CRC Press.
  • Poddar, A., Bandopadhyay, A., & Chakraborty, S. (2020). Near-wall hydrodynamic slip triggers swimming state transition of micro- organisms. Journal of Fluid Mechanics, 894. https://doi.org/10.1017/jfm.2020.243.
  • Poddar, A., Bandopadhyay, A., & Chakraborty, S. (2021). Steering a thermally activated micromotor with a nearby isothermal wall. Journal of Fluid Mechanics, 915. https://doi.org/10.1017/jfm.2021.27.
  • Polin, M., Grier, D. G., & Quake, S. R. (2006). Anomalous vibrational dispersion in holographically trapped colloidal arrays. Physical Review Letters, 96(8), 088101. https://doi.org/10.1103/PhysRevLett.96.088101.
  • Puertas, A. M., De Las Nieves, F. J., & Cuetos, A. (2015). Computer simulations of charged colloids in confinement. Journal of Colloid and Interface Science, 440, 292–298. https://doi.org/10.1016/j.jcis.2014.10.044.
  • Rallabandi, B., Oppenheimer, N., Zion, M. Y. B., & Stone, H. A. (2018). Membrane-induced hydroelastic migration of a particle surfing its own wave. Nature Physics, 1. https://doi.org/10.1038/s41567-018-0272-z.
  • Rallabandi, B., Saintyves, B., Jules, T., Salez, T., Schönecker, C., Mahadevan, L., & Stone, H. A. (2017). Rotation of an immersed cylinder sliding near a thin elastic coating. Physical Review Fluids, 2(7), 074102. https://doi.org/10.1103/PhysRevFluids.2.074102.
  • Richter, T. (2017). Fluid-structure interactions. Models, analysis and finite elements ( Lecture notes in computational science and engineering, Vol. 118). Springer.
  • Rogers, S. A., Lisicki, M., Cichocki, B., Dhont, J. K. G., & Lang, P. R. (2012). Rotational diffusion of spherical colloids close to a wall. Physical Review Letters, 109(9), 098305. https://doi.org/10.1103/PhysRevLett.109.098305.
  • Saintyves, B., Jules, T., Salez, T., & Mahadevan, L. (2016). Self-sustained lift and low friction via soft lubrication. Proceedings of the National Academy of Sciences, 113(21), 5847–5849. https://doi.org/10.1073/pnas.1525462113.
  • Salez, T., & Mahadevan, L. (2015). Elastohydrodynamics of a sliding, spinning and sedimenting cylinder near a soft wall. Journal of Fluid Mechanics, 779, 181–196. https://doi.org/10.1017/jfm.2015.425.
  • Shaebani, M. R., Wysocki, A., Winkler, R. G., Gompper, G., & Rieger, H. (2020). Computational models for active matter. Nature Reviews Physics, 1–19. https://doi.org/10.1038/s42254-020-0152-1
  • Shaik, V. A., & Ardekani, A. M. (2017). Point force singularities outside a drop covered with an incompressible surfactant: Image systems and their applications. Physical Review Fluids, 2(11), 113606. https://doi.org/10.1103/PhysRevFluids.2.113606.
  • Shail, R., & Packham, B. A. (1987). Some asymmetric Stokes-flow problems. The Journal of Engineering Mathematics, 21(4), 331. https://doi.org/10.1007/BF00132682.
  • Shen, Z., Coupier, G., Kaoui, B., Polack, B., Harting, J., Misbah, C., & Podgorski, T. (2016). Inversion of hematocrit partition at microfluidic bifurcations. Microvascular Research, 105, 40–46. https://doi.org/10.1016/j.mvr.2015.12.009.
  • Sneddon, I. N. (1960). The elementary solution of dual integral equations. The Glasgow Mathematical Journal, 4(3), 108. https://doi.org/10.1017/S2040618500034006.
  • Sprenger, A. R., Shaik, V. A., Ardekani, A. M., Lisicki, M., Mathijssen, A. J. T. M., Guzmán-Lastra, F., Löwen, H., Menzel, A. M., & Daddi-Moussa-Ider, A. (2020). Towards an analytical description of active microswimmers in clean and in surfactant-covered drops. European Physical Journal E, 43(9), 1–18. https://doi.org/10.1140/epje/i2020-11980-9.
  • Swan, J. W., & Brady, J. F. (2010). Particle motion between parallel walls: Hydrodynamics and simulation. Physics of Fluids, 22(10), 103301. https://doi.org/10.1063/1.3487748.
  • Tanzosh, J. P., & Stone, H. A. (1996). A general approach for analyzing the arbitrary motion of a circular disk in a Stokes flow. Chemical Engineering Communications, 148(1), 333–346. https://doi.org/10.1080/00986449608936523.
  • Todd, K., Chou, H. -T., Amasha, S., & Goldhaber-Gordon, D. (2009). Quantum dot behavior in graphene nanoconstrictions. Nano Letters, 9(1), 416–421. https://doi.org/10.1021/nl803291b.
  • Tränkle, B., Ruh, D., & Rohrbach, A. (2016). Interaction dynamics of two diffusing particles: Contact times and influence of nearby surfaces. Soft Matter, 12(10), 2729–2736. https://doi.org/10.1039/C5SM03085D.
  • Tsori, Y. (2020). Bistable colloidal orientation in polar liquid near a charged wall. Journal of Colloid and Interface Science, 559, 45–50. https://doi.org/10.1016/j.jcis.2019.09.096.
  • Wang, W., & Huang, P. (2014). Anisotropic mobility of particles near the interface of two immiscible liquids. Physics of Fluids, 26(9), 092003. https://doi.org/10.1063/1.4895737.
  • Wang, X., Wang, S., Veerappan, V., Byun, C. K., Nguyen, H., Gendhar, B., Allen, R. D., & Liu, S. (2008). Bare nanocapillary for DNA separation and genotyping analysis in gel-free solutions without application of external electric field. Analytical Chemistry, 80(14), 5583–5589. https://doi.org/10.1021/ac800549k.
  • Widder, D. V. (2015). Laplace transform (PMS-6). Princeton University Press.
  • Wioland, H., Woodhouse, F. G., Dunkel, J., Kessler, J. O., & Goldstein, R. E. (2013). Confinement stabilizes a bacterial suspension into a spiral vortex. Physical Review Letters, 110(26), 268102. https://doi.org/10.1103/PhysRevLett.110.268102.
  • Wolfram, S. (1991). Mathematica: A system for doing mathematics by computer. Addison Wesley Longman Publishing Co., Inc.
  • Zhang, N., Tan, H., & Yeung, E. S. (1999). Automated and integrated system for high-throughput dna genotyping directly from blood. Analytical Chemistry, 71(6), 1138–1145. https://doi.org/10.1021/ac981139j.
  • Zhang, S., Wang, Y., Onck, P., & Den Toonder, J. (2020). A concise review of microfluidic particle manipulation methods. Microfluidics and Nanofluidics, 24, 1–20. https://doi.org/10.1007/s10404-019-2306-y.
  • Zhang, Z., Bertin, V., Arshad, M., Raphael, E., Salez, T., & Maali, A. (2020). Direct measurement of the elastohydrodynamic lift force at the nanoscale. Physical Review Letters, 124(5), 054502. https://doi.org/10.1103/PhysRevLett.124.054502.
  • Zöttl, A., & Stark, H. (2016). Emergent behavior in active colloids. Journal of Physics: Condensed Matter, 28, 253001. https://doi.org/10.1088/0953-8984/28/25/253001.