Shaping the gradients driving phoretic micro-swimmers: influence of swimming speed, budget of carbonic acid and environment
Tóm tắt
pH gradient-driven modular micro-swimmers are investigated as a model for a large variety of quasi-two-dimensional chemi-phoretic self-propelled entities. Using three-channel micro-photometry, we obtain a precise large field mapping of pH at a spatial resolution of a few microns and a pH resolution of
$$\sim 0.02~\hbox {pH}$$
units for swimmers of different velocities propelling on two differently charged substrates. We model our results in terms of solutions of the three-dimensional advection–diffusion equation for a 1:1 electrolyte, i.e. carbonic acid, which is produced by ion exchange and consumed by equilibration with dissolved
$$\hbox {CO}_{2}$$
. We demonstrate the dependence of gradient shape and steepness on swimmer speed, diffusivity of chemicals, as well as the fuel budget. Moreover, we experimentally observe a subtle, but significant feedback of the swimmer’s immediate environment in terms of a substrate charge-mediated solvent convection. We discuss our findings in view of different recent results from other micro-fluidic or active matter investigations. We anticipate that they are relevant for quantitative modelling and targeted applications of diffusio-phoretic flows in general and artificial micro-swimmers in particular.
Tài liệu tham khảo
E.M. Purcell, Am. J. Phys. 45, 3–11 (1977). https://doi.org/10.1119/1.10903
J.L. Anderson, Ann. Rev. Fluid Mech. 21, 61–99 (1989). https://doi.org/10.1146/annurev.fl.21.010189.000425
Á.V. Delgado, F. Carrique, R. Roa, E. Ruiz-Reina, Curr. Opin. Colloid Interface Sci. 24, 32–43 (2016). https://doi.org/10.1063/5.0010692
D. Botin, F. Carrique, E. Ruiz-Reina, T. Palberg, J. Chem Phys. 152, 244902 (2020). https://doi.org/10.1063/5.0010692
A. Würger, Rep. Prog. Phys. 73, 126601 (2010). https://doi.org/10.1088/0034-4885/73/12/126601
F.M. Weinert, C.B. Mast, D. Braun, Phys. Chem. Chem. Phys. 13, 9918–9928 (2011). https://doi.org/10.1039/C0CP02359K
H. Jiang, N. Yoshinaga, M. Sano, Phys. Rev. Lett. 105, 268302 (2010). https://doi.org/10.1103/PhysRevLett.105.268302
J.L. Anderson, D.C. Prieve, Sep. Purific. Rev. 13, 67–103 (1984). https://doi.org/10.1080/03602548408068407
D. Velegol, A. Garg, R. Guha, A. Kar, M. Kumar, Soft Matter 12, 4686–4703 (2016). https://doi.org/10.1039/C6SM00052E
P.O. Staffeld, J.A. Quinn, J. Colloid Interface Sci. 13, 69–87 (1989). https://doi.org/10.1016/0021-9797(89)90079-9
J. Palacci, B. Abécassis, C. Cottin-Bizonne, C. Ybert, L. Bocquet, Phys. Rev. Lett. 10, 138302 (2010). https://doi.org/10.1103/PhysRevLett.104.138302
J. Palacci, B. Abécassis, C. Cottin-Bizonne, C. Ybert, L. Bocquet, 980–994 (2010). https://doi.org/10.1039/C1SM06395B
T.-Y. Chang, D. Velegol, J. Colloid Interface Sci. 424, 120–123 (2014). https://doi.org/10.1016/j.jcis.2014.03.003
R. Niu, T. Palberg, Soft Matter 14, 3435–3442 (2018). https://doi.org/10.1039/C8SM00256H
S. Battat, J.T. Ault, S. Khodaparast, H.A. Stone, Soft Matter 15, 3879–3885 (2019). https://doi.org/10.1039/C9SM00427K
M.J. Esplandiu, D. Reguera, J. Fraxeidas, Soft Matter 16, 3717–3726 (2020). https://doi.org/10.1039/D0SM00170H
J.M. Schurr, B.S. Fujimoto, L. Huynh, D.T. Chiu, J. Phys. Chem. B 117, 7626–7652 (2013). https://doi.org/10.1021/jp302587d
H. Stark, Acc. Chem. Res. 51, 2681 (2018). https://doi.org/10.1021/acs.accounts.8b00259
U.B. Kaub, L. Alvarez, Eur. Phys. J. Spec. Top. 225, 2119–2139 (2016). https://doi.org/10.1140/epjst/e2016-60097-1
D.P. Singh, U. Choudhury, P. Fischer, A.G. Mark, Adv. Mater. 29, 1701328 (2017). https://doi.org/10.1002/adma.201701328
A. Aubret, M. Youssef, S. Sacanna, J. Palacci, Nat. Phys. 14, 1114–1118 (2018). https://doi.org/10.1038/s41567-018-0227-4
T. Speck, Soft Matter 16, 2652–2663 (2020). https://doi.org/10.1039/D0SM00176G
S. Heckel, J. Grauer, M. Semmler, T. Gemming, H. Löwen, B. Liebchen, J. Simmchen, Langmuir (2020). https://doi.org/10.1021/acs.langmuir.0c01568
J.L. Moran, P.M. Wheat, J.D. Posner, Phys. Rev. E 81, 065302(R) (2010). https://doi.org/10.1103/PhysRevE.81.065302
A. Reinmüller, H.J. Schöpe, T. Palberg, Langmuir 29, 1738–1742 (2013). https://doi.org/10.1021/la3046466
W. Duan, W. Wang, S. Das, V. Yadav, T.E. Mallouk, A. Sen, Annu. Rev. Anal. Chem. 8, 311–333 (2015). https://doi.org/10.1146/annurev-anchem-071114-040125
J.L. Moran, J.D. Posner, Annu. Rev. Fluid Mech. 49, 511–540 (2017). https://doi.org/10.1146/annurev-fluid-122414-034456
C. Kurzthaler, C. Devailly, J. Arlt, T. Franosch, W.C.K. Poon, V.A. Martinez, A.T. Brown, Phys. Rev. Lett. 121, 078001 (2018). https://doi.org/10.1103/PhysRevLett.121.078001
C. Zhou, H.P. Zhang, J. Tang, W. Wang, Langmuir 34, 3289–3295 (2018). https://doi.org/10.1021/acs.langmuir.7b04301
R. Niu, A. Fischer, T. Palberg, T. Speck, ACS Nano 12, 10932–10938 (2018). https://doi.org/10.1021/acsnano.8b04221
X. Chen, C. Zhou, W. Wang, Chem. Asian J. 14, 2388–2405 (2019). https://doi.org/10.1002/asia.201900377
T. Speck, Phys. Rev. E 99, 060602(R) (2019). https://doi.org/10.1103/PhysRevE.99.060602
T. Speck, J. Tallieur, J. Palacci, New J. Phys. 22, 060201 (2020). https://doi.org/10.1088/1367-2630/ab90d9
R. Kapral, J. Chem. Phys. 138, 020901 (2013). https://doi.org/10.1063/1.4773981
A. Altemose, M.A. Sánchez-Farrán, W. Duan, S. Schulz, A. Borhan, V.H. Crespi, A. Sen, Angew. Chem. Int. Ed. 56, 7817–7821 (2017). https://doi.org/10.1002/anie.201703239
C. Zhou, X. Chen, Z. Han, W. Wang, ACS Nano 13, 4064–4072 (2019). https://doi.org/10.1021/acsnano.9b08421
J. Palacci, S. Sacanna, A. Vatchinsky, P.M. Chaikin, D.J. Pine, J. Am. Chem. Soc. 135, 15978–15981 (2013). https://doi.org/10.1021/ja406090s
D. Feldmann, S.R. Maduar, M. Santer, N. Lomadze, O.I. Vinogradova, S. Santer, Sci. Rep. 6, 36443 (2016). https://doi.org/10.1038/srep36443
F.A. Lavergne, H. Wendehenne, T. Bäuerle, C. Bechinger, Science 364, 70–74 (2019). https://doi.org/10.1126/science.aau5347
J. Sachs, S.N. Kottapalli, P. Fischer, D. Botin, T. Palberg, Colloid Polym. Sci. (2020). https://doi.org/10.1007/s00396-020-04693-6
M.A. Fernandez-Rodriguez, F. Grillo, L. Alvarez, L. Alvarez, M. Rathlef, I. Buttinoni, G. Volpe, L. Isa, Nat. Commun. 11, 4223 (2020). https://doi.org/10.1038/s41467-020-17864-4
C.C. Overly, K.D. Lee, E. Berthiaume, P.J. Hollenbeck, Proc. Natl. Am. Soc. 92, 3156–3160 (1995). https://doi.org/10.1523/JNEUROSCI.16-19-06056.1996
J. Diao, L. Young, S. Kim, E. Fogarty, S. Heilman, P. Zhou, M. Shuler, M. Wu, M. DeLisa, Lab Chip 6, 381–388 (2006). https://doi.org/10.1039/B511958H
S. Krag Gjetting, C. Karkov Ytting, A. Schulz, A. Thoe Fuglsang, J. Exp. Botany63, 3207-3218 (2012). https://doi.org/10.1093/jxb/ers040
K. Shinohara, Y. Sugii, K. Okamoto, H. Madarame, A. Hibara, M. Tokeshi, T. Kitamori, Meas. Sci. Technol. 15, 955–960 (2004). https://doi.org/10.1088/0957-0233/15/5/025
F.M. Möller, F. Kriegel, M. Kieß, V. Sojo, D. Braun, Angew. Chem. Int. Ed. 56, 2340–2344 (2017). https://doi.org/10.1002/anie.201610781
C. Wu, J. Dai, X. Li, L. Gao, J. Wang, J. Liu, J. Zheng, X. Zhan, J. Chen, X. Cheng, M. Yang, J. Tang, Nat. Nanotechnol. (2020). https://doi.org/10.1038/s41565-020-00825-9
Y. Avnir, Y. Barenholz, Anal. Biochem. 347, 34–41 (2005). https://doi.org/10.1016/j.ab.2005.09.026
J. Isaksson, D. Nilsson, P. Kjäll, N.D. Robinson, A. Richter-Dahlfors, M. Berggren, Organ. Electron. 9, 303–309 (2008). https://doi.org/10.1016/j.orgel.2007.11.011
U.B. Kaupp, N.D. Kashikar, I. Weyand, Annu. Rev. Physiol. 70, 93 (2008). https://doi.org/10.1146/annurev.physiol.70.113006.100654
B. Liebchen, H. Löwen, Acc. Chem. Res. 51, 2982 (2018). https://doi.org/10.1021/acs.accounts.8b00215
R. Niu, T. Palberg, Soft Matter 14, 7554–7568 (2018). https://doi.org/10.1039/C8SM00995C
R. Niu, D. Botin, A. Reinmüller, T. Palberg, Langmuir 33, 3450–3457 (2017). https://doi.org/10.1021/acs.langmuir.7b00288
B. Liebchen, R. Niu, T. Palberg, H. Löwen, Phys. Rev. E 98, 052610 (2018). https://doi.org/10.1103/PhysRevE.98.052610
B. Liebchen, D. Marenduzzo, I. Pagonabarraga, M.E. Cates, Phys. Rev. Lett. 115, 258301 (2015). https://doi.org/10.1103/PhysRevLett.115.258301
B. Liebchen, H. Löwen, in K. Lindenberg, R. Metzler, G. Oshanin (eds.) Chemical Kinetics Beyond the Textbook (World Scientific, 2019) pp. 493-516
R. Niu, S. Khodorov, J. Weber, A. Reinmüller, T. Palberg, NJP 19, 115014 (2017). arXiv:1708.02003
D. Botin, J. Wenzel, R. Niu, T. Palberg, Soft Matter 14, 8191–8204 (2018). https://doi.org/10.1039/C8SM00934A
A.A. Farniya, M.J. Esplandiu, D. Reguera, A. Bachtold, Phys. Rev. Lett. 111, 168301 (2013). https://doi.org/10.1103/PhysRevLett.111.168301
M.J. Esplandiu, A.A. Farniya, D. Reguera, J. Chem. Phys. 144, 124702 (2016). https://doi.org/10.1063/1.4944319
R. Niu, P. Kreissl, A.T. Brown, G. Rempfer, D. Botin, C. Holm, T. Palberg, J. de Graaf, Soft Matter 13, 1505–1518 (2017). https://doi.org/10.1039/C6SM02240E
J. Bodin, Water Resour. Res. 51, 1860–1871 (2015). https://doi.org/10.1002/2014WR015910
M. Heidari, A. Bregulla, S. Muinos Landin, F. Cichos, R. von Klitzing, Langmuir 36, 7775 (2020). https://doi.org/10.1021/acs.langmuir.0c00461
F.J. Millero, Geochim. Cosmochim. Acta. 59, 661–677 (1995). https://doi.org/10.1016/0016-7037(94)00354-O
F.J. Millero, R. Feistel, D.G. Wright, T.J. McDougall, Deep-Sea Res. I(55), 50–72 (2008). https://doi.org/10.1016/j.dsr.2007.10.001
E. Ruiz-Reina, F. Carrique, J. Phys. Chem. B 112, 11960–11967 (2008). https://doi.org/10.1021/jp8027885
P. Vanysek, CRC Handbook of Chemistry and Physics, 83rd edn. CRC Press, Boca Raton, pp. 76–78 (2002). https://doi.org/10.1016/j.gca.2011.02.010
R.E. Zeebe, Geochim. Cosmochim. Acta 75, 2483–2498 (2011). https://doi.org/10.1016/j.gca.2011.02.010
K. Shinohara, Y. Sugii, A. Hibara, M. Tokeshi, T. Kitamori, K. Okamoto, Exp. Fluids 38, 117–122 (2004). https://doi.org/10.1007/s00348-004-0906-z
A. Hibara, M. Tokeshi, K. Uchiyama, H. Hisamoto, T. Kitamori, Anal. Sci. 17, 89–93 (2001). https://doi.org/10.2116/analsci.17.89
S. Battat, J.T. Ault, S. Khodaparast, H.A. Stone, Soft Matter 15, 3879–3885 (2019). https://doi.org/10.1039/C9SM00427K