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Bacterial gliding fluid dynamics on a layer of non-Newtonian slime: perturbation and numerical study. (English) Zbl 1343.92298

Summary: Gliding bacteria are an assorted group of rod-shaped prokaryotes that adhere to and glide on certain layers of ooze slime attached to a substratum. Due to the absence of organelles of motility, such as flagella, the gliding motion is caused by the waves moving down the outer surface of these rod-shaped cells. In the present study we employ an undulating surface model to investigate the motility of bacteria on a layer of non-Newtonian slime. The rheological behavior of the slime is characterized by an appropriate constitutive equation, namely the Carreau model. Employing the balances of mass and momentum conservation, the hydrodynamic undulating surface model is transformed into a fourth-order nonlinear differential equation in terms of a stream function under the long wavelength assumption. A perturbation approach is adopted to obtain closed form expressions for stream function, pressure rise per wavelength, forces generated by the organism and power required for propulsion. A numerical technique based on an implicit finite difference scheme is also employed to investigate various features of the model for large values of the rheological parameters of the slime. Verification of the numerical solutions is achieved with a variational finite element method (FEM). The computations demonstrate that the speed of the glider decreases as the rheology of the slime changes from shear-thinning (pseudo-plastic) to shear-thickening (dilatant). Moreover, the viscoelastic nature of the slime tends to increase the swimming speed for the shear-thinning case. The fluid flow in the pumping (generated where the organism is not free to move but instead generates a net fluid flow beneath it) is also investigated in detail. The study is relevant to marine anti-bacterial fouling and medical hygiene biophysics.

MSC:

92C99 Physiological, cellular and medical topics
76A05 Non-Newtonian fluids
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[1] Ali, N.; Abbasi, A.; Ahmad, I., Channel flow of Ellis fluid due to peristalsis, AIP Adv., 5, 097214 (2015)
[2] Ali, N.; Zaman, A.; Anwar Bég, O., Numerical simulation of unsteady micropolar hemodynamics in a tapered catheterized artery with a combination of stenosis and aneurysm, Med. Biol. Eng. Comput. (2015)
[3] Ali, N.; Zaman, A.; Sajid, M.; Nieto, J. J.; Torres, A., Unsteady non-Newtonian blood flow through a tapered overlapping stenosed catheterized vessel, Math. Biosci., 269, 94-103 (2015) · Zbl 1367.92027
[4] Alouges, F.; DeSimone, A.; Lefebvre, A., Optimal strokes of low Reynolds number swimmers: an example, J. Nonlinear Sci., 18, 277-302 (2008) · Zbl 1146.76062
[5] Alouges, F.; DeSimone, A.; Lefebvre, A., Optimal strokes of axisymmetric microswimmers, Eur. Phys. J. E, 28, 279-284 (2009)
[6] Ambrose, E. J., The movement of fibrocytes, Exp. Cell Res., Suppl. 9, S54-S73 (1961)
[7] Bég, O. Anwar; Bég, Tasveer A.; Bhargava, R.; Rawat, S.; Tripathi, D., Finite element study of pulsatile magneto-hemodynamic non-Newtonian flow and drug diffusion in a porous medium channel, J. Mech. Med. Biol., 12, 1250081.1-1250081.26 (2012)
[8] Bhargava, R.; Sharma, S.; Anwar Bég, O.; Zueco, J., Finite element study of nonlinear two-dimensional deoxygenated biomagnetic micropolar flow, Commun. Nonlinear Sci. Numer. Simul., 15, 1210-1233 (2010) · Zbl 1221.76217
[9] Burchard, A. C.; Burchard, R. P.; Kloetzel, J. A., Intracellular, periodic structures in the gliding bacterium Myxococcus xanthus, J. Bacteriol., 132, 666-672 (1977)
[10] Burchard, R. P., Gliding motility and taxes, (Rosenberg, E., Myxobacteria: Development and Cell Interactions (1984), Springer: Springer Berlin), 139-161
[11] Costerton, J. W.; Murray, R. G.; Robinow, C. F., Observations on the motility and the structure of Vitreoscilla, Can. J. Microbiol., 7, 329-339 (1961)
[13] Dal Maso, G.; DeSimone, A.; Morandotti, M., An existence and uniqueness result for the self-propelled motion of micro-swimmers, SIAM J. Math. Anal., 43, 1345-1368 (2011) · Zbl 1375.76229
[14] Dickson, M. R.; Kouprach, S.; Humphrey, B. A.; Marshall, K. C., Does gliding motility depend on undulating membranes?, Micron, 11, 381-382 (1980)
[15] Duxbury, T.; Humphrey, B. A.; Marshall, K. C., Continuous observations of bacterial gliding motility in a dialysis micro-chamber: the effects of inhibitors, Arch. Microbiol., 124, 169-175 (1980)
[16] Guasto, J. S.; Rusconi, R.; Stocker, R., Fluid mechanics of planktonic micro-organisms, Ann. Rev. Fluid Mech., 44, 373-400 (2012) · Zbl 1358.76086
[17] Gupta, D.; Kumar, L.; Anwar Bég, O.; Singh, B., Finite element simulation of mixed convection flow of micropolar fluid over a shrinking sheet with thermal radiation, Proc. IMechE- E: J. Process Mech. Eng., 228, 61-72 (2014)
[18] Halfen, L. N., Gliding motility of Oscillatoria, ultrastructural and chemical characterization of the fibrillar layer, J. Phycol., 9, 248-253 (1970)
[19] Halfen, L. N.; Castenholz, R. W., Gliding in the blue-green alga: a possible mechanism, Nature, 225, 1163-1165 (1970)
[20] Halfen, L. N.; Castenholz., R. W., Gliding in a blue-green: a possible mechanism, Nature, 225, 1163-1165 (1970)
[21] Halfen, L. N.; Castenholz, R. W., Gliding in the blue-green alga, J. Phycol., 7, 133-144 (1971)
[22] Hayat, T.; Wang, Y.; Siddiqui, A. M.; Asghar., S., A mathematical model for the study of gliding motion of bacteria on a layer of non-Newtonian slime, Math. Methods Appl. Sci., 27, 1447-1468 (2004) · Zbl 1151.76646
[23] Humphrey, B. A.; Dickson, M. R.; Marshall, K. C., Physicochemical and in situ observations on the adhesion of gliding bacteria to surfaces, Arch. Microbiol., 120, 231-238 (1979)
[24] Jarosch., R., Gliding, (Lewin, R. A., In Physiology and Biochemistry of Algae (1962), Academic Press: Academic Press New York), 573-581
[25] Koch, D. L.; Subramanian, G., Collective hydrodynamics of swimming microorganisms: living fluids, Ann. Rev. Fluid Mech., 43, 637-659 (2011) · Zbl 1299.76320
[26] Lauga, E.; DiLuzio, W. R.; Whitesides, G. M.; Stone, H. A., Swimming in circles: motion of bacteria near solid boundaries, Biophys. J., 90, 400-412 (2006)
[27] Lew, H. S.; Fung, Y. C.; Lowenstein, C. B., Peristaltic carrying and mixing of chyme in small intestine, J. Biomech., 4, 297-315 (1971)
[28] Lopez, D.; Lauga, E., Dynamics of swimming bacteria at complex interfaces, Phys. Fluids, 26, 071902 (2014)
[29] Majumdar, P.; Ekin, A.; Webster, D. C., Thermoset siloxane-urethane fouling release coatings, (Provder, T.; Baghdachi, J., Smart Coatings (2007), American Chemical Society), 61-75
[32] O’Brien., R. W., The gliding motion of a bacterium, Flexibactor strain BH 3, J. Aust. Math. Soc. (Ser. B), 23, 2-16 (1981) · Zbl 0473.76130
[33] Pate, J. L., Gliding motility in prokaryotic cells, Can. J. Microbiol., 34, 459-465 (1988)
[34] Rana, P.; Anwar Bég, O., Mixed convection flow along an inclined permeable plate: effect of magnetic field, nanolayer conductivity and nanoparticle diameter, Appl. Nanosci., 5, 569-581 (2015)
[35] Rana, P.; Bhargava, R.; Anwar Bég, O., Finite element modeling of conjugate mixed convection flow of \(Al_2 O_3\)-water nanofluid from an inclined slender hollow cylinder, Phys. Scr., 88, 15 (2013)
[36] Rao, S. S., The Finite Element Method in Engineering (2004), Elsevier: Elsevier USA
[37] Riley, E. E.; Lauga, E., Small-amplitude swimmers can self-propel faster in viscoelastic fluids, J. Theor. Biol., 382, 345-355 (2015) · Zbl 1343.92053
[38] Rusconi, R.; Guasto, J. S.; Stocker, R., Bacterial transport is suppressed by fluid shear, Nat. Phys., 10, 212-217 (2014)
[39] Shivapooja, P.; Wang, Q.; Orihuela, B.; Rittschof, D.; López, G. P.; Zhao, X., Bioinspired surfaces with dynamic topography for active control of biofouling, Adv. Mater., 25, 1430-1434 (2013)
[40] Siddiqui, A. M.; Burchard, R. P.; Schwarz., W. H., An undulating surface model for the motility of bacteria gliding on a layer of non-Newtonian slime, Int. J. Non-Linear Mech., 36, 743-761 (2001) · Zbl 1345.76130
[41] Wang, Y.; Hayat, T.; Siddiqui, A. M., Gliding motion of bacteria on a power-law slime, Math. Methods Appl. Sci., 28, 329-347 (2005) · Zbl 1075.35058
[42] Zaman, A.; Ali, N.; Sajid, M.; Hayat, T., Effects of unsteadiness and non-Newtonian rheology on blood flow through a tapered time-variant stenotic artery, AIP advances, 5, 037129 (2015), http://dx.doi.org/10.1063/1.4916043
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