Bacterial habitats are often associated with fluid flow environments. There is a lack of models 10 of the twitching motility of bacteria in shear flows. In this work, a three-dimensional modelling 11 approach of Computational Fluid Dynamics (CFD) coupled with the Discrete Element Method 12 (DEM) is proposed to study bacterial twitching on flat and groove surfaces under shear flow 13 conditions. Rod-shaped bacteria are modelled as groups of spherical particles and Type IV pili 14 attached to bacteria are modelled as dynamic springs which can elongate, retract, attach and 15 detach. The CFD-DEM model of rod-shape bacteria is validated against orbiting of immotile 16 bacteria in shear flows. The effects of fluid flow rate and surface topography on twitching 17 motility are studied. The model can successfully predict upstream twitching motility of rod-18 shaped bacteria in shear flows. Our model can predict that there would be an optimal range of 19 wall shear stress in which bacterial upstream twitching is most efficient. The results also 20 indicate that when bacteria twitch on groove surfaces, they are likely to accumulate around the 21 downstream side of the groove walls.22 23 24 25 29the surface using appendages called type IV pili (TFP) 2-5 to "explore" the substratum to find 30 suitable sites for growth and thus biofilm formation. Pili emanate from bacterial surface and 31 † The author is currently affiliated with the Department of Oncology, University of Oxford, UK.2 they can be up to several µm long (though they are nm in diameter 6 ). Bacterial twitching 32 occurs through cycles of polymerization and de-polymerization of type IV pili 7,8 .
33Polymerization causes the pilus to elongate and eventually attaching into surfaces. De-34 polymerization makes the pilus to retract and detaching from the surfaces. Pili retraction 35 produces pulling forces on the bacterium, which will be pulled in the direction of the vector 36 sum of the pili forces, resulting in a jerky movement (Figure 1). A typical TFP can produce a 37 force exceeding 100 pN 9 and then a bundle of pili can produce pulling forces up to several nN 38 10 . Bacteria may use pili not only for twitching but also for cell-cell interactions 11,12 , surface 39 sensing 13,14 and DNA uptake 15 .
40Twitching motility could depend on many factors including surface properties, pili 41 arrangement on bacterial surface, and environmental conditions such as oxygen concentration 42 and fluid flow rate 16 . For example, when pili emanate only at the poles of bacteria (e.g.,
43Pseudomonas aeruginosa), the bacteria will have persistent motion 17,18 . But, if pili are all 44 around the cell body (e.g., Neisseria gonorrhoeae), the bacteria will have trapped or diffusive 45 motion due to the tug of war mechanism 19,20 . If a pilus detaches while all the pili are in high 46 tension and anti-parallel configuration, the bacterium will suddenly align along the resultant 47 direction of the remaining bounded-pili causing a sudden change of the twitching direction.
48This is ...