# Low Reynolds Number Swimming Near Interfaces in Multi-Fluid Media
## 4 Discussion  
In this paper, we carry out a computational investigation of the classical swimming sheet problem within heterogeneous media, based on a two-fluid mixture model and the Immersed Boundary Method. The swimmer moves in a low-viscosity region surrounded by a more viscous bulk fluid, with different fluid layers separated by interfaces. For the situation in which the volume fraction of one fluid vanishes in part of the domain, numerical regularization is used to solve the model equations. The mixture model and numerical regularization obviate the need to track the interface explicitly and enforce the interface conditions. This greatly simplifies the computational algorithm, especially for problems in which the interfaces are dynamic. Good agreement is obtained between numerical simulations and the analytical results for locomotions in layers of single phase fluid. According to our best knowledge, this is the first time that such problems are simulated by a combination of the IB method and the interface-capturing strategy. The numerical results show that both the thrust and the drag on the swimmer increase with the increase viscosity differences between fluid layers and the decrease of the interface-swimmer distance. The rate of increment for the thrust is greater than that for the drag. This always leads to faster swimming, an effect more substantial for swimmers near non-deformable interfaces. We also investigate locomotions within layers of fluid mixtures. Relative motion and phase separation between components in the mixture can be induced by the waving swimmer. The results illustrate that the swimming speed depends in a non-trivial way on several parameters. With other conditions being the same, larger frictional forces reduce the relative motion and phase separation in the mixture. This always makes the swimmer move faster. For swimming close to the interface, the confinement effect dominates. The reduction of viscosity for the mixture near the swimmer (through the increase of \(\theta_{\text{s}}\) or the decrease of \(\theta_{\text{n}}\)) strengthens the confinement effect from the bulk fluid. This tends to speed up the swimming motion. The situation is more complicated if the interfaces are further away from the swimmer. Depending on the values of H and \(\xi\), the swimming speed can be boosted or reduced by lowering the network fraction near the swimmer. Therefore, swimmers in a two-fluid mixture near free interfaces can move faster or slower than that in a single fluid, depending on their distances from the interface, the composition of the fluid mixture, as well as the magnitude of the frictional force between components in the mixture. This conclusion can be potentially related to the disparity of experimental results on microorganism swimming [28; 29]. The computational framework described in the paper can be applied to the study of locomotions of microorganisms within various biofluid media, especially for the cases where swimmers are near free deformable interfaces. The flexibility of the method also makes it a suitable tool to investigate problems in which structural properties of the fluid media are altered by the dynamic swimmer. For example, it is observed that gastric mucin undergoes a phase transition from a viscoelastic gel to a viscous solution, triggered by the urease production from the ulcer-causing pathogen Helicobacter pylori [1]. This localized de-gelling process enables the bacterium to swim through a fluidic pocket (surrounded by gel) and cause infection. The analytical work in [30] based on a simplified model illustrates that the size of the fluid zone plays important roles in determining the physics of motility. However, the gel-sol transition dynamics, chemical reactions, and mucus transport are ignored. Extensions of our computational model can provide a unified framework for the investigation of such locomotive problems in multi-fluid heterogeneous media.