RESUMO
Microorganisms often move through viscoelastic environments, as biological fluids frequently have a rich microstructure owing to the presence of large polymeric molecules. Research on the effect of fluid elasticity on the swimming kinematics of these organisms has usually been focused on those that move via cilia or flagellum. Experimentally, Shen (X. N. Shen et al., Phys. Rev. Lett., 2011, 106, 208101) reported that the nematode C. elegans, a model organism used to study undulatory motion, swims more slowly as the Deborah number describing the fluid's elasticity is increased. This phenomenon has not been thoroughly studied via a fully resolved three-dimensional simulation; moreover, the effect of fluid elasticity on the swimming speed of organisms moving via euglenoid movement, such as E. gracilis, is completely unknown. In this study, we discuss the simulation of the arbitrary motion of an undulating or pulsating swimmer that occupies finite volume in three dimensions, with the ability to specify any differential viscoelastic rheological model for the surrounding fluid. To accomplish this task, we use a modified version of the Immersed Finite Element Method presented in a previous paper by Guido and Saadat in 2018 (A. Saadat et al., Phys. Rev. E, 2018, 98, 063316). In particular, this version allows for the simulation of deformable swimmers such that they evolve through an arbitrary set of specified shapes via a conformation-driven force. From our analysis, we observe several key trends not found in previous two-dimensional simulations or theoretical analyses for C. elegans, as well as novel results for the amoeboid motion. In particular, we find that regions of high polymer stress concentrated at the head and tail of the swimming C. elegans are created by strong extensional flow fields and are associated with a decrease in swimming speed for a given swimming stroke. In contrast, in two dimensions these regions of stress are commonly found distributed along the entire body, likely owing to the lack of a third dimension for polymer relaxation. A comparison of swim speeds shows that the calculations in two-dimensional simulations result in an over-prediction of the speed reduction. We believe that our simulation tool accurately captures the swimming motion of the two aforementioned model swimmers and furthermore, allows for the simulation of multiple deformable swimmers, as well as more complex swimming geometries. This methodology opens many new possibilities for future studies of swimmers in viscoelastic fluids.
RESUMO
This paper adds to the tool kit of stochastic simulations based on a very simple idea. Applicable to both SSA and Tau-leap algorithms, it can notably reduce computational times. Stochastic simulations are based on computing sample paths based on the generation of random numbers with either exactly stipulated distribution functions as in SSA (Gillespie, 1977) or in the method of interval of quiescence (Shah et al., 1977) or distribution functions featuring approximations designed to promote efficiency (as in Tau-leap algorithms (Cao et al., 2006; Tian and Burrage, 2004; Peng et al., 2007; Gillespie, 2001; Ramkrishna et al., 2014) where a leap condition with the parameter epsilon is used). The usual strategy involves sequential computation of a large number of sample paths over a bounded time interval which is covered by a set of discrete time subintervals obtained by random number generation. The strategy here departs from the foregoing by parallelizing the generation of random subintervals for the set of sample paths until all sample paths have been computed for the stated time interval. The advantage of this procedure lies in the fact that the time for initiation of the random number generator has been notably reduced. Many examples are demonstrated from SSA as well as Tau-leap algorithms to establish that the advantage of the approach is much more than conceptual.
