In the Stokes limit the corresponding swimming velocity is in the opposite direction to that for transverse deformation. The rotational velocity follows from the requirement that besides the net mean force also the net mean torque exerted on the fluid vanish. Reynolds stress, but the corresponding net mean force on the fluid per unit area again vanishes, as is seen by integration. Conversely the force per unit area exerted by the sheet on the fluid vanishes. Brownian dynamics simulations, this pressure is shown to be the force per unit area transmitted by the active particles. A model that incorporates a detailed description of the cortical network growth, myo-II, and cortical-network interactions, combined with the transport of actin monomers and other components in the CSK, will be very complex, and to date the cortex has been described as an active gel in simplified treatments of cortical flow (Joanny & Prost 2009, Prost et al.
Although the hypothesis of quasi-two-dimensionality underlying our analysis (as well as that of most of the literature on simplified model foils) can be partially justified alluding to the aspect ratio of the propulsive appendage, it is clear that the inherent 3D nature of this type of flows needs to be further analysed and included in realistic models. We will show that tension gradients in the membrane can generate movement without shape changes, which we call ’swimming’, of a cell submerged in a fluid. Thus the membrane functions more like an elastic than a viscous material, and the drag force due to cortical flow creates an opposed tension gradient in the membrane. Evans & Needham (1987) define the tension as the average of the stresses along the principal directions of the surface, but these are rarely available. Recently, a few experimental and theoretical studies have addressed the role of non-Newtonian stresses in the fluid, with conflicting conclusions as to their impact on locomotion.
In such environment, movement assumes an important role, and while their fluid environment imposes movement in its own via currents and turbulence, many planktonic organisms, even algae, have locomotion ability. Simulations of two rigid bodies executing pre-specified motion indicate that flow-mediated interactions can lead to substantial drag reduction and may even generate thrust intermittently. POSTSUBSCRIPT can be thought of as a drag coefficient with the dimension of the viscosity per unit length. POSTSUBSCRIPT (Salbreux et al. POSTSUBSCRIPT should eventually increase with diminishing algal contributions when the thermal fluctuation starts to play the dominant role. In a locally thermal enviroenment, however, they correspond to indistinguisheable configurations of the free energy. However, there is ongoing debate on the importance of near-wall effects and the level at which to truncate the hydrodynamic moment expansion spagnolie12 . However, vesicles have no cortical layer and red blood cells have a very thin layer of spectrin — which contains no molecular motors — attached to the membrane. Since amoeboid cells have a less-structured CSK, the cell shape is primarily determined by the distribution of internal forces in the membrane and the forces in the cortex. 2013), we compute its first variation with respect to a deformation, which gives the membrane force, and to this we add the cortical forces directly.
He considered small amplitude deformation, corresponding to small Reynolds number, and arena goggles the Stokes limit of high viscosity. The swimming of an elliptical disk at small Reynolds number is studied on the basis of a perturbative solution of the Navier-Stokes equations for fluid flow near a deformable infinite sheet. Seminal work by GI Taylor examined swimming speeds of an infinite sheet in 2D and an infinite cylinder with circular cross section of small radius in 3D, propagating lateral displacement waves Taylor (1951, 1952). In these studies, it was shown that the second order swimming speed scales quadratically with amplitude and linearly with frequency for small amplitude bending. The seminal work of Taylor 1 was concerned with the swimming of a planar sheet with transverse plane wave surface deformation. The fluid is caused to move by periodic surface deformation of the body. The results may be compared with those derived for a slab with symmetric surface deformation leading to symmetry of the flow on both sides 8 . We review our numerical approach in Sections IV.1-IV.3 before presenting results in Section IV.4. Since the forces are simply specified, we can consider both the case in which there is a cortical flow that generates stresses, and the case in which the cortex is under stress but not flowing with this approach.