A swimming bacterium in a two-fluid model of a polymer solution
arxiv(2024)
摘要
We analyse the motion of a flagellated bacterium in a two-fluid medium using
slender body theory. The two-fluid model is useful for describing a body moving
through a complex fluid with a microstructure whose length scale is comparable
to the characteristic scale of the body. This is true for bacterial motion in
biological fluids (entangled polymer solutions), where the entanglement results
in a porous microstructure with typical pore diameters comparable to or larger
than the flagellar bundle diameter but smaller than the diameter of the
bacterial head. Thus the polymer and solvent satisfy different boundary
conditions on the flagellar bundle and move with different velocities close to
it. This gives rise to a screening length L_B within which the fluids
exchange momentum and the relative velocity between the two fluids decays. In
this work, both the solvent and polymer of the two-fluid medium are modeled as
Newtonian fluids with different viscosities μ_s and μ_p (viscosity
ratio λ = μ_p/μ_s), thereby capturing the effects solely introduced
by the microstructure of the complex fluid. From our calculations, we observe
an increased drag anisotropy for a rigid, slender flagellar bundle moving
through this two-fluid medium, resulting in an enhanced swimming velocity of
the organism. The results are sensitive to the interaction between the bundle
and the polymer and we discuss two physical scenarios corresponding to two
types of interaction. Our model provides an explanation for the experimentally
observed enhancement of swimming velocity of bacteria in entangled polymer
solutions and motivates further experimental investigations.
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