论文标题
从Stokes流的扩散质量转移到低雷诺数Marangoni Boats
From diffusive mass transfer in Stokes flow to low Reynolds number Marangoni boats
论文作者
论文摘要
我们提出了一种在低雷诺数数字上的对称，半球体马龙尼船（肥皂或樟脑船）的自我推广的理论。推进是通过水溶性表面活性剂分子的释放（扩散发射或溶解）产生的，该分子调节空气水界面张力。推进需要不对称释放，也需要自发对称性，通过耦合到完全对称的游泳者的耦合。我们在分析和数值上研究球体中的扩散 - 引入问题，均以恒定浓度和恒定通量边界条件。我们得出了在恒定通量边界条件和努塞尔（Nusselt）数量（总发射通量和扩散通量的无量纲比）下的浓度曲线的新结果。基于这些结果，我们分析了Marangoni船的小型Marangoni推进（小矮人人数），并表明存在两个游泳状态，低速速度的扩散状态以及高游泳速度的对流式的政权。我们既描述了大型Marangoni推进的极限（高pelet数），也描述了近似分析理论蒸发的影响。游泳速度取决于力平衡，我们获得了Marangoni力的一般表达，这两种直接的Marangoni力是从表面张力梯度和Marangoni流动力中的直接的。我们揭示了Marangoni流量的贡献是在推进过程中发挥向前还是向后的力。我们的主要结果是小子数量和游泳速度之间的关系。自发的对称性破坏，因此，对于一个临界小伙子数字上方的完全对称的游泳者而进行游泳，对于大型系统尺寸而言，它变得很小。我们在不对称的情况下找到了对称游泳者的超临界游泳分叉和避免的分叉。
We present a theory for the self-propulsion of symmetric, half spherical Marangoni boats (soap or camphor boats) at low Reynolds numbers. Propulsion is generated by release (diffusive emission or dissolution) of water-soluble surfactant molecules, which modulate the air-water interfacial tension. Propulsion either requires asymmetric release or spontaneous symmetry breaking by coupling to advection for a perfectly symmetrical swimmer. We study the diffusion-advection problem for a sphere in Stokes flow analytically and numerically both for constant concentration and constant flux boundary conditions. We derive novel results for concentration profiles under constant flux boundary conditions and for the Nusselt number (the dimensionless ratio of total emitted flux and diffusive flux). Based on these results, we analyze the Marangoni boat for small Marangoni propulsion (low Peclet number) and show that two swimming regimes exist, a diffusive regime at low velocities and an advection-dominated regime at high swimmer velocities. We describe both the limit of large Marangoni propulsion (high Peclet number) and the effects from evaporation by approximative analytical theories. The swimming velocity is determined by force balance, and we obtain a general expression for the Marangoni forces, which comprises both direct Marangoni forces from the surface tension gradient and Marangoni flow forces. We unravel, whether the Marangoni flow contribution is exerting a forward or backward force during propulsion. Our main result is the relation between Peclet number and swimming velocity. Spontaneous symmetry breaking and, thus, swimming occurs for a perfectly symmetrical swimmer above a critical Peclet number, which becomes small for large system sizes. We find a supercritical swimming bifurcation for a symmetric swimmer and an avoided bifurcation in the presence of an asymmetry.
