自由表面下的爬行：水蜗牛运动
Crawling beneath the free surface: Water snail locomotion
摘要：
陆地蜗牛通过粘性运动进行移动。通过肌肉收缩和足部扩张，它们将剪切应力波通过一层薄薄的粘液传递到固体基底上。由于自由表面不能支持剪切应力，粘附运动是不是一个可行的推进机制的水蜗牛旅行下的自由表面倒置。然而，淡水蜗牛Sorbeoconcha physidae的运动让人想起它的陆地同行，由蜗牛脚的波动产生，蜗牛脚与自由表面被一层薄薄的粘液隔开。在这里，一个润滑模型被用来描述在小幅度的界面变形的限制下的粘液流。通过假设蜗牛脚的形状是一个行波正弦波和粘液是牛顿的，得到的接口形状的演化方程和蜗牛上的所得推进力计算。这个推进力被发现是非零的毛细管数的中等值，但在高和低毛细管数的限制消失。在物理上，这种力的产生是因为蜗牛的脚使自由表面变形，从而在耦合到脚的形貌的粘液层内产生曲率压力和润滑流动。
英文摘要：
Land snails move via adhesive locomotion. Through muscular contraction and expansion of their foot, they transmit waves of shear stress through a thin layer of mucus onto a solid substrate. Since a free surface cannot support shear stress, adhesive locomotion is not a viable propulsion mechanism for water snails that travel inverted beneath the free surface. Nevertheless, the motion of the freshwater snail, Sorbeoconcha physidae, is reminiscent of that of its terrestrial counterparts, being generated by the undulation of the snail foot that is separated from the free surface by a thin layer of mucus. Here, a lubrication model is used to describe the mucus flow in the limit of small amplitude interfacial deformations. By assuming the shape of the snail foot to be a traveling sine wave and the mucus to be Newtonian, an evolution equation for the interface shape is obtained and the resulting propulsive force on the snail is calculated. This propulsive force is found to be non-zero for moderate values of Capillary number but vanishes in the limits of high and low Capillary numbers. Physically, this force arises because the snail's foot deforms the free surface, thereby generating curvature pressures and lubrication flows inside the mucus layer that couple to the topography of the foot.
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