微通道内单向流动的一些等周结果
Some isoperimetric results concerning undirectional flows in microchannels
摘要：
处理了三个等周结果。(i)在给定的压力梯度下，对于具有给定（横截面）面积的所有通道，使稳定流最大化的通道$Q_{\rm steady}$具有圆形横截面。(ii)考虑从规定的初始条件开始的流动，该初始条件从规定的施加的压力梯度发展，周期性的或稳定的。对于这样的流动，在具有给定面积的所有通道中，通常最慢地接近长期、周期或稳定流动的是圆盘横截面。(iii)对于多边形，$n$ -gon，通道，与优化形状是规则的$n$ -gon的类似结果进行了讨论
英文摘要：
Three isoperimetric results are treated. (i) At a given pressure gradient, for all channels with given (cross-sectional) area that which maximises the steady flow $Q_{\rm steady}$ has a circular cross-section. (ii) Consider flows starting from prescribed initial conditions developing from a prescribed imposed pressure gradient, either periodic or steady. For such flows, amongst all channels with given area, that which generically has the slowest approach to the long-term, periodic or steady, flow is the circular disk cross-section. (iii) Similar results for polygonal, $n$-gon, channels, with the optimising shape being the regular $n$-gon are discussed
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