Well‐Posed Treatment of Space‐Charge Layers in the Electroneutral Limit of Electrodiffusion

The electroneutral model describes cellular electrical activity, accounting for ionic concentration dynamics without resolution of the fine spatial scales of the space‐charge layer. This is done by asserting that the ionic solution is electrically neutral at each point in space. However, electroneutrality is inconsistent with the original boundary conditions at cell membranes. We consider three separate methods of resolving this inconsistency that result in well‐posed models that are accurate approximations to a detailed model in which the space‐charge layer is fully resolved. A particular electrodiffusion problem is utilized to make the discussion specific.© 2015 Wiley Periodicals, Inc.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/134413/1/cpa21611.pd

Flexible clap and fling in tiny insect flight

Of the insects that have been filmed in flight, those that are 1 mm in length or less often clap their wings together at the end of each upstroke and fling them apart at the beginning of each downstroke. This ;clap and fling' motion is thought to augment the lift forces generated during flight. What has not been highlighted in previous work is that very large forces are required to clap the wings together and to fling the wings apart at the low Reynolds numbers relevant to these tiny insects. In this paper, we use the immersed boundary method to simulate clap and fling in rigid and flexible wings. We find that the drag forces generated during fling with rigid wings can be up to 10 times larger than what would be produced without the effects of wing-wing interaction. As the horizontal components of the forces generated during the end of the upstroke and beginning of the downstroke cancel as a result of the motion of the two wings, these forces cannot be used to generate thrust. As a result, clap and fling appears to be rather inefficient for the smallest flying insects. We also add flexibility to the wings and find that the maximum drag force generated during the fling can be reduced by about 50%. In some instances, the net lift forces generated are also improved relative to the rigid wing case