A Research On Capillary Capture Of Floating Particles By Elliptical Cylinders

Small solid objects tend to attract or repel each other when they are floating on water,which is caused by capillary interaction forces.Floating particles can be captured by other solid objects for capillary attraction.This essay focuses on the capillary attraction and the mechanism that floating particles are captured by elliptical cylinders.Capillary attraction results in capillary capture.Meniscus shape is much related to capillary interaction forces.If meniscus shape of the floating object is determined,capillary interaction forces can be got by the energy method.This essay begins with solving the linearized Young-Laplace equation,to introduce how to get meniscuses of spheres and cylinders.After that,Mathieu functions are used to acquire the meniscus shape of elliptical cylinders.Then,it is convenient to obtain formula of capillary interaction force between an elliptical cylinder and a sphere.This formula is complicated in its form,but by its graph it can be verified that the meniscus height nearby the endpoint of the minor axis is larger than that of the major axis.Besides,the result shows that the capillary force will increase if length of one axis of the elliptical cylinder increase with length of another axis fixed.The motion of particles in elliptical cylinder flow filed can be governed by the B.B.O equation.Floating particles are affected by capillary forces.As a result,the capillary term should join the B.B.O equation.The B.B.O equation is solved together with the flow filed,through which it can be determined whether a single particle is captured.For particles in different position,the mechanism of capillary capture is discussed.When a particle gets far from the elliptical cylinder,its trajectory fits well with the streamline that passes through the starting point of the particle.When the particle gets nearby the elliptical cylinder,its trajectory tends to get close to the elliptical cylinder.Besides,it can be found that increasing the length of the minor axis can obviously increase the capture efficiency,which agrees with the capillary interaction forces.