Research On Occlusion Threshold In Capillary Tubes Under Transverse Body Forces

The capillary forces are firmly established by comprehensive studies spanning several centuries.Nowadays,the research on capillary phenomenon is getting deeper.In contrast,the simplest question that may be asked when a capillary is turned to the horizontal,namely,“Does the liquid spill out?” has not been fully answered.Blockage of small channels by liquid plugs or gas bubbles can be problematic in many technologies such as fuel cells and intensified chemical processes.This paper reports on the application of the explicit mathematically rigorous occlusion criterion which derived by Manning,Collicott and Finn to find a static configuration in liquid partially filling a horizontal tube under transverse body forces,the occluding free surface of the fluid is an equilibrium capillary surface spanning the tube.The research results are as follows:(1)The critical Bond numbers for existence of occluding capillary surfaces in circular pipe,concentric annulus and rectangular channels are studied.For Bond numbers are more than the critical Bond numbers,only the unbounded solution can exist and no plug is possible,but for Bond numbers are less than the critical bond numbers,the bounded solution(a plug)is possible and the unbounded solution may also be possible.(2)The critical Bond numbers of the concentric annulus are studied.Three topologies are calculated,the transition between the two topologies is accompanied by a kink of the curve of the critical Bond numbers.Increasing the aspect ratio(defined as inner circle radius to outer circle radius ratio)maybe can reduce the critical Bond numbers.The larger difference between the contact angle of the inner circle and the contact angle of the outer circle,the smaller the critical bond numbers.(3)The critical Bond numbers of the rectangular tubes are studied for different settings of the non-uniform contact angles.The maximum of the critical Bond number is obtained,which is attained for the bottom contact angle is 45,the top contact angle is 135,and the side contact angles are 90.While,the minimum is also obtained,which is attained for the left and bottom contact angles are 45,the right and top contact angles are 135.(4)The influence of the aspect ratio(defined as the width-to-height ratio)of rectangular cross section on the critical Bond numbers is examined.Unlike the cases for the square,besides one topology,another topology occurs close to the corners in the rectangle with the aspect ratio 2.The aspect ratio has negligible influence on the maximum and minimum critical Bond numbers.Optimization of the non-uniform contact angles can facilitate or effectively block the capillary plugs in rectangular tube regardless of the aspect ratios.