Volume 40, July 2013Applied Mathematics In Savoie - AMIS 2012: Multiphase flow in industrial and environmental engineering
|Page(s)||16 - 33|
|Published online||25 July 2013|
Drop Pinch-Off for Discrete Flows from a Capillary
1 School of Computing, Mathematics and
Digital Technology, Manchester Metropolitan University, Manchester, M1 5GD, UK
2 School of Mechanical Engineering, University of Leeds, Leeds, LS2 9JT, UK
The problem of drop formation and pinch-off from a capillary tube under the influence of gravity has been extensively studied when the internal capillary pressure gradient is constant. This ensures a continuous time independent flow field inside the capillary tube typically of the Poiseuille flow type. Characteristic drop ejection behaviour includes: periodic drop ejection, drop ejection with associated satellite production, complex dripping, chaotic behaviour and jetting. It is well known that this characteristic behaviour is governed by the Weber (We) and Ohnesorge (Oh) numbers (for a given Bond number) and may be delineated in a We verses Oh operability diagram. An in-depth physical understanding of drop ejection is also of great importance to industry where the tight control of drop size and ejection velocity are of critical importance in industrial processes such as sealants used in electronics assembly and inkjet printing. However, the use of such a continuous flow approach for drop ejection in industry is often impractical since such flows cannot be operator controlled. For this reason it is important to investigate so-called discrete pipe flows where the flow can be turned on and off at will. This means the flow inside the pipe is now time-dependent being controlled in a step-wise fashion. As a first stage in the investigation of drop pinch-off behaviour in discrete pipe flows this paper will study the critical pinch-off time required for drop ejection starting from a pendant drop. This is the discrete amount of time the pipe flow is turned on for in order for a drop to be ejected from the capillary. A Newtonian incompressible free-surface CFD flow code developed at the University of Leeds is used to investigate the critical pinch-off time for a range of internal pipe velocities (the central flow maximum in Poiseuille flow). It is found that the time required for drop ejection to occur decreases exponentially with internal pipe velocity. These characteristic times are also far smaller than typical static drop release times expected from Harkins and Brown analyses. The phenomenology of the process is due to the creation of a capillary wave at the pipe exit upon the sudden turning on of the flow inside the pipe. The capillary wave acts to transport fluid from the upper part of the forming pendant drop at the end of the capillary to the lower part of the drop both lowering the pendant drop centre-of-mass and thinning the neck region connecting the drop to the pipe. This allows the drop to be pinched off at an earlier than expected time as compared to static drop release times.
© EDP Sciences, SMAI 2013
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