2014

SMAS/NIASRA JOINT COLLOQUIUM | 2014

Title

A numerical model of a lymphatic vessel

Speaker

Chris Bertram (University of Sydney)

Date

31 July 2014

Abstract

The talk will detail challenges overcome in implementing a new numerical model of a multi-segment lymph vessel, as an intended constituent part of an eventual comprehensive lymphatic network model. The lymphatic system exists to return water and protein that escape from capillary blood vessels into the body's distributed extracellular space. It is also an important part of the immune system that deals with microbial and particulate challenges. Unlike blood vessels, which are passive elastic conduits, lymph vessels actively transport fluid by the intermittent contraction of segments between one-way valves. The numerical challenges include simultaneous solution of all segments subject to up- and downstream boundary conditions, hysteresis, strong nonlinearities, solution discontinuities, and other complex behaviours. The success of our model brings closer the time when it can be used to provide prediction of the outcome of lymphatic vascular surgery to combat the limb swelling that can result from lymph node excision.


Title

Curvature contraction of convex hypersurfaces

Speaker

James McCoy 

Date

4 April, 2014

Abstract

Convex hypersurfaces contracting by their curvature have been of widespread mathematical interest since Huisken's seminal work on the mean curvature flow in 1984. This flow and others were introduced in the 1950s as models for the annealing process in metals; curvature flows more generally have various other practical applications as well as applications in topological classification of hypersurfaces. I will discuss some old and new results for fully nonlinear curvature contraction flow of convex hypersurfaces, considering in particular cases of self-similar solutions, flat sides and non-smooth initial data and speeds.


Title

Drop Pinch-Off for Discrete Flows from a Capillary

Speaker

Frank Bierbrauer (Manchester Metropolitan University)

Date

8 August 2014

Abstract

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-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.

Last reviewed: 12 August, 2014