Blood flow

i) Introduction

One of our main interest is to capture the correct behaviour of a blood flow inside a capillary, where the hydrodynamics of each cell has to be resolved explicitly. At this length scale, the conventional method of CFD solvers of considering blood as a uniform non-Newtonian liquid is not valid. The main characteristic of flow through capillaries is the initialisation of the inflammatory response. It is characterised by the migration of leukocytes (white blood cells) out from the main blood stream into the surface of the wall (margination), followed by their rolling until they find an intercellular space in which they squeeze into. This phenomenon has been studied widely experimentally but a net lack of simulations cannot be ignored. Only basic models are currently available where no robust conclusions can be deduced from. The aim of this section is therefore to apply our model to blood flow in capillaries.

ii) Stenosis

When one has a too fatty diet, his/her carotid artery gets blocked (blockage that can reach 95 per cent) leading to serious complications. Stenosis plays an important role in cardiovascular disease and leads to a wide range of complications such as strokes. Our model could be used to model the behaviour of such a configuration. A preliminary simulation shows the potential of the method

The length scale here is obviously not respected for the carotid artery (its width is of the order of several hundreds of cells across) but finds its application for diabetic patients where small capillaries contracts leading to a stagnation of blood in the inferior members leading to swelling.

iii) Blood wash device

In some cases, a patient has to have its blood washed from its impurity. The 'dirty' blood has to go through a big cavity containing filters and active chemicals that fix the unwanted impurity. Blood needs to be continuously sheared in order not to cloth (formation of cluster). Eventual clusters could jam the filter of the machine leading to expensive maintenance and in extreme case, the loss of the patient.

The simulation below shows many droplets (cells) being subjected to gravity onto a surrounding fluid. For the demonstration purposes, the droplets (cells) are set to be heavier than the plasma. Significant mixing occurs. This model would be very well suited to investigate any non-mixing of low shear zone in any cavity.

Micro-fluidic

i) Introduction

The micro-fluidic regime is characterised by a low Re and a low Ca. It is by definition highly interface dominated and classical CFD solvers encounter great difficulties to deal efficiently with it. We have designed, with our current lattice Boltzmann method, all the steps forward to handle this regime efficiently. The following demonstrates the method.

ii) First configuration: binary fluid

This configuration is taken from Professor David A. Weitz group at the Division of Engineering and Applied Sciences / Department of Physics, Harvard University, Cambridge, MA 02138 www.deas.harvard.edu/projects

This one to one comparison demonstrated the scope of the technic. This simulation took only a few hours on a standard PC. The difference of wetting property at the angles of left inlet might be explained by wetting differences and lattice resolution at the boundary.

iii) Second configuration: flow focusing, N component

The flow focusing configuration has been characterised by Anna et al.: S. L. Anna, N. Bontoux, H. A. Stone, Applied Physics Letters 82(3), 2003.