# Research Interests: Visco-plastic lubrication

Typically, a multi-layer flow of 2 viscous fluids in a pipe or channel is unstable, either unconditionally or at very low Reynolds numbers. The cause of the problem is a linear interfacial instability. This instability may be suppressed by choice of viscosity ratio or suitable surface tension, but is not eliminated with purely viscous flows.

If the lubricating fluid is chosen to be a yield stress fluid, many of these instability problems disappear. By carefully selecting the lubricating fluid properties, it is possible to maintain an unyielded ring of lubricating fluid surrounding the interface. This has the effect of preventing interfacial instabilities.

Visco-plastic lubrication paradigm: the viscous core fluid is lubricated by a yield stress fluid keeping an unyielded plug at interface

These types of flows are stable, i.e. no interfacial disturbances, even to small finite perturbations of the flow. This has been shown mathematically, using linear and energy stability methods, and has been demonstrated in more than 100 laboratory scale experiments.

We have established stable flows over lengths of the order of 1000 radii of the inner fluid and at inner fluid Reynolds numbers in the 100-1000 range. For industrial applications, a simple one-dimensional model has been effectively used as a control/design model. Using this model and flow rate control we are able to vary the radii of the inner fluid by 10-20%.

Figure 1: Example computations of the basic flows found during visco-plastic lubrication: inner fluid is Newtonian, outer fluid is Bingham fluid.

Figure 2: Snapshots of a typical experiment: (a) t = 0s, (b) t = 3s, (c) t = 5s, (d) t = 10s, (e) t = 15s, (f) t = 30s,  (g) t = 40s, (h) t = 50s, (i) t = 70s, (j) t = 90s, (k) t = 110s, (l) t = 140s, (m) t = 200s, (n) t = 300s. The axial length of the pictures is 2:2m.

The flow remains stable after the start up phase, in which initial instabilities are advected from the tube.

Figure 3:

(a) Typical set of experimental results plotted with respect to flow rates of the two fluids, compared against model predictions. Stable: ±, unstable 4 and £.  Predicted transition region is shaded, with boundaries denoting ¿Y = 13 § 1Pa.  (b) Measured Ri versus predicted Ri.

### Current directions and industrial application possibilities:

We are currently looking at extending both the experimental and theoretical approaches to multi-layer flows in which the inner fluid is visco-elastic.

With regard to applications, we have various ideas and are interested in pursuing collaborative industrial research towards development of pilot scale test facilities in any of the following areas:

-         Multi-layer extrusion

-         Coating of products

-         Heavy oil pipelining

-         Coal water slurry pipelining

Contact: Ian Frigaard or Mark Martinez

### Relevant publications:

1.       I.A. Frigaard, “Super-stable parallel flows of multiple visco-plastic fluids.” J. Non-Newtonian Fluid Mech., 100, pp. 49-76, (2001).

2.       M. Moyers-Gonzalez, “Nonlinearly stable multilayer viscoplastic flows”, MSc thesis, University of British Columbia, (2002).

3.       M. Moyers-Gonzalez and I.A. Frigaard, “Numerical solution of duct flows of multiple visco-plastic fluids” Journal of Non-Newtonian Fluid Mechanics, 127, pp. 227-241, (2004).

4.       M. Moyers-Gonzalez, I.A. Frigaard and C. Nouar, “Nonlinear stability of a visco-plastically lubricated shear flow.” Journal of Fluid Mechanics, 506, pp.117-146, (2004).

5.       C.K. Huen, “Experimental studies of visco-plastic lubrication”, MASc thesis, University of British Columbia, (2005).

6.       C.K. Huen, I.A. Frigaard and D.M. Martinez, “Experimental studies of multi-layer flows using a visco-plastic lubricant, J. of Non-Newtonian Fluid Mechanics, to appear.

Contributors:

-         I. Frigaard

-         C.K. Huen

-         M. Martinez

-         M. Moyers-Gonzalez

-         C. Nouar