
Research Interests: Viscoplastic
lubrication



Typically, a multilayer
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. 
Viscoplastic
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 1001000 range. For
industrial applications, a simple onedimensional 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 1020%. 
Figure 1: Example computations of the basic
flows found during viscoplastic 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 R_{i} versus predicted R_{i}_{.} 

Current directions and industrial application possibilities:We are currently looking at
extending both the experimental and theoretical approaches to multilayer
flows in which the inner fluid is viscoelastic. 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: 
Multilayer
extrusion 
Coating of
products 
Heavy oil
pipelining 
Coal water
slurry pipelining Contact: Ian Frigaard or Mark Martinez 

Relevant publications:1.
I.A. Frigaard,
“Superstable parallel flows of multiple viscoplastic
fluids.” J. NonNewtonian Fluid Mech., 100, pp. 4976, (2001). 2.
M. MoyersGonzalez, “Nonlinearly stable
multilayer viscoplastic flows”, MSc
thesis, 3.
M. MoyersGonzalez and I.A. Frigaard, “Numerical solution of duct flows of multiple viscoplastic fluids” Journal of NonNewtonian Fluid
Mechanics, 127, pp. 227241, (2004). 4.
M. MoyersGonzalez, I.A. Frigaard and C. Nouar, “Nonlinear stability of a viscoplastically lubricated shear flow.” Journal of
Fluid Mechanics, 506, pp.117146, (2004). 5.
C.K. Huen, “Experimental studies of viscoplastic lubrication”, MASc
thesis, 6.
C.K. Huen, I.A. Frigaard
and D.M. Martinez, “Experimental studies of multilayer flows
using a viscoplastic lubricant”,
J. of NonNewtonian Fluid Mechanics, to appear. Contributors: 
I. Frigaard 
C.K. Huen 
M. Martinez  M. MoyersGonzalez  C. Nouar 