Project. A microfluidic device was designed by Micronics (Redmond, WA) and adapted for metabolic...

Project. A microfluidic device was designed
by Micronics (Redmond, WA) and adapted for metabolic fingerprinting
applications by Drs. Colin Mansfield and R. Anthony Shaw at the NRC Institute
for Biodiagnostics in Canada. The purpose was to take a sample of serum
(comprising both metabolites and proteins) and use diffusion across a
serum/water interface to partly extract metabolites for diagnostic or
analytical characterization. The efficacy of this process was assessed and
optimized by specifically targeting the extraction of serum creatinine (a
representative metabolite) at the expense of serum albumin (a representative
protein). With that accomplished, infrared spectroscopy could be used to
characterize the metabolite-rich aqueous stream with minimal interference from
serum proteins. The convection and diffusion problem is specified in Chapter 11
(Problem 11.28);

here, consider just the flow problem. First
consider flow into the device shown in Figure 10.33. The height is 330 mm and
the two inlet portions each are 110 mm high. The depth is 4.5 mm, but solve the
problem in two dimensions. The flow rates are 2 μL/s for the receiver
(water; top stream) and 1 μL/s for the sample. For the flow problem in
this chapter, take the viscosity as 1.6 mPa s for both fluids; this is changed
in Problem 11.28.

(a) Solve for the streamlines at the inlet
in the geometry shown below.

(b) Compare that with a geometry that has a
knife edge at a height of 165 mm. Further details about the device can be
obtained from the Comsol website (Finlayson and Shaw, 2010), the book website,
and Schattka et al. (2011).

Problem 11.28

When fluid is flowing between two flat
plates and there is a hole or slit in the bottom plate, there is also a
difference between the pressure at the bottom of the hole/slit and the top
plate. This is called the hole pressure and the effect can be used to measure the
first normal stress coefficient of polymers (a measure of elasticity). Here
consider a Newtonian fluid and solve the hole pressure problem in two
dimensions (i.e., for a slit) when W = H = L for Re = 1 (see Figure 10.34).
Plot the pressure on the bottom of the hole and the top just across it.^{1}

^{1}This
problem was the first problem solved by the Galerkin finite element method by
the author and his students (Jackson and Finlayson, 1982a,b). At the time, we
wrote our own finite element code, computers were much slower and very much
smaller, so only 12, 29, and 110 elements were used for a 2D problem. Despite
that limitation, comparison with experiment was quite reasonable for Newtonian
fluids.