### Abstract:

The parallel implementation of a large number of functional units is necessary for
any industrial scale microfluidic process. The concept of a 'numbering up'
strategy where a single highly optimized functional unit that has a low individual
production is replicated a large number of times to create a device that has the
necessary output. Designing a system using this strategy assumes that the final
device will have the performance characteristics of the individual unit. In reality
there will be a distribution of operating conditions clustered around the set
point, and this will impact the performance of the overall device. The main
operating condition of the microfluidic device under consideration here is the
average
fluid velocity in each channel.
Most techniques that could measure the
fluid velocity in each channel require an
optical path to the measurement point. For a device with a large number of
channels, it is highly unlikely that every channel will be accessible for observation.
Even if they were, it would be extremely time consuming to measure each
channel individually. Another approach would be to use an impulse response test
to infer the velocity distribution; if an adequately narrow input pulse would yield
a output pulse that would be a reasonable approximation of the system response
function. In the case at hand, the input pulse is too broad to be able to directly
infer the velocity distribution from the output pulse. A numerical deconvolution
technique was applied to the data to be able to effectively remove the error
associated with the input pulse. For sufficiently accurate impulse response data,
this method would yield an accurate estimate of the system response function.
Once an estimate of the velocity distribution is known, a method for inferring the
performance impact is needed. Two approaches were used: 1. A stochastic
simulation that directly generates possible device internal states and then
calculates the performance; and 2. A theoretical approach based on the
performance surface and and assumed velocity distribution form. Both methods
require knowledge of the performance surface of an individual channel with
respect to the local velocity. To generate this surface a finite volume was
developed in FORTRAN that directly simulates a single microchannel pair. The
stochastic model predicted a negative performance impact with increasing
velocity distribution variance. A theoretical model was developed that calculates
the difference between the real and ideal case using the covariance matrix and
Hessian as well as provides a framework for predicting the sign of the deviation in
advance.