Interdisciplinary Applied Mathematics

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Ф dy= —=


The resulting volumetric flowrate per channel width, normalized by huHS, becomes


Q



2 dP* o( S*


з^Г + 2 v1_7^



(7.29)


Since most of the microfluidic experiments are performed by imposing a certain amount of pressure drop along the microchannel, we use equation


(7.29)    to correlate the volumetric flowrate with the imposed pressure drop. Also, for applications with specified volumetric flowrate, one can always obtain the resulting pressure variation along the channel using equation


(7.29) .


The shear stress on the wall for the mixed electroosmotic/pressure-driven flow region is found by differentiating (7.27) with respect to n, and utilizing equation (7.8), which results in


/g _ up*


-y/2cosh(a:) — 2cosh(cri[>c)——.    (7.30)


a    d£


This is an implicit exact relation under the assumptions of our analysis, which requires ф*. Assuming that ф* =0 (valid for a > 1 and XD ^ h), the following approximate relation can be found:


/a _ ИР*


— J2 cosh(a) — 2——.    (7-31)


a    d£


The first    term    on    the    right-hand-side is    due    to    the    variation    of    velocity


within the EDL, while the second term is due to the parabolic velocity profile. The shear stress in the mixed electroosmotic/pressure-driven flow region is enhanced due to the presence of the EDL.


The aforementioned analytical results can be used to validate the numerical computations. In the following we demonstrate the mixed electroosmotic/pressure-driven flows in a channel that is made out of two different materials. The first material exhibits negligible electroosmotic effects, and it is used at    the    entry and    exit    portions    of    the    channel.    The    second mate

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