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Applying Eq. (7) to the interface between the upstream reservoir and the sample ((x = 0)), assuming that the upstream reservoir evacuates to an infinite downstream reservoir across the sample, and integrating along L yields k_{D} = frac{2Lmu }{A}frac{{V_{u} }}{{P_{u}^{2} - P_{d}^{2} }}frac{{dP_{u} }}{dt}.
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