This letter postulates a generalized fundamental formulation to model the influence of surface characteristics on pressure-driven liquid transport through microchannels. Probabilistic effects pertaining to the influence of roughness elements and uncertainties in wall conditions due to the presence of a random distribution of nanobubbles are represented spectrally by employing a stochastic version of the Navier-Stokes equations. A generalized mathematical expression is eventually arrived at, by normalizing these characteristics, which can act as a fundamental scientific guideline towards the design of microfluidic channels.
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