Linear temporal instabilities and transient energy growth in rotating curved microchannel flow

Owing to the inspiration from the advancements in microfluidic device applications, we analyze linear stability and maximum energy growth amplification in rotating curved microchannel flows. We numerically investigate linear perturbations to a fully developed stable base flow in a rotating curved microchannel by employing the spectral collocation method after transforming the Navier–Stokes system into coupled Orr–Sommerfeld and Squire equations. We estimate the temporal growth rate of the Tollmein–Schlichting wave and the neutral stability bounds driven by the Coriolis and centrifugal forces. At low rotational numbers and small curvature of the channel, we identify four distinct modal instabilities based on the positive growth rate, even at a low Reynolds number within the range for microfluidic devices. By investigating marginal instabilities and critical parameter values, we propose designs for efficient and portable curved microchannels aimed at controlling mixing efficiency. The novelty of the present study is the introduction of curvature of a curved microchannel in a rotating system and its impact on Dean vortices, predicting an early transition to instabilities. Our findings reveal the unstable regions of transient energy growth in a rotating curved microchannel, as highlighted by numerical range and eigenspectrum. Eigenspectrum analysis cannot precisely estimate instabilities, but numerical ranges of transient energy growth offer this capability. In comparison to earlier studies, we report a lower critical Reynolds number of 44 and a critical Dean number of 20 for moderate rotation rates and small curvature of the channel. Employing the transient energy growth analysis, we determine the efficient mixing time, revealing a decreasing function of the Dean number. The concept presented here can potentially assist in the manipulation of interactions of multiple vortices for further studies in mixing phenomena.