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Register a new userRotational Instabilities in Microchannel Flows
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Mixing in numerous medical and chemical applications, involving overly long microchannels, can be enhanced by inducing flow instabilities. The channel length, is thus shortened in the inertial microfluidics regime due to the enhanced mixing, thereby rendering the device compact and portable. Motivated by the emerging applications of lab-on-a-CD based compact microfluidic devices, we analyze the linear stability of rotationally actuated microchannel flows commonly deployed for biochemical and biomedical applications. The solution of the coupled system of Orr-Sommerfeld (OS) and Squire (SQ) equations yields the growth rate and the neutral curve of the two types of instabilities: (i) the Tollmien-Schlichting (TS) wave and (ii) the Coriolis force-driven instability. We report the existence of four distinct unstable modes (Modes I-IV) at low Reynolds numbers of which only the existence of Mode I is previously known for the present flow configuration. Furthermore, Modes I and II exhibit competing characteristics. We infer that Modes III and IV might cause strong mixing locally by virtue of strong velocity perturbation in proximity to the interface. We quantify the potential of all the modes to induce such localized mixing near the interface using the notion of penetration depth. Further, insight into the mechanism of energy transfer, drawn from the evaluation of kinetic-energy budget, reveals that the Reynolds stress first transfers energy from the mean flow to the streamwise velocity fluctuations. The Coriolis force, thereafter, redistributes the axial momentum into spanwise and wall-normal directions, generating the frequently observed roll-cell structures. A qualitative comparison of our predictions with reported experiments on roll-cells indicates co-existence of Modes I and II.
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Instability of stratified multi-phase flow in a rotating platform becomes important because of a potential role in micro-mixing and micro-machines. Centrifugal actuation can play an important role in driving the flow and Coriolis force can enhance the mixing in a short span by destabilizing the flow. In this study, we focus on the impact of the Coriolis force on a rotating viscosity-stratified flow with a thin diffusive mixed layer between two fluid layers. Modal stability analysis is used to estimate the critical parameters, namely Rotation number, Reynolds number, and wave number, which are responsible to modulate the instability mechanism for different viscosity contrasts. Present study explores competing influences of rotational forces against the viscous and inertial forces. Correspondingly, rotational direction (clockwise/anticlockwise) shows a significant effect on the spatio-temporal instability mechanism and anticlockwise rotation promotes the instability. Usually, miscible viscosity stratified flow with respect to streamwise disturbance becomes more unstable for a thinner mixed layer. On the contrary, our numerical computation confirms a completely contrasting scenario, considering Coriolis force driven instability of a miscible system on account of spanwise disturbances. Possible physical mechanisms for the same are discussed in terms of base flow and energy fluctuation among perturbed and base flow. Comparison of two and three-dimensional instability is done to give a clear-cut idea about the linear instability of the flow system considered herein. Velocity and viscosity perturbation distributions display a critical bonding between the vortices near and away from mixed layer, which may be responsible for the variation of instability with respect to viscosity ratio and rotational direction.
A kinematic approach for the identification of flow instabilities is proposed. By defining a flow instability in the Lagrangian frame as the increased folding of lines of fluid particles, subtle perturbations and unstable growth thereof are detected early based solely on the curvature change of material lines over finite time. The material line curvature is objective, parametrization independent, and can be applied to flows of general complexity without knowledge of the base flow. An analytic connection between the growth of Eulerian velocity modes perturbing a general shear flow and the induced flow map and Lagrangian curvature change is derived. The approach is verified to capture instabilities promptly in a temporally developing jet flow, an unstable separated shear flow over a cambered airfoil, and in the onset of a wake instability behind a circular cylinder.
In this paper, the interfacial motion between two immiscible viscous fluids in the confined geometry of a Hele-Shaw cell is studied. We consider the influence of a thin wetting film trailing behind the displaced fluid, which dynamically affects the pressure drop at the fluid-fluid interface by introducing a nonlinear dependence on the interfacial velocity. In this framework, two cases of interest are analyzed: The injection-driven flow (expanding evolution), and the lifting plate flow (shrinking evolution). In particular, we investigate the possibility of controlling the development of fingering instabilities in these two different Hele-Shaw setups when wetting effects are taken into account. By employing linear stability theory, we find the proper time-dependent injection rate $Q(t)$ and the time-dependent lifting speed ${dot b}(t)$ required to control the number of emerging fingers during the expanding and shrinking evolution, respectively. Our results indicate that the consideration of wetting leads to an increase in the magnitude of $Q(t)$ [and ${dot b}(t)$] in comparison to the non-wetting strategy. Moreover, a spectrally accurate boundary integral approach is utilized to examine the validity and effectiveness of the controlling protocols at the fully nonlinear regime of the dynamics and confirms that the proposed injection and lifting schemes are feasible strategies to prescribe the morphologies of the resulting patterns in the presence of the wetting film.
In this study, we use numerical simulations to investigate the flow field induced by a single magnetic microrobot rotating with a constant angular speed about an axis perpendicular to an underlying surface. A parallel solver for steady Stokes flow equations based on the boundary-element method is used for simulating these flows. A simple transformation is introduced to extend the predictive capability of the solver to cases with small unsteadiness. Flows induced by four simple robot shapes are investigated: sphere, upright cylinder, horizontally-laid cylinder, and five-pointed star-shaped prism. Shapes with cross-sections that are axisymmetric about the rotation axis (sphere and upright cylinder) generate time-invariant flow fields, which could be useful for applications such as micromanipulation. Non-axisymmetric shapes (horizontally-laid cylinder and the star-shaped prism) induce significant unsteadiness inside the flow field, which could be desirable for applications such as micromixing. Furthermore, a slender horizontally-laid cylinder generates substantially three-dimensional flows, an added benefit for micromixing applications. The presence of nearby walls such as a bottom substrate or sidewalls has a retarding effect on the induced flows, which is quantified. Finally, we present the driving torque and power-consumption of these microrobots rotating in viscous liquids. The numerical modeling platform used in this work can enable future optimal microrobot designs for a given application requirement.
This fluid dynamics video shows drops of water being transported by a mean flow of oil, in a microchannel shaped as a logarithmic spiral. The channel shape means that the drops are submitted to an increasing shear and elongation as they flow nearer to the center of the spiral. A critical point is reached at which a long singular tail is observed behind the drops, indicating that the drops are accelerating. This is called Tip streaming.
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