3 results
Wavy Marangoni effect and strategic slip-pattern-driven species transport in micro-confined sandwiched liquid films
- Shubham Agrawal, Prasanta Kumar Das, Purbarun Dhar
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- Journal:
- Journal of Fluid Mechanics / Volume 976 / 10 December 2023
- Published online by Cambridge University Press:
- 06 December 2023, A26
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In microfluidic systems, analyte/reagent mixing is essential to achieve rapid chemical/biochemical reactions. The low Reynolds number (Re) flow, however, makes passive mixing difficult and necessitates the use of some external stimulus to cause disturbance in the system. Here, we report how a periodic thermocapillary effect may interact with strategically patterned wall wettability and boost the mixing dynamics in a micro-confined ternary-liquid film system. Approximate, yet without compromise on the physics involved, analytical solutions to the energy and Navier–Stokes equations under creeping flow conditions are obtained to comprehend the thermal and hydrodynamic characteristics of the thermo-capillarity. In the binary fluid limit, our model is validated with the findings of Pendse & Esmaeeli (Intl J. Therm. Sci., vol. 49, 2010, pp. 1147–1155), and good agreement is found. The flow characteristics in the ternary-liquid system due to discrete wall temperatures is also demonstrated via finite-element-based numerical simulations, and agreement with the semi-analytical solution is noted. The qualitative study of the flow pattern reveals that enhanced mixing is obtained as a result of vortical motion created by the interplay of the periodic thermo-capillarity-driven interfacial flow and wall slip. The observation is further consolidated from the numerical simulation of the species transport equation. The species distribution so obtained is compared with fully developed laminar flow for the same inlet concentration. Our study further investigates the effects of the fluids’ relative thermal conductivity, wall slip length, relative film thickness and thermal (or slip) phase differences on the mixing efficiency of the proposed arrangement. While wall slip, relative film thickness and relative thermal conductivity regulate mixing in the top and bottom layers, phase difference determines how well the middle fluid layer mixes. Slip at the walls creates vortex distortions to get a strong churning effect. The lower thermal conductivity of the top and bottom fluids weakens the thermocapillary flow; however, the dominance of the patterned slip improves mixing in such cases.
Internal hydraulic jump in plane Poiseuille two-layer flow: theoretical, numerical and experimental study
- Mrinmoy Dhar, Subhabrata Ray, Gargi Das, Prasanta Kumar Das
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- Journal:
- Journal of Fluid Mechanics / Volume 912 / 10 April 2021
- Published online by Cambridge University Press:
- 16 February 2021, A45
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This paper discusses a hitherto unexplored flow phenomenon, namely the internal hydraulic jump in thin films during co-current and counter-current two-layer flow between parallel plates. The problem corresponds to a special case of plane Poiseuille flow where the velocity profile changes continuously in the streamwise distance. Since an exact solution of Navier–Stokes equations is not possible, we reformulate the approximate shallow water theory, conventionally adopted to analyse viscous jumps in single-layer laminar flow. The standalone theory has been extensively validated with experimental data for coflow of the two phases and numerical simulations for both co- and counter-current flow. In the limit of zero viscosity ratio, the theoretical results reduce to the expression proposed by Dhar et al. (J. Fluid Mech., vol. 884, no. A11, 2020, pp. 1–26) for single-layer viscous jumps. For a holistic understanding, numerical simulations are used to unravel the physics at the jump, where the analysis displays singularity. The theory in conjunction with simulation reveals recirculation zones even in co-current laminar flow and delineates wavy, smooth and submerged jumps, displayed as a phase diagram. We thus demonstrate the efficacy of shallow water theory which, despite the approximations involved, can be used as a reliable tool for a priori prediction of viscous jumps in two-layer flow with much less effort and resources compared to numerical simulations. Use of an approximate analysis to obtain multifaceted results for a complex flow phenomenon has rarely been explored previously. This paper is also the first study reporting experiments on viscous jumps for two-layer flow in a shallow water analogue.
Planar hydraulic jumps in thin film flow
- Mrinmoy Dhar, Gargi Das, Prasanta Kumar Das
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- Journal:
- Journal of Fluid Mechanics / Volume 884 / 10 February 2020
- Published online by Cambridge University Press:
- 05 December 2019, A11
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We reformulate shallow water theory to understand viscous shear induced natural hydraulic jumps in channels slightly deviated from the horizontal. One of the interesting contributions of the study is a modified expression for Froude number to predict jumps in inclined channels. The proposed Froude number is different from the conventional expression which incorporates channel inclination as a straight forward component of gravity. This highlights the complexity that a jump can generate even in single phase laminar flow. We also obtain an analytical expression for predicting jump strength and show that the scaling relationship originally proposed for jump location in horizontal channels is applicable for both upslope and downslope flows. As expected, upslope flow aids jump formation and beyond a critical adverse tilt, a submerged jump results in subcritical flow right from the entry. On the other hand, both Reynolds number and channel tilt suppress the tendency to jump in downslope flows and below a critical downslope inclination, the flow remains supercritical throughout the channel length. The film thickness for fully developed flow can be predicted from the exact solution of the Navier–Stokes equations. As the theory encounters a singularity in the jump region, numerical simulations and experimental results have been used to obtain additional insights into the physics of jump formation. They have revealed the existence of submerged jump, wavy jump, smooth jump and no jump conditions as a function of liquid Reynolds number, scaled channel length and channel inclination. Such a variety of jump geometries in planar laminar flow has not been reported earlier. Both theory and simulations also reveal that the linear free surface profile upstream of the jump is a function of Reynolds number only, while the downstream profiles can be tuned by changing both Reynolds number as well as the channel length and tilt over the range of parameters studied. We thus demonstrate that, despite the simplicity and the approximations involved, shallow water equations formulated assuming self-similar velocity profiles can elucidate the physics of planar laminar jumps over slight inclinations, difficult to avoid in practice. The analytical and simulated results have been extensively validated with experimental data obtained from a specially designed test rig which ensures laminar flow before and after the jump. To the authors’ knowledge, almost no experimental study has to date been reported on films ‘thin enough’ to remain laminar even after the planar jump.