R. Usha

Bio: R. Usha is an academic researcher from Indian Institute of Technology Madras. The author has contributed to research in topics: Reynolds number & Instability. The author has an hindex of 17, co-authored 85 publications receiving 1061 citations. Previous affiliations of R. Usha include University of Hyderabad & Anna University.

Interfacial instability in pressure-driven core-annular pipe flow of a Newtonian and a Herschel–Bulkley fluid

Abstract: The linear stability characteristics of pressure-driven core-annular flow of a Newtonian core fluid and a Herschel–Bulkley annular fluid is investigated. The fluids are assumed to have the same density and separated by a sharp interface. The modified Orr–Sommerfeld equations for each layer are derived and solved using an efficient spectral collocation method considering a configuration without any unyielded region. The effect of various dimensionless parameters, such as the Bingham number (Bn), the flow index (n), the interface radius (R0) and the inverse capillary number (Γ) on the instability characteristics of the flow is investigated, and an energy budget analysis is conducted to explain the physical mechanism of the instability observed. We found that axisymmetric mode is the most dominant unstable mode for the interfacial flow configuration considered in the present work, which is in contrast to miscible core-annular flows. It is observed that increasing Bn has a non-monotonic effect on the growth rate of the axisymmetric mode, and two dominant modes appear at high Bn. We found that increasing the thickness of the core fluid increases the bandwidth of the unstable wavenumbers and destabilises the short waves; however, displays a non-monotonic trend in the growth rate curves. The instability behaviour observed for different sets of parameters are investigated by conducting an energy budget analysis and analysing the disturbance eigenfunctions and the basic velocity profiles.

Stability of viscosity stratified flows down an incline: Role of miscibility and wall slip

Abstract: The effects of wall velocity slip on the linear stability of a gravity-driven miscible two-fluid flow down an incline are examined. The fluids have the matched density but different viscosity. A smooth viscosity stratification is achieved due to the presence of a thin mixed layer between the fluids. The results show that the presence of slip exhibits a promise for stabilizing the miscible flow system by raising the critical Reynolds number at the onset and decreasing the bandwidth of unstable wave numbers beyond the threshold of the dominant instability. This is different from its role in the case of a single fluid down a slippery substrate where slip destabilizes the flow system at the onset. Though the stability properties are analogous to the same flow system down a rigid substrate, slip is shown to delay the surface mode instability for any viscosity contrast. It has a damping/promoting effect on the overlap modes (which exist due to the overlap of critical layer of dominant disturbance with the mixed layer) when the mixed layer is away/close from/to the slippery inclined wall. The trend of slip effect is influenced by the location of the mixed layer, the location of more viscous fluid, and the mass diffusivity of the two fluids. The stabilizing characteristics of slip can be favourably used to suppress the non-linear breakdown which may happen due to the coexistence of the unstable modes in a flow over a substrate with no slip. The results of the present study suggest that it is desirable to design a slippery surface with appropriate slip sensitivity in order to meet a particular need for a specific application.

Stability of viscosity stratified flows down an incline: Role of miscibility and wall slip

Abstract: The effects of wall velocity slip on the linear stability of a gravity-driven miscible two-fluid flow down an incline are examined. The fluids have the matched density but different viscosity. A smooth viscosity stratification is achieved due to the presence of a thin mixed layer between the fluids. The results show that the presence of slip exhibits a promise for stabilizing the miscible flow system by raising the critical Reynolds number at the onset and decreasing the bandwidth of unstable wave numbers beyond the threshold of the dominant instability. This is different from its role in the case of a single fluid down a slippery substrate where slip destabilizes the flow system at the onset. Though the stability properties are analogous to the same flow system down a rigid substrate, slip is shown to delay the surface mode instability for any viscosity contrast. It has a damping/promoting effect on the overlap modes (which exist due to the overlap of critical layer of dominant disturbance with the mixed layer) when the mixed layer is away/close from/to the slippery inclined wall. The trend of slip effect is influenced by the location of the mixed layer, the location of more viscous fluid and the mass diffusivity of the two fluids. The stabilizing characteristics of slip can be favourably used to suppress the non-linear breakdown which may happen due to the coexistence of the unstable modes in a flow over a substrate with no slip. The results of the present study suggest that it is desirable to design a slippery surface with appropriate slip sensitivity in order to meet a particular need for a specific application.

Dynamics and stability of thin liquid films

Abstract: The dynamics and stability of thin liquid films have fascinated scientists over many decades: the observations of regular wave patterns in film flows down a windowpane or along guttering, the patterning of dewetting droplets, and the fingering of viscous flows down a slope are all examples that are familiar in daily life. Thin film flows occur over a wide range of length scales and are central to numerous areas of engineering, geophysics, and biophysics; these include nanofluidics and microfluidics, coating flows, intensive processing, lava flows, dynamics of continental ice sheets, tear-film rupture, and surfactant replacement therapy. These flows have attracted considerable attention in the literature, which have resulted in many significant developments in experimental, analytical, and numerical research in this area. These include advances in understanding dewetting, thermocapillary- and surfactant-driven films, falling films and films flowing over structured, compliant, and rapidly rotating substrates, and evaporating films as well as those manipulated via use of electric fields to produce nanoscale patterns. These developments are reviewed in this paper and open problems and exciting research avenues in this thriving area of fluid mechanics are also highlighted.

Viscous flow due to a shrinking sheet

Abstract: The viscous flow induced by a shrinking sheet is studied. Existence and (non)uniqueness are proved. Exact solutions, both numerical and in closed form, are found.

Principles Of Enhanced Heat Transfer

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