Double-diffusive two-fluid flow in a slippery channel: A linear stability analysis
TL;DR: In this article, the effect of velocity slip at the walls on the linear stability characteristics of two-fluid three-layer channel flow was investigated in the presence of double diffusive (DD) phenomenon.
Abstract: The effect of velocity slip at the walls on the linear stability characteristics of two-fluid three-layer channel flow (the equivalent core-annular configuration in case of pipe) is investigated in the presence of double diffusive (DD) phenomenon. The fluids are miscible and consist of two solute species having different rates of diffusion. The fluids are assumed to be of the same density, but varying viscosity, which depends on the concentration of the solute species. It is found that the flow stabilizes when the less viscous fluid is present in the region adjacent to the slippery channel walls in the single-component (SC) system but becomes unstable at low Reynolds numbers in the presence of DD effect. As the mixed region of the fluids moves towards the channel walls, a new unstable mode (DD mode), distinct from the Tollman Schlichting (TS) mode, arises at Reynolds numbers smaller than the critical Reynolds number for the TS mode. We also found that this mode becomes more prominent when the mixed layer overlaps with the critical layer. It is shown that the slip parameter has nonmonotonic effect on the stability characteristics in this system. Through energy budget analysis, the dual role of slip is explained. The effect of slip is influenced by the location of mixed layer, the log-mobility ratio of the faster diffusing scalar, diffusivity, and the ratio of diffusion coefficients of the two species. Increasing the value of the slip parameter delays the first occurrence of the DD-mode. It is possible to achieve stabilization or destabilization by controlling the various physical parameters in the flow system. In the present study, we suggest an effective and realistic way to control three-layer miscible channel flow with viscosity stratification.
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TL;DR: A mathematical model for the cilia-generated propulsion of an electrically-conducting viscoelastic physiological fluid in a ciliated channel under the action of magnetic field is discussed.
Abstract: Bionic systems frequently feature electromagnetic pumping and offer significant advantages over conventional designs via intelligent bio-inspired properties. Complex wall
features observed in nature also provide efficient mechanisms which can be utilized in biomimetic
designs. The characteristics of biological fluids are frequently non-Newtonian in nature. In many natural systems super-hydrophobic slip is witnessed. Motivated by these phenomena, in the present article, we present a mathematical model for the cilia-generated propulsion of an electrically-conducting viscoelastic physiological fluid in a ciliated channel under the action of an externally
applied static magnetic field. The rheological behavior of the fluid is simulated with the Johnson-Segalman constitutive model which allows internal wall slip. The regular or coordinated movement of the ciliated edges (which line the internal walls of the channel) is represented by a metachronal wave motion in the horizontal direction which generate a two-dimensional velocity profile with the parabolic profile in the vertical direction. This mechanism is imposed as a periodic moving velocity boundary condition which generates propulsion in the channel flow. Under the
classical lubrication approximation (long wavelength and low Reynolds' number), the boundary value problem is rendered non-dimensional and solved analytically with a perturbation technique. The influence of the geometric, rheological (slip and Weissenberg number) and magnetic
parameters on the velocity, pressure gradient and the pressure rise (evaluated via the stream function in symbolic software) are presented graphically and interpreted at length.
11 citations
Cites background from "Double-diffusive two-fluid flow in ..."
...Many researcher (Ghosh et al. 2014a, 2014b, 2015; Chattopadhyay et al. 2017) studied the stabiity and instability of miscible two fluid flow with the slip at a wall in a rigid stratified system....
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11 citations
TL;DR: In this article, the authors investigated the stability properties of a pressure-driven channel flow of two miscible fluids flowing in a layered manner in the presence of two scalar components diffusing at different rates [double-diffusive (DD) phenomenon].
Abstract: The linear stability characteristics of a pressure-driven channel flow of two miscible fluids flowing in a layered manner are investigated in the presence of two scalar components diffusing at different rates [double-diffusive (DD) phenomenon]. The fluids are assumed to have the same density but different viscosities. The parameters varied are the Reynolds number, Schmidt number, and thickness of the bottom layer. It is observed that the linear stability behavior in the presence of the DD effect is strikingly different from that observed in the single-component (SC) system. While the SC two-layer configuration is stable, the DD two-layer flow becomes unstable at low and moderate Reynolds numbers. It is found that increasing the diffusivity ratio of the faster to the slower diffusing scalar destabilizes the system. A region of instability distinct from that of the Tollmien–Schlichting (TS) mode appears for some combinations of the log-mobility ratios of the slower and faster diffusing scalars. This unstable region grows as the diffusivity ratio increases and the thickness of the bottom layer decreases. For a constant diffusivity ratio, decreasing the Schmidt number of the slower diffusing scalar also increases the region of instability. An energy budget analysis is conducted to understand the underlying mechanism of this instability. Two mechanisms, namely, (i) the rate of energy transfer from the basic flow to the disturbance and (ii) the disturbance energy due to mean viscosity gradient, are found to be the significant contributors to the increase in the rate of change of the disturbance kinetic energy.
11 citations
Additional excerpts
...[28] explored the effect of wall velocity slip on the DD instability mode observed in the previous study [26]....
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TL;DR: In this paper, the authors investigated the effects of diffusivity ratio, log-mobility ratios of the slower and faster diffusing species and Reynolds number on the flow dynamics in axisymmetric pipe.
Abstract: The pressure-driven displacement flow of a less viscous fluid initially occupying an axisymmetric pipe by a highly viscous fluid is investigated. The fluids consist of two species diffusing at different rates. The fluids are assumed to be Newtonian, incompressible with the same density, but of different viscosity modelled as an exponential function of the concentration of both the species. A parametric study investigating the effects of diffusivity ratio, log-mobility ratios of the slower and faster diffusing species and Reynolds number on the flow dynamics is conducted. Our results demonstrate the presence of instability patterns due to double-diffusive effect in situations when a less viscous fluid displaces a highly viscous fluid. These instabilities are qualitatively different from those observed in planar channel. The intensity of these instabilities increases with increasing the values of diffusivity ratio. It is demonstrated that a highly viscous stenosis region is created near the entrance of the pipe due to double-diffusive effect, providing a favourable condition to start the instability. In addition to this, because of double-diffusive effect locally at some portion of the pipe, the less viscous fluid becomes the displacing fluid, which promotes the development of instability.
10 citations
TL;DR: In this article, the linear instability characteristics of a core-annular pipe flow of a Newtonian fluid and a Bingham fluid separated by a mixed region is investigated. And the authors investigate the effect of the yield stress of the annular fluid on the stability behavior.
Abstract: The linear instability characteristics of a core-annular pipe flow of a Newtonian fluid and a Bingham fluid separated by a mixed region is investigated. The main objective of this study is to investigate the effect of the yield stress of the annular fluid on the stability behaviour. The present linear stability analysis reveals that the corkscrew mode is the most dangerous mode for the parameters considered. The Bingham number seems to destabilise the flow via modifying the velocity profile. The mechanism of instability is found to be inviscid in nature. An energy budget analysis shows that the energy due to the gradient of viscosity perturbation in the radial direction, and the transfer of energy from the basic flow to the perturbation via the “Reynolds stress” term are responsible for the instability observed. The positive contributions of these terms towards instability increases with increasing the yield stress. The critical Reynolds number also decreases with increasing the Bingham number for the corkscrew mode, which indicates the destabilising influence of the yield stress.
8 citations
Cites methods from "Double-diffusive two-fluid flow in ..."
...A parallel flow approximation is employed in prescribing the thickness q to be uniform [35]....
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References
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Book•
16 Jun 1994
TL;DR: The direct simulation Monte Carlo (or DSMC) method has, in recent years, become widely used in engineering and scientific studies of gas flows that involve low densities or very small physical dimensions as mentioned in this paper.
Abstract: The direct simulation Monte Carlo (or DSMC) method has, in recent years, become widely used in engineering and scientific studies of gas flows that involve low densities or very small physical dimensions. This method is a direct physical simulation of the motion of representative molecules, rather than a numerical solution of the equations that provide a mathematical model of the flow. These computations are no longer expensive and the period since the 1976 publication of the original Molecular Gas Dynamics has seen enormous improvements in the molecular models, the procedures, and the implementation strategies for the DSMC method. The molecular theory of gas flows is developed from first principles and is extended to cover the new models and procedures. Note: The disk that originally came with this book is no longer available. However, the same information is available from the author's website (http://gab.com.au/)
5,311 citations
TL;DR: In this article, a review of recent developments in the hydro- dynamic stability theory of spatially developing flows pertaining to absolute/convective and local/global instability concepts is presented.
Abstract: The goal of this survey is to review recent developments in the hydro dynamic stability theory of spatially developing flows pertaining to absolute/convective and local/global instability concepts. We wish to dem onstrate how these notions can be used effectively to obtain a qualitative and quantitative description of the spatio-temporal dynamics of open shear flows, such as mixing layers, jets, wakes, boundary layers, plane Poiseuille flow, etc. In this review, we only consider open flows where fluid particles do not remain within the physical domain of interest but are advected through downstream flow boundaries. Thus, for the most part, flows in "boxes" (Rayleigh-Benard convection in finite-size cells, Taylor-Couette flow between concentric rotating cylinders, etc.) are not discussed. Further more, the implications of local/global and absolute/convective instability concepts for geophysical flows are only alluded to briefly. In many of the flows of interest here, the mean-velocity profile is non-
1,988 citations
TL;DR: In this paper, the authors present results from molecular dynamics simulations of newtonian liquids under shear which indicate that there exists a general nonlinear relationship between the amount of slip and the local shear rate at a solid surface.
Abstract: Modelling fluid flows past a surface is a general problem in science and engineering, and requires some assumption about the nature of the fluid motion (the boundary condition) at the solid interface. One of the simplest boundary conditions is the no-slip condition1,2, which dictates that a liquid element adjacent to the surface assumes the velocity of the surface. Although this condition has been remarkably successful in reproducing the characteristics of many types of flow, there exist situations in which it leads to singular or unrealistic behaviour—for example, the spreading of a liquid on a solid substrate3,4,5,6,7,8, corner flow9,10 and the extrusion of polymer melts from a capillary tube11,12,13. Numerous boundary conditions that allow for finite slip at the solid interface have been used to rectify these difficulties4,5,11,13,14. But these phenomenological models fail to provide a universal picture of the momentum transport that occurs at liquid/solid interfaces. Here we present results from molecular dynamics simulations of newtonian liquids under shear which indicate that there exists a general nonlinear relationship between the amount of slip and the local shear rate at a solid surface. The boundary condition is controlled by the extent to which the liquid ‘feels’ corrugations in the surface energy of the solid (owing in the present case to the atomic close-packing). Our generalized boundary condition allows us to relate the degree of slip to the underlying static properties and dynamic interactions of the walls and the fluid.
1,144 citations
TL;DR: In this article, the velocity profiles of water flowing through 30×300 μm channels were measured to within 450 nm of the micro-channel surface and the measured velocity profiles were consistent with solutions of Stokes' equation and the well accepted no-slip boundary condition.
Abstract: Micron-resolution particle image velocimetry is used to measure the velocity profiles of water flowing through 30×300 μm channels. The velocity profiles are measured to within 450 nm of the microchannel surface. When the surface is hydrophilic (uncoated glass), the measured velocity profiles are consistent with solutions of Stokes’ equation and the well-accepted no-slip boundary condition. However, when the microchannel surface is coated with a 2.3 nm thick monolayer of hydrophobic octadecyltrichlorosilane, an apparent velocity slip is measured just above the solid surface. This velocity is approximately 10% of the free-stream velocity and yields a slip length of approximately 1 μm. For this slip length, slip flow is negligible for length scales greater than 1 mm, but must be considered at the micro- and nano scales.
923 citations