@article{chattopadhyay_2024, title={Falling liquid film down a non-uniformly heated slippery inclined plane with odd viscosity effects}, volume={218}, ISSN={["1879-2189"]}, url={https://doi.org/10.1016/j.ijheatmasstransfer.2023.124807}, DOI={10.1016/j.ijheatmasstransfer.2023.124807}, abstractNote={The study examines the impact of the odd component of the Cauchy stress tensor, linked to the breakdown of time-reversal symmetry, on the linear instability analysis of a viscous fluid layer flowing down a non-uniformly heated and slippery inclined plane. Using a long-wave series expansion within an Orr-Sommerfeld-type boundary value problem, the critical Reynolds number is derived. The results of the linear long wavelength instability in the case of infinitesimal wavenumbers reveal that odd viscosity stabilizes the flow, while wall slip destabilizes it. The noteworthy finding is that thermocapillarity significantly enhances stability, provided gas temperature matches wall temperature.}, journal={INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER}, author={Chattopadhyay, Souradip}, year={2024}, month={Jan} }
 @article{desai_chattopadhyay_gaonkar_2024, title={Falling liquid films on a uniformly heated compliant substrate with broken time-reversal symmetry}, volume={125}, ISSN={["1095-8622"]}, url={https://doi.org/10.1016/j.jfluidstructs.2023.104064}, DOI={10.1016/j.jfluidstructs.2023.104064}, abstractNote={This study aims to analyze the dynamics of a thin Newtonian liquid film on a uniformly heated compliant substrate. We consider the violation of time-reversal symmetry in the liquid, resulting in an additional non-zero term in the liquid stress tensor. Using the long-wave expansion technique, we derive a set of coupled equations governing the film thickness and substrate deformation, accounting for inertia, surface tension, thermocapillarity, and odd viscosity. Through linear stability analysis and spatiotemporal simulations, we observe that the compliant substrate enhances instability, while wall heating exacerbates it. However, the introduction of odd viscosity effectively suppresses these instabilities, as confirmed by the agreement between simulation and theoretical predictions.}, journal={JOURNAL OF FLUIDS AND STRUCTURES}, author={Desai, Akshay S. and Chattopadhyay, Souradip and Gaonkar, Amar K.}, year={2024}, month={Mar} }
 @inbook{desai_chattopadhyay_gaonkar_mukhopadhyay_2024, title={Nonlinear Stability of a Thin Viscoelastic Film Down a Vertical Wall: A Numerical Study}, url={https://doi.org/10.1007/978-3-031-50631-4_6}, DOI={10.1007/978-3-031-50631-4_6}, abstractNote={We numerically investigate the dynamics of a thin viscoelastic liquid flowing down a vertical wall, based on the earlier study of Cheng et al. (J. Phys. D: Appl. Phys., vol. 33, 2000, 1674–1682). They discussed only the linear and weakly nonlinear stability analysis. However, nonlinear effects are more important when the amplitude of the disturbance is small but finite, and therefore, a nonlinear study is very much essential. Further, based on the linear and weakly nonlinear study of Zhao and Jian (Physica Scripta, vol. 96, 2021, 055214), we numerically present the effect of odd viscosity in this case. We also identify how energy transfers from the basic state to the disturbance in this case. Our numerical results support the analytical predictions of the linear and weakly nonlinear theories.}, author={Desai, Akshay S. and Chattopadhyay, Souradip and Gaonkar, Amar K. and Mukhopadhyay, Anandamoy}, year={2024} }
 @article{chattopadhyay_desai_gaonkar_mukhopadhyay_2023, title={Role of odd viscosity on falling films over compliant substrates}, volume={8}, ISSN={["2469-990X"]}, url={https://doi.org/10.1103/PhysRevFluids.8.064003}, DOI={10.1103/PhysRevFluids.8.064003}, abstractNote={We investigate the stability of a thin film flow on a compliant substrate with broken time-reversal symmetry. The broken time-reversal symmetry induces odd viscosity in the liquid. Using coupled equations encompassing the film and substrate, we ascertain that inclusion of a compliant substrate induces instability within the system. Nonetheless, the introduction of odd viscosity notably enhances its stability. Furthermore, under conditions of weak nonlinearity, the incorporation of odd viscosity can effectively mitigate the occurrence of chaotic behavior arising from compliant substrates. Numerical simulations confirm that odd viscosity has a substantial impact on substrate deflection.}, number={6}, journal={PHYSICAL REVIEW FLUIDS}, author={Chattopadhyay, Souradip and Desai, Akshay S. and Gaonkar, Amar K. and Mukhopadhyay, Anandamoy}, year={2023}, month={Jun} }
 @article{desai_chattopadhyay_gaonkar_mukhopadhyay_2023, title={Shear imposed falling film with odd viscosity effects}, volume={153}, ISSN={["1878-5638"]}, url={https://doi.org/10.1016/j.ijnonlinmec.2023.104422}, DOI={10.1016/j.ijnonlinmec.2023.104422}, abstractNote={This study examines the behavior of a thin liquid film flowing on an inclined plane subject to imposed shear stress. The liquid’s time-reversal symmetry is broken, and we consider the odd part of the viscosity to describe the Navier–Stokes equation. To investigate the interplay between the imposed shear and odd viscosity on the flow dynamics, we develop a weighted residual model (WRM). We determine the model’s critical Reynolds number (Rec) through linear stability analysis. Our findings indicate that uphill shear tends to stabilize the flow, while downhill shear enhances the instability, albeit reduced by the presence of odd viscosity. We also construct an Orr–Sommerfeld (OS) type eigenvalue problem for normal mode analysis and derive Rec. We discover that in the longwave regime, RecWRM=RecOS. Finally, our numerical simulations of the model align well with our linear stability analysis.}, journal={INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS}, author={Desai, Akshay S. and Chattopadhyay, Souradip and Gaonkar, Amar K. and Mukhopadhyay, Anandamoy}, year={2023}, month={Jul} }
 @article{desai_chattopadhyay_gaonkar_2023, title={Shear imposed falling liquid films on a slippery substrate with Marangoni effects: Effect of odd}, volume={156}, ISSN={["1878-5638"]}, url={https://doi.org/10.1016/j.ijnonlinmec.2023.104507}, DOI={10.1016/j.ijnonlinmec.2023.104507}, abstractNote={We investigate the behavior of a thin fluid with disrupted time-reversal symmetry on a uniformly heated inclined surface under external shear stress using modified Navier–Stokes equations, an energy conservation equation, and incorporating a Navier slip condition. Critical conditions for instability onset are determined by a linear stability analysis within the Orr–Sommerfeld framework. We derive a first-order Benney-type evolution equation to study long-wave instabilities. We find slippery substrate, imposed shear stress along the flow direction, and Marangoni number consistently destabilize the flow, while odd viscosity and imposed counter-flow shear stabilize it. A weakly nonlinear analysis using multiple scales reveal distinct zones of instability. Marangoni number, slip length, odd viscosity, and imposed shear direction significantly impact stability and instability regions. Numerical simulations of the free surface evolution equation of a flow system under consideration provide clear evidence of the contributions of thermocapillary, slip length, odd viscosity, and imposed shear direction. Furthermore, our analysis of linear and weakly nonlinear stability, as well as our numerical simulations, exhibit remarkable consistency.}, journal={INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS}, author={Desai, Akshay S. and Chattopadhyay, Souradip and Gaonkar, Amar K.}, year={2023}, month={Nov} }
 @article{desai_chattopadhyay_gaonkar_barua_mukhopadhyay_2023, title={Suppression of Wave Instability in a Liquid Film Flow Down a Non-Uniformly Heated Slippery Inclined Plane Using Odd Viscosity}, volume={145}, ISSN={["1528-901X"]}, url={http://dx.doi.org/10.1115/1.4062471}, DOI={10.1115/1.4062471}, abstractNote={Abstract}, number={9}, journal={JOURNAL OF FLUIDS ENGINEERING-TRANSACTIONS OF THE ASME}, publisher={ASME International}, author={Desai, Akshay S. and Chattopadhyay, Souradip and Gaonkar, Amar K. and Barua, Amlan K. and Mukhopadhyay, Anandamoy}, year={2023}, month={Sep} }
 @article{chattopadhyay_ji_2023, title={Thermocapillary thin film flows on a slippery substrate with odd viscosity effects}, volume={455}, ISSN={["1872-8022"]}, url={http://dx.doi.org/10.1016/j.physd.2023.133883}, DOI={10.1016/j.physd.2023.133883}, abstractNote={This study investigates the behavior of a thin liquid with odd viscosity effects as it flows down a uniformly heated, slippery inclined plane, where the liquid’s time-reversal symmetry is broken. The breaking of symmetry results in interesting effects, as the antisymmetric part of the fluid stress tensor does not vanish. Two models, the Benney-type equation model (BEM) and the weighted residual model (WRM), are constructed to account for the combined effects of slip length, thermocapillarity, and odd viscosity. A detailed stability analysis determines both models’ critical Reynolds numbers Rec. For small slip lengths, the first-order WRM is better at capturing the instability threshold than the first-order BEM. While both models account for the effects of odd viscosity and thermocapillarity, only the Rec of WRM incorporates the wall slip effects. Another significant finding is that the BEM effectively avoids the issue of finite-time blow-up by incorporating odd viscosity. Additionally, employing a weakly nonlinear stability analysis with multiple scales uncovers four flow regions in BEM: supercritical stable, subcritical unstable, unconditional stable, and explosive zones. Two separate bifurcation scenarios emerge for various wave numbers: supercritical within a specific range and subcritical for larger wave numbers. The presence of odd viscosity alleviates the reduction of the unconditional stable zone and the increase in the explosive zone, which are caused by the combined influence of slip and thermal effects. Numerical investigation of traveling wave solutions of WRM shows that wave height is promoted by slip and thermal effects but reduced with increasing odd viscosity coefficient. Further numerical simulations of WRM on a larger domain demonstrate the stabilizing effects of odd viscosity and its interaction with destabilizing slip and thermocapillary effects.}, journal={Physica D: Nonlinear Phenomena}, publisher={Elsevier BV}, author={Chattopadhyay, S. and Ji, H.}, year={2023}, month={Dec}, pages={133883} }
 @article{chattopadhyay_2023, title={Thin liquid films on a slippery vertical cylinder in presence of chemical reaction}, volume={282}, ISSN={["1873-4405"]}, url={https://doi.org/10.1016/j.ces.2023.119211}, DOI={10.1016/j.ces.2023.119211}, abstractNote={In industrial settings, chemical reactions often affect thin liquid films that flow down vertical cylinders. However, the effect of non-isothermal reactions on the dynamics of these films is not fully comprehended. To address this issue, this study investigates the behavior and stability of thin film flows on uniformly heated vertical cylinders that exhibit wall slippage when subjected to a pseudo-zero-order exothermic or endothermic chemical reaction. A reduced model is developed for thin liquid films flowing down vertical cylinders in the presence of exothermic or endothermic chemical reactions, assuming the film thickness is much smaller than the cylinder radius. The heat from the reaction and/or wall heating initiates a thermocapillary Marangoni effect, which is further enhanced by wall slippage, directly affecting the dynamics of the free surface. Linear and weakly nonlinear stability analyses show that wall slip amplifies the instability, while exothermic reactions stabilize the system and endothermic reactions destabilize it. It is also found that chemical reactions significantly influence the supercritical stable, subcritical unstable, unconditional stable, and explosive zones of the thin film. A direct numerical simulation confirms the results of linear and weakly nonlinear analyses.}, journal={CHEMICAL ENGINEERING SCIENCE}, author={Chattopadhyay, Souradip}, year={2023}, month={Dec} }
 @article{chattopadhyay_desai_2022, title={Dynamics and stability of weakly viscoelastic film flowing down a uniformly heated slippery incline}, volume={7}, url={https://doi.org/10.1103/PhysRevFluids.7.064007}, DOI={10.1103/PhysRevFluids.7.064007}, abstractNote={A theoretical model is presented to investigate the stability of a thin viscoelastic fluid draining down a uniformly heated slippery inclined plane. The instability is enhanced as the slippery length and viscoelasticity increase. When the wall is heated, the instability is reinforced.}, number={6}, journal={Physical Review Fluids}, author={Chattopadhyay, Souradip and Desai, Akshay S.}, year={2022}, month={Jun} }
 @article{chattopadhyay_subedar_gaonkar_barua_mukhopadhyay_2022, title={Effect of odd-viscosity on the dynamics and stability of a thin liquid film flowing down on a vertical moving plate}, volume={140}, url={https://doi.org/10.1016/j.ijnonlinmec.2022.103905}, DOI={10.1016/j.ijnonlinmec.2022.103905}, abstractNote={In this study, we focus on the problem of hydrodynamic instability of a thin, viscous, Newtonian liquid film with broken time-reversal-symmetry flowing down along the surface of a vertical moving plate. The presence of odd viscosity gives rise to new terms in the pressure gradient of the flow. Utilizing the classical long-wave perturbation method, we obtain the analytical solutions as well as derive the nonlinear evolution equation of Benney-type in terms of film thickness h(x,t) which is significantly modified due to the presence of odd viscosity in the liquid. We solve the linear model by using the normal mode approach and for three different conditions, namely, the quiescent, up-moving and down-moving plate velocity. The linear study shows that the effect of the down-moving motion of the vertical plate is to enhance the stability of the film flow whereas the up-moving motion of the vertical plate tends to reduce it. Further, the study shows that odd viscosity always has a stabilizing effect on the flow field. In addition, the Orr–Sommerfeld equation is also derived and solved analytically to obtain the critical Reynolds number. Finally, we show the numerical solution of the evolution equation in a periodic domain which clearly demonstrates the role of odd-viscosity on the dynamics of the plate motions of thin film flows coating in isothermal environments. Our study clearly shows how odd viscosity influences the stability of the flow.}, journal={International Journal of Non-Linear Mechanics}, author={Chattopadhyay, Souradip and Subedar, Gowri Y. and Gaonkar, Amar K. and Barua, Amlan K. and Mukhopadhyay, Anandamoy}, year={2022}, month={Apr} }
 @inbook{mukhopadhyay_chattopadhyay_barua_2022, title={Effects of Strong Viscosity with Variable Fluid Properties on Falling Film Instability}, url={http://dx.doi.org/10.1007/978-3-030-81162-4_7}, DOI={10.1007/978-3-030-81162-4_7}, abstractNote={The stability and dynamics of a gravity-driven, viscous, incompressible, Newtonian thin liquid film draining down a uniformly heated inclined plane are examined. We assume the thermophysical properties of the film such as density, surface tension, and thermal diffusivity vary linearly, whereas the viscosity varies exponentially with the small variation of temperature. Employing the classical long-wave expansion technique, a nonlinear evolution equation of Benney type, is derived in terms of film thickness h(x, t). The linear stability analysis is performed using the normal mode approach and a critical Reynolds number is obtained. The linear study reveals that the flow is more stable when the variation of viscosity is exponential as compared to a linear variation. The variation of density also affects the linear stability criteria. The method of multiple scales is used to investigate the weakly nonlinear stability of the flow, and we observe that for the variation of Kμ, Kρ, Kσ both the supercritical stable and subcritical unstable zones are possible together with the unconditional stable and explosive zones. Finally, we perform the numerical simulation in a periodic domain and confirm the results obtained by linear and weakly nonlinear studies.}, booktitle={NODYCON Conference Proceedings Series}, publisher={Springer International Publishing}, author={Mukhopadhyay, Anandamoy and Chattopadhyay, Souradip and Barua, Amlan K.}, year={2022}, pages={75–85} }
 @article{chattopadhyay_boragunde_gaonkar_barua_mukhopadhyay_2022, title={Falling liquid films on a slippery substrate with variable fluid properties}, volume={147}, url={https://doi.org/10.1016/j.ijnonlinmec.2022.104200}, DOI={10.1016/j.ijnonlinmec.2022.104200}, abstractNote={We investigate the stability of a gravity-driven, thin, Newtonian liquid flowing on a uniformly heated slippery inclined plane. We construct a mathematical model of the flow that comprises the Navier–Stokes equation coupled with the equation of energy. While the rest of the boundary conditions are standard for thin-film problems, we apply a Navier slip boundary condition at the solid–liquid interface. We assume that the fluid thermophysical properties — density, dynamical viscosity, surface tension, and thermal diffusivity vary linearly with temperature as long as the change in temperature is small. In the analysis part, we follow the standard long-wave theory and construct a nonlinear evolution equation for the film thickness. This is followed by a linear and weakly nonlinear stability analysis. The linear analysis allows us to compute the critical Reynolds number of our problem and from this study, we conclude that the slippery substrate destabilizes the film flow. The weakly nonlinear stability analysis finds a finer description of various stable/unstable zones. Finally, we perform a numerical simulation of the evolution equation in a periodic domain using spectral methods. Our numerical results support the analytical predictions of the instability threshold using the linear and weakly nonlinear theories. The influence of the small Biot number is also investigated in presence of the slip length together with the variable fluid properties.}, journal={International Journal of Non-Linear Mechanics}, author={Chattopadhyay, Souradip and Boragunde, Pavanvasudev and Gaonkar, Amar K. and Barua, Amlan K. and Mukhopadhyay, Anandamoy}, year={2022}, month={Dec} }
 @article{chattopadhyay_mukhopadhyay_2022, title={Weakly viscoelastic film flowing down a rotating inclined plane}, volume={34}, url={https://doi.org/10.1063/5.0077366}, DOI={10.1063/5.0077366}, abstractNote={We investigate the nonlinear stability of a thin viscoelastic film flowing under the effects of gravity and Coriolis and centrifugal forces. We assume that the viscoelastic liquid satisfies the rheological property of Walters' liquid B″. We may consider this case as a viscoelastic flow down a rotating cone and far from the apex. Using the classical long wave expansion technique, we derive a nonlinear evolution equation describing the shape of the liquid interface as a function of space and time and also derive its stability characteristics. We solve the physical system in a two-step procedure. In the first step, we use the normal mode method to characterize the linear nature. The linear study reveals that the linear growth rate is invariant with the Coriolis effect but is significantly affected by the viscoelastic parameter Γ as well as the Taylor number Ta. It is found that both Γ and Ta destabilize the flow. In the second step, we solve an elaborated nonlinear film flow model based on the method of multiple scales and demarcate different instability zones. The weakly nonlinear study shows that with an increase in Γ and Ta, the supercritical stable region and the explosion area increase whereas the unconditional stable and the subcritical unstable region shrink. Finally, on validating our analytical predictions by performing a direct numerical simulation, a good agreement between the results of the linear stability analysis, weakly nonlinear stability analysis, and the numerical simulations is found.}, number={1}, journal={Physics of Fluids}, author={Chattopadhyay, Souradip and Mukhopadhyay, Anandamoy}, year={2022}, month={Jan} }
 @article{chattopadhyay_2021, title={Influence of the odd viscosity on a falling film down a slippery inclined plane}, volume={33}, url={https://doi.org/10.1063/5.0051183}, DOI={10.1063/5.0051183}, abstractNote={The stability of a thin viscous Newtonian fluid with broken time-reversal-symmetry draining down a slippery inclined plane is examined. The presence of the odd part of the Cauchy stress tensor with an odd viscosity coefficient brings new characteristics in fluid flow as it gives rise to new terms in the pressure gradient of the flow. By odd viscosity, it is meant that apart from the well-known coefficient of shear viscosity, a classical liquid with broken time-reversal symmetry is endowed with a second viscosity coefficient. The model implements a Navier slip condition at the solid–liquid interface with the slip length being the parameter that measures the deviation from the no-slip condition. The classical long-wave expansion technique is performed and a nonlinear evolution equation of Benney-type is derived in terms of film thickness h(x, t), which is significantly modified due to the presence of odd viscosity in the liquid. The parameters governing the film flow system and the slippery substrate strongly influence the waveforms and their amplitudes and hence the stability of the fluid. The linear stability analysis is performed using the normal mode approach and a critical Reynolds number is obtained. The results of the linear stability analysis reveal that larger odd viscosity leads to the higher critical Reynolds number while the higher slip length makes the critical Reynolds number lower. In other words, odd viscosity has a stabilizing effect while the slip length promotes instability. Based on the method of multiple scales, a weakly nonlinear stability analysis is carried out, which shows that there is a range of wave numbers with a supercritical bifurcation and a range of larger wave numbers with a subcritical bifurcation. Different instability zones are also demarcated. The weakly nonlinear study shows that with an increase in the odd viscosity, the supercritical stable region and the explosion area shrink, whereas the unconditional stable and the subcritical unstable regions increase. It has also been shown that the spatial uniform solution corresponding to the sideband disturbance may be stable in the unstable region. The spatiotemporal evolution of the model has been analyzed numerically by employing the Crank–Nicolson method in a periodic domain for different values of the odd viscosity and slip length. The nonlinear simulations are found to be in good agreement with the linear and weakly nonlinear stability analysis.}, number={6}, journal={Physics of Fluids}, publisher={AIP Publishing}, author={Chattopadhyay, Souradip}, year={2021}, month={Jun}, pages={062106} }
 @article{chattopadhyay_2021, title={Odd-viscosity-induced instability of a thin film with variable density}, volume={33}, url={https://doi.org/10.1063/5.0057068}, DOI={10.1063/5.0057068}, abstractNote={The stability of a two-dimensional gravity-driven thin viscous Newtonian fluid with broken time-reversal-symmetry draining down a uniformly heated inclined plane is discussed. The presence of the odd part of the Cauchy stress tensor with an odd viscosity coefficient brings new characteristics in fluid flow. A theoretical model is implemented, which captures the dependence of the surface tension on temperature, and the model also allows for variation in the density of the liquid with a thermal difference. The coupled effect of odd viscosity, variable density, and surface tension has been investigated both analytically and numerically. A nonlinear evolution equation of the free surface is derived by the method of systematic asymptotic expansion. A linear stability analysis is carried out, which yields the critical conditions for the onset of instability in long-wave perturbations. New interesting results illustrating how the critical Reynolds number depends on the odd viscosity as well as other various dimensionless parameters have been obtained. In addition, a weakly nonlinear stability analysis is performed based on the method of multiple scales from which a complex Ginzburg–Landau equation is obtained. It is observed that the film not only has supercritical stable and subcritical unstable zones, but also unconditional stable and explosive zones. It has been also shown that the spatial uniform solution corresponding to the sideband disturbance may be stable in the unstable region. Employing the Crank–Nicolson method in a periodic domain, the spatiotemporal evolution of the model has been analyzed numerically for different values of the odd viscosity as well as other flow parameters. Nonlinear simulations are found to be in good agreement with the linear and weakly nonlinear stability analysis. The results are conducive to the further development of related experiments.}, number={8}, journal={Physics of Fluids}, author={Chattopadhyay, Souradip}, year={2021}, month={Aug} }
 @article{chattopadhyay_2021, title={Thermocapillary instability in the presence of uniform normal electric field: effect of odd viscosity}, volume={131}, url={https://doi.org/10.1007/s10665-021-10178-4}, DOI={10.1007/s10665-021-10178-4}, number={1}, journal={Journal of Engineering Mathematics}, author={Chattopadhyay, Souradip}, year={2021}, month={Dec} }
 @article{chattopadhyay_mukhopadhyay_barua_gaonkar_2021, title={Thermocapillary instability on a film falling down a non-uniformly heated slippery incline}, volume={133}, url={https://doi.org/10.1016/j.ijnonlinmec.2021.103718}, DOI={10.1016/j.ijnonlinmec.2021.103718}, abstractNote={A gravity-driven, thin, incompressible liquid film flow on a non-uniformly heated, slippery inclined plane is considered within the framework of the long-wave approximation method. A mathematical model incorporating variation in surface tension with temperature has been formulated by coupling the Navier–Stokes equation, governing the flow, with the equation of energy. For the slippery substrate, the Navier slip boundary condition is used at the solid–liquid interface. An evolution equation is formed in terms of the free surface, which includes the effects of inertia, thermocapillary as well as slip length. Using the normal mode approach, linear stability analysis is carried out and a critical Reynolds number is obtained, which reflects its dependence on the Marangoni number Mn as well as slip length δ. This depicts that δ and Mn both have the destabilization effect on the flow field. The linear study also reveals that the inertia force has a negligible effect compare to the thermocapillary or slip. In addition, the study highlights a critical Marangoni number at which the instability sets in when the thermocapillary stress attains a critical value. The method of multiple scales is used to investigate the weakly nonlinear stability analysis of the flow. The study interprets that the variation of Mn and δ have substantial effects on different stable/unstable zones. It also shows that within a considered parametric domain, the unconditional stable zone completely vanishes for any value of Mn, when the slip length δ attains a critical value. The study also divulges that in the subcritical unstable (supercritical stable) zone the threshold amplitude (ζa) decreases (increases) with the increment of Mn and δ. Further, we discussed the spatial uniform solution of the complex Ginzburg–Landau equation for sideband disturbances. Employing the Crank–Nicolson method, the nonlinear evolution equation of the free surface is solved numerically in a periodic domain, considering the sinusoidal initial perturbation of small amplitude. The nonlinear simulations are found to be in good agreement with the linear and weakly nonlinear stability analysis. The evolution of the maximum hmax and minimum hmin thickness amplifies, for small change of Mn and δ. Further, it shows that the influence of the thermocapillary force amplifies the destabilizing nature of δ. The traveling wave solution confirms the existence of a fixed point for the considered parametric domain, chosen from the experimental data. Finally, the Hopf bifurcation of the fixed point exhibits that the nonlinear wave speed at the transcritical point increases as δ increases but decreases as Mn increases. The noteworthy result which arises from the study is that a transcritical Hopf bifurcation exists if the slip length δ>max16Mn−13,12Mn−23−Mn.}, journal={International Journal of Non-Linear Mechanics}, author={Chattopadhyay, Souradip and Mukhopadhyay, Anandamoy and Barua, Amlan K. and Gaonkar, Amar K.}, year={2021}, month={Jul} }
 @article{chattopadhyay_desai_gaonkar_barua_mukhopadhyay_2021, title={Weakly viscoelastic film on a slippery slope}, volume={33}, url={https://doi.org/10.1063/5.0070495}, DOI={10.1063/5.0070495}, abstractNote={We study the stability of weakly viscoelastic film (Walter's B″) flowing down under gravity along a slippery inclined plane. The focus is to investigate the interaction of the bottom slip with the viscoelastic parameter as well as the influence of the other flow parameters on the stability of the flow. For the slippery substrate, we use the Navier-slip boundary condition at the solid–liquid interface. The dimensionless slip length β is first assumed to be small and its order is considered same as the order of the film aspect ratio ϵ=H/L, where H is the mean film thickness and L is a typical wavelength. To discuss the coupled effect of slip length β and viscoelastic parameter γ, we have used the classical Benney equation model (BEM) as well as the weighted residual method (WRM). For linear stability, the normal mode analysis is carried out to capture the instability threshold. The critical Reynolds numbers (Rec) are obtained for BEM and WRM separately for the system. We found that the first-order WRM is a better choice to capture the instability threshold in comparison with a first-order BEM when β is small. Another noteworthy result we obtain is that, in the absence of β, WRM and BEM yield the same expression for the critical Reynolds number. Further, we have extended the study for moderate values of β, that is, β of order unity and it is found that both BEM and WRM are able to capture the effects of β and γ. We derive the Orr–Sommerfeld (OS) type eigenvalue problem and an asymptotic analysis is performed for small perturbation wavenumbers, which gives an expression for the critical Reynolds number for the instability of very long perturbations. The critical Reynolds number obtained by the OS eigenvalue problem exactly matches with that obtained by BEM. Finally, we validate our analytical predictions by performing a direct numerical simulation of the WRM and good agreement between the results of the linear stability analysis, weighted residual model, and the numerical simulations is found.}, number={11}, journal={Physics of Fluids}, author={Chattopadhyay, Souradip and Desai, Akshay S. and Gaonkar, Amar K. and Barua, Amlan K. and Mukhopadhyay, Anandamoy}, year={2021}, month={Nov} }
 @article{mukhopadhyay_chattopadhyay_barua_2020, title={Stability of thin film flowing down the outer surface of a rotating non-uniformly heated vertical cylinder}, volume={100}, url={https://doi.org/10.1007/s11071-020-05558-x}, DOI={10.1007/s11071-020-05558-x}, number={2}, journal={Nonlinear Dynamics}, publisher={Springer Science and Business Media LLC}, author={Mukhopadhyay, Anandamoy and Chattopadhyay, Souradip and Barua, Amlan K.}, year={2020}, month={Apr}, pages={1143–1172} }
 @article{a review on hydrodynamical stability of thin film flowing along an inclined plane_2019, url={http://dx.doi.org/10.33187/jmsm.458359}, DOI={10.33187/jmsm.458359}, abstractNote={The dynamics and stability of thin liquid films have fascinated scientists over many decades. 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, lava flows, coating flows, tear-film rupture, dynamics of continental ice sheets and surfactant replacement therapy. Study of falling film instability has its wide applications in the practical field of industry and engineering. Practical applications in industrial processing motivate the recent research to investigate the factors which may affect the formation of waves on the surface of the coating layers and/or to determine the ways to overcome or to minimize the unwanted factors within the desired limit of tolerance. The dynamics of a liquid film flowing down a plane under the action of gravity is a problem which appears in many technological and natural systems, namely large scale geophysical environments such as lava flows or spillways, daily life scenarios such as water flowing down a window pane or a slippery road on a rainy day, chemical engineering processes such as evaporators, heat exchanges and falling film reactors or surface coating. The aim of this paper is to throw light on the studies conducted on hydrodynamical stability.}, journal={Journal of Mathematical Sciences and Modelling}, year={2019}, month={Aug} }
 @article{mukhopadhyay_chattopadhyay_barua_2019, title={Stability of thin liquid film flowing down a rotating horizontal or inclined plane by momentum-integral method}, volume={75}, url={https://doi.org/10.1016/j.euromechflu.2018.12.002}, DOI={10.1016/j.euromechflu.2018.12.002}, abstractNote={In this study we investigate the linear as well as the weakly nonlinear stability of a thin liquid film flowing down a rotating horizontal or inclined plane. The analysis is carried out using the momentum-integral method, which is valid for small as well as large Reynolds number (Re). A single free surface equation is obtained considering self-similar velocity profiles for specific ranges of flow parameters. Considering sinusoidal perturbation of the free surface and taking into consideration the linear terms from the free surface equation we obtain the linear phase speed along x-direction cx and the critical wave number kc. It is found that the linear phase speed decreases with the increasing value of the parameter G which is directly proportional to the square root of the Coriolis force, the angle of propagation of the wave ϕ and the angle of inclination (θ) of the inclined plane but it increases with the increasing value of Taylor number (Ta). The study also points out the variation of the region of instability with the variation of G,ϕ,θ,Re and Ta. It is found that as G increases, the region of instability decreases, which reflects the stabilizing role of Coriolis force. It is observed that as the angle of propagation of the wave ϕ increases from 0 to 0.6725, the unstable region decreases but increases if ϕ varies from 0.6725 to 2.2, thereafter again decreases up to ϕ=π. Also it is shown that for ϕ = 0, the region of instability decreases as θ increases but the situation becomes reverse if ϕ=π4. The Taylor number Ta plays a double role. For ϕ = 0, π6, the linear unstable zone increases as Ta increases but for ϕ=π4, the situation reverses. Also it is found that the region of instability always decreases for the variation of small as well as moderate Reynolds number, up to a critical value of the propagation angle ϕc. But for small values of Re when ϕ>ϕc, the unstable region first decreases up to a critical value of Re, then again increases up to another critical value of Re and ultimately decreases for moderate values of Re. Weakly nonlinear stability analysis reveals the dependence of J2 in the Landau’s equation and imaginary part of the complex frequency ωi on the variation of the Coriolis and centrifugal forces. Both the forces ensure the existence of supercritical and unconditional stable zones. The nonlinear study confirms the stabilizing role of the Coriolis force and the destabilizing role of the centrifugal force as obtained in the linear stability analysis. We also obtained that in the supercritical stable zone the threshold amplitude decreases (increases) as the Coriolis force (centrifugal force) increases. Finally we find that the nonlinear phase speed decreases with the increase of the Coriolis force but increases with the small increment of the centrifugal force.}, journal={European Journal of Mechanics - B/Fluids}, publisher={Elsevier BV}, author={Mukhopadhyay, Anandamoy and Chattopadhyay, Souradip and Barua, Amlan K.}, year={2019}, month={May}, pages={58–70} }
 @article{mukhopadhyay_chattopadhyay_2018, title={Long wave instability of thin film flowing down an inclined plane with linear variation of thermophysical properties for very small Biot number}, volume={100}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85041484681&partnerID=MN8TOARS}, DOI={10.1016/j.ijnonlinmec.2018.01.005}, abstractNote={We investigated interfacial instability of a thin liquid film flowing down an inclined plane, considering the linear variation of fluid properties such as density, dynamical viscosity, surface tension and thermal diffusivity, for the small variation of temperature. Using long wave expansion method and considering order analysis specially for very small Biot number (Bi) we obtained a single surface equation in terms of the free surface h(x,t). Considering sinusoidal perturbation method we carried out linear stability analysis and obtained the critical Reynolds number (Rec) and linear phase speed (cr), both of which depend on Kμ,Kρ but independent of Kσ,Kκ. Using the method of multiple scales, weakly nonlinear stability analysis is carried out. We demarcated subcritical, supercritical, unconditional and explosive zones and their variations for the variation of Kμ,Kρ and Kσ. Also we discussed the variations of threshold amplitude in the subcritical as well as in the supercritical zones for the variation of Kμ,Kρ and Kσ. Finally we discussed the variation of nonlinear wave speed Ncr for the variation of Kμ,Kρ and Kσ.}, journal={International Journal of Non-Linear Mechanics}, author={Mukhopadhyay, A. and Chattopadhyay, S.}, year={2018}, pages={20–29} }