arXiv subjects

Sutapa Mandal

Publications and source records attributed to Sutapa Mandal.

5 recordsLinked to original sources

arXiv2026

Electrophoretic motion of a liquid droplet with Brinkman-screened internal hydrodynamics

We develop a theory for the electrophoresis of a spherical porous liquid droplet with prescribed uniform surface charge. The exterior electrokinetics is governed by the Poisson-Nernst-Planck-Stokes equations, while the internal liquid motion is described by the Brinkman-Debye-Bueche equation. A regular perturbation expansion in the applied electric field reduces the governing equations to coupled radial ordinary differential equations. In the Debye-Hückel regime, we derive a closed-form mobility expression valid for arbitrary Debye layer thickness. The analysis shows that the porous interior modifies clean-droplet electrophoresis through a single Brinkman-screened hydrodynamic resistance, yielding a continuous transition between clean-droplet and rigid-particle limits. Numerical solutions beyond the low-potential regime reveal a non-universal role of permeability: increasing the Darcy number can either suppress or enhance the mobility. This reversal is determined by the sign of the interfacial-velocity mode, which is governed by the competition between tangential Maxwell traction and hydrodynamic shear generated by electric-double-layer distortion. Dielectric polarization, surface charge and double-layer thickness can reverse the internal circulation, while the Darcy number controls how strongly this circulation is transmitted through the porous interior. This permeability sensitivity is especially pronounced for highly polarizable droplets in the thin-double-layer regime. The theory provides a basis for tuning electrokinetic transport of soft porous droplets in microfluidic and biomedical technologies.

physics.flu-dyn↗

arXiv2025

Effect of oblique horizontal magnetic field on convection rolls

We investigate the effect of external horizontal magnetic field applied on the convection rolls obliquely (at an angle $ϕ$ with the $x$-axis) in electrically conducting low Prandtl number fluids under the paradigm of the Rayleigh-Bénard convection by performing three-dimensional direct numerical simulations. The control parameters, namely, the Chandrasekhar number ($\mathrm{Q}$) and the reduced Rayleigh number $r$ (ratio of Rayleigh number to critical Rayleigh number), are varied in the ranges $0 \leq \mathrm{Q} \leq 1000$ and $1 \leq r \leq 20$ for the Prandtl numbers $\mathrm{Pr} = 0.1$ and $0.2$ by considering three horizontal aspect ratios ($Γ$): $\frac{1}{2}$, $1$ and $2$. In the absence of the magnetic field, the convection starts in the form of steady rolls including the one parallel to the $x$-axis. As the oblique horizontal magnetic field is switched on at an angle $ϕ\in (0^\circ, ~90^\circ]$ with the $x$-axis, it is observed that the Lorentz force generated by the component of the magnetic field transverse to the axis of the convection rolls inhibits convection in the form of steady rolls. Thus, with the application of the magnetic field, the convection is suppressed and restarts for a higher Rayleigh number in the form of steady convection rolls. The rolls can either be oriented along the $x$-axis (steady parallel rolls, SPR) or oriented at an angle $45^\circ$ (steady oblique rolls, SOR$^+$) with the $x$-axis depending on the choices of the parameters. A rich bifurcation structure with standing and traveling patterns emerges at higher $r$. The oscillatory instability of steady rolls scales as $ \mathrm{Q}^α$ with distinct exponents for weak and strong magnetic fields. Additionally, heat transfer decreases with increasing $ ϕ$ for given $ \mathrm{Q} $ and $ \mathrm{Pr} $.

physics.flu-dyn↗

arXiv2024

Transitions near the onset of stationary rotating magnetoconvection: role of magnetic Prandtl number

We investigate the instabilities and associated bifurcation structure near the onset of rotating magnetoconvection of low Prandtl number fluids by performing three dimensional direct numerical simulations. Previous studies considered zero magnetic Prandtl number ($\mathrm{Pm}$) limit for the investigation of bifurcation structure near the onset of convection. Here we numerically investigate the effect of $\mathrm{Pm}$ on the bifurcation structure. The classical Rayleigh-Bénard convection setup in the presence of horizontal magnetic field and rotation about the vertical axis are considered for the study. The control parameters, including the Taylor number ($\mathrm{Ta}$), Chandrasekhar number ($\mathrm{Q}$), reduced Rayleigh number ($\mathrm{r}$), and magnetic Prandtl number ($\mathrm{Pm}$) are varied in the ranges $0 < \mathrm{Ta}\leq 500$, $0 < \mathrm{Q}\leq 1000$, $0.8\leq \mathrm{r} \leq 2$ and $0 < \mathrm{Pm} < 1$ by considering Prandtl numbers $\mathrm{Pr}= 0.025$ and $0.1$. The investigation reveals the presence of supercritical, subcritical and hybrid transitions to convection. These transitions leads to infinitesimal and finite amplitude fluid patterns at the onset of convection. The finite amplitude solutions can be both stationary and time dependent. The bifurcation structures associated with these flow patterns at the onset are studied in detail. For very small $\mathrm{Pm}$, the bifurcation structure is found to be qualitatively similar to the ones observed in the $\mathrm{Pm}\rightarrow 0$ limit. However, as $\mathrm{Pm}$ is increased, several new solutions appear at the onset and the resulting bifurcation structures are greatly modified.

physics.flu-dyn↗

arXiv2024

One dimensional models for supercritical and subcritical transitions in rotating convection

Numerous study on natural and man made systems including rotating convection report the phenomena of supercritical and subcritical transitions from one state to another with the variation of relevant control parameters. However, the complexity of the rotating convection system even under the idealized Rayleigh-Bénard geometry, hindered the simplest possible description of these transitions to convection. Here we present an one dimensional description of the stationary subcritical and supercritical transitions to rotating Rayleigh-Bénard convection both for rigid and free-slip boundary conditions. The analysis of the one dimensional models and performance of three dimensional direct numerical simulations of the system show qualitatively similar results in a wide region of the parameter space. A brief discussion on time dependent convection of overstable origin is also presented.

physics.flu-dyn↗

arXiv2023

Effect of horizontal magnetic field on Küppers-Lortz instability

We investigate the effect of an external horizontal magnetic field on the Küppers-Lortz instability (KLI) in rotating Rayleigh-Bénard convection of Boussinesq fluids using weakly nonlinear theory along with linear theory. By KLI, we mean the instability where the two-dimensional roll solutions of the system occurring at the onset of convection becomes unstable against the perturbations by rolls oriented at different angle with the previous one as the rotation rate exceeds a critical value. The governing parameters, namely, the Prandtl number ($\mathrm{Pr}$), Taylor number ($\mathrm{Ta}$) and Chandrasekhar number ($\mathrm{Q}$) are varied in the ranges $0.8 \leq \mathrm{Pr} < \infty$, $0 < \mathrm{Ta} \leq 10^4$ and $0 \leq \mathrm{Q} \leq 10^4$ respectively by considering the vanishingly small magnetic Prandtl number limit. In the $\mathrm{Pr}\rightarrow \infty$ limit, magnetic field is found to inhibit the KLI by enhancing the critical Taylor number ($\mathrm{Ta}_c$) for its onset. On the other hand, for finite Prandtl number fluids, KLI is favored for lower $\mathrm{Q}$, and it is inhibited for higher $\mathrm{Q}$. Interestingly, in the finite Prandtl number range both KLI and small angle instability are manifested depending on the Prandtl number. No small angle instability is observed for $\mathrm{Pr} \geq 50$ and the rotation induced KLI is inhibited predominantly by the magnetic field. While, for $\mathrm{Pr} < 50$, along with the Küppers-Lortz instability, small angle instability is also observed. However, in this case, KLI is favored for lower $\mathrm{Q}$, while it is inhibited for higher $\mathrm{Q}$.

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