arXiv subjects

Navaneeth K. Marath

Publications and source records attributed to Navaneeth K. Marath.

4 recordsLinked to original sources

arXiv2025

Dynamics of an internally actuated weakly elastic sphere in a general quadratic flow

Internally actuated elastic particles are widely used in biomedical applications. It is imperative to understand the dynamics of such particles in pressure-driven microfluidic devices to manipulate their motion. We analytically examine the dynamics of an internally actuated elastic particle translating in a general unbounded quadratic flow in the inertialess limit. We consider the particle as a compressible weakly elastic sphere, and its motion is controlled by applying an external point force and a point torque at the centre of its undeformed shape. The fluid and the particle are modelled using the Stokes and the Navier elasticity equations, respectively. We use the domain perturbation method to capture the particle deformation. The point force and the point torque are obtained until \textit{O}($\alpha^2$), assuming $\alpha\ll 1$. Here, $\alpha$ is the measure of the particle elastic strain induced due to the fluid viscous stress. We present the results for the particle motion in a general unbounded quadratic flow. The results are simplified further for the motion along the centreline in the quadratic component of three Poiseuille flows: 1) elliptical Poiseuille, 2) plane Poiseuille, and 3) Hagen-Poiseuille flows. In the general quadratic flow, the point force at \textit{O}($\alpha$) is aligned with the particle velocity, while the force at \textit{O}($\alpha^2$) acts at an angle to the velocity. Furthermore, the torque is non-zero due to elastic effects at \textit{O}($\alpha$) and \textit{O}($\alpha^2$). For all the three Poiseuille flows, the point force until \textit{O}($\alpha^2$) is aligned with the particle velocity, while the torque comes as zero.

physics.flu-dyn↗

arXiv2021

The rotation of a sedimenting anisotropic particle in a linearly stratified ambient

We derive the torque on a spheroid of an arbitrary aspect ratio $κ$ sedimenting in a linearly stratified ambient. The analysis demarcates regions in parameter space corresponding to broadside-on and edgewise (longside-on) settling in the limit $Re, Ri_v \ll 1$, where $Re = ρ_0UL/μ$ and $Ri_v =γL^3g/μU$, the Reynolds and viscous Richardson numbers, respectively, are dimensionless measures of the importance of inertial and buoyancy forces relative to viscous ones. Here, $L$ is the spheroid semi-major axis, $U$ an appropriate settling velocity scale, $μ$ the fluid viscosity, and $γ\,(>0)$ the (constant)\,density gradient characterizing the stably stratified ambient, with $ρ_0$ being the fluid density taken to be a constant within the Boussinesq framework. A reciprocal theorem formulation identifies three contributions to the torque: (1) an $O(Re)$ inertial contribution that already exists in a homogeneous ambient, and orients the spheroid broadside-on; (2) an $O(Ri_v)$ hydrostatic contribution due to the ambient linear stratification that also orients the spheroid broadside-on; and (3) a hydrodynamic contribution arising from the perturbation of the ambient stratification by the spheroid whose nature depends on $Pe$; $Pe = UL/D$ being the Peclet number with $D$ the diffusivity of the stratifying agent. For $Pe \gg 1$, the hydrodynamic contribution is $O(Ri_v^{\frac{2}{3}}$) in the Stokes stratification regime characterized by $Re \ll Ri_v^{\frac{1}{3}}$, and orients the spheroid edgewise regardless of $κ$. The differing orientation dependencies of the inertial and large-$Pe$ hydrodynamic stratification torques imply that the broadside-on and edgewise settling regimes are separated by two distinct $κ$-dependent critical curves in the $Ri_v/Re^{\frac{3}{2}}-κ$ plane. The predictions are consistent with recent experimental observations.

physics.flu-dyn↗

arXiv2020

Impurity effects in thermal regelation

When a particle is placed in a material with a lower bulk melting temperature, intermolecular forces can lead to the existence of a premelted liquid film of the lower melting temperature material. Despite the system being below the melting temperatures of both solids, the liquid film is a consequence of thermodynamic equilibrium, controlled by intermolecular, ionic and other interactions. An imposed temperature gradient drives the translation of the particle by a process of melting and refreezing known as thermal regelation. We calculate the rate of regelation of spherical particles surrounded by premelted films that contain ionic impurities. The impurities enhance the rate of motion thereby influencing the dynamics of single particles and distributions of particles, which we describe in addition to the consequences in natural and technological settings.

cond-mat.soft↗

arXiv2019

Hydrodynamic interactions and the diffusivity of spheroidal particles

It is intuitive that the diffusivity of an isolated particle differs from those in a monodisperse suspension, in which hydrodynamic interactions between the particles are operative. Batchelor (1976,1983) calculated how hydrodynamic interactions influenced the diffusivity of a dilute suspension of spherical particles and Russel et al.(1991), and Brady (1994) treated non-dilute (higher particle volume fraction) suspensions. Although most particles lack perfect sphericity, little is known about the effects of hydrodynamic interactions on the diffusivity of spheroidal particles, which are the simplest shapes that can be used to model anisotropic particles. Here, we calculate the effects of hydrodynamic interactions on the translational and rotational diffusivities of spheroidal particles of arbitrary aspect ratio, in dilute monodisperse suspensions. The origin of the hydrodynamic anisotropy is that found in the stresslet field for the induced-dipole induced-dipole interaction. However, in the dilute limit the anisotropy effects are at the level of a few percent. These effects have influence in a vast range of settings, from partially frozen colloidal suspensions to the dynamics of cytoplasm.

physics.flu-dyn↗