We study the motion of a hot particle in a viscous liquid at low Reynolds numbers, which is inspired by recent experiments with Brownian particles heated by a laser. The difference in temperature between a particle and the ambient fluid causes a spatial variation of the viscosity in the vicinity of the solid body. We derive a general analytical expression determining the force and the torque on a particle for low Péclet numbers by exploiting the Lorentz reciprocal theorem. For small temperature and viscosity variations, a perturbation analysis is implemented to evaluate the leading-order correction to the hydrodynamic force and torque on the particle. The results are applied to describe dynamics of a uniformly hot spherical particle and to spherical particles with a nonuniform surface temperature described by dipole and quadrupole moments. Among other results, we find for dipolar thermal fields that there is coupling of the translational and rotational motions when there are local viscosity variations; such coupling is absent in an isothermal fluid.

No abstract

The presence of a particle with specified velocity inside a cylindrical channel affects the pressure-field along the length of the conduit. In this article, we quantify this effect by using a new general method, which describes hydrodynamic interactions between a cylindrical confinement and a spherical particle under creeping flow assumption. The generality of the scheme enables us to consider arbitrary values for system-defining parameters like cylinder-to-sphere ratio or separation between their centers. As a result, we can obtain accurate results for the parameter values hitherto unexplored by previous studies. Our simulations include three cases. First, we consider a fixed spherical obstacle in a pressure-driven flow through the cylinder and find the additional pressure drop due to the blockage. Then, we compute the pressure created by the pistonlike effect of a translating sphere inside a cylinder-bound quiescent fluid. Finally, we analyze the far-field pressure variation due to rotation of an asymmetrically situated sphere in confined quiescent fluid. For limiting cases, our calculations agree with existing results within 0.5% relative error. Moreover, the efficiency of the scheme is exploited in a dynamic simulation where flow dynamics due to a sedimenting sphere under gravity inside a cylinder with different inclination is explored. We determine the particle trajectory as well as the time-dependent far-field pressure-difference created due to the sedimentation process. The results agree well with approximate analytical expressions describing the underlying physics.

No abstract

In this article, we discuss the effect of the bounding cylinder on the rheology of a dilute suspension. We consider a colloidal solution of spherical particles flowing through a cylinder under creeping motion assumption. For transport of such particulate fluid, the increase in the viscous loss due to the existence of suspended particles can be described in terms of enhanced effective viscosity eta(eff) for the medium. Einstein's formula quantifies this increase in viscosity when the flow-domain is unbounded. For bounded domain, however, the increase in viscosity is not only dictated by the properties of the solutes but also affected by the geometry of the confinement. We illustrate this effect of geometry on the effective viscosity by accurately resolving the viscous interaction between a freely suspended sphere and a confining cylinder. First, we take into account a solution of equal spheres, and present the effective viscosity for different cylinder to sphere size ratio as well as for different excluded volume near the cylinder periphery for electrostatic interactions. Then, we also consider a variation in size distribution and determine the rheological properties for different means and variances of the distribution.