Shape fluctuations of a deformable body in a randomly stirred host fluid

Abstract

We consider a deformable body immersed in an incompressible fluid that is randomly stirred. Sticking to physical situations in which the body departs only slightly from its spherical shape, we investigate the deformations of the body. The shape is decomposed into spherical harmonic modes. We study the correlations of these modes for a general class of random flows that include, as a special case, the flow due to thermal agitation. Our results are general, in the sense that they are applicable to a large class of deformable bodies with energy that depends only on the shape of the body, and a general class of random flows.

Droplet shape fluctuations in agitated emulsions—Beyond the dilute limit

“…The response of a single object immersed in a host liquid to an external random flow has been described in previous work [1]. The results are sketchily repeated here for the benefit of the reader as the general equations obtained here are to be exploited in the next section by replacing the external velocity field by the velocity field seen by the object when a finite density of deformable objects is immersed in the liquid.…”

“…The substitution q → 1/R is due to the fact that only distances smaller than R are relevant in the evaluation of the shape fluctuations. The viscous time scale τ ν should be compared with the deformation-decay time scale, which for the example of objects governed by surface tension is given by: τ def = νρ m R/λ where ρ m is the mass density of the liquid and λ is the surface tension [1]. This is an example of a general situation in which the time scale associated with deformation of the object, depends naturally on physical parameters characterizing the object.…”

“…The bracketed term is the projection operator that removes the longitudinal part of ⃗ u, and therefore yields a general transverse velocity field ⃗ v ext . Next, the correlations of the external velocity are expressed using the correlations of the general field ⃗ u [1].…”

“…(3) gives the shape correlations of a single object, that has been described previously [1]. The second term represents the correction to the shape correlations due to a small but finite density of deformable objects.…”

“…Single deformable objects such as droplets of one liquid dispersed in another liquid fluctuate in shape in response to random external stirring [1]. The purpose of this paper is to investigate the effect of interaction between such deformable objects [2] on the way that each object deforms due to external stirring.…”