5.1 Introduction

We now turn our attention to particles that are not rigid. By definition, the relative positions of material points within these particles are not fixed, so that the application of external forces usually deforms them. It will be recalled that the deformations of small particles were divided into deformations without change of volume and uniform expansions. The first of these is briefly considered in this chapter. Volume changes are considered in Chapter 6.

Shape deformations can, in principle, be induced in all types of particles, provided the forces applied to them are sufficiently large. But, because in suspensions those forces are small, solid particles normally retain their shape. We therefore limit the present discussion to small bubbles and droplets, keeping in mind that interfacial effects now come into play.

Bubbles and droplets that are not exposed to any external force must be spherical. This follows from the Young-Laplace equation, (2.1.11), which shows that the pressure difference across a curved interface, at any point of the interface, is proportional to the curvature, , of the interface at that point. If no forces are applied, the pressure difference must be the same for all points on the interface and that means that the curvature is constant over the whole surface.

But even when external fields are present, small droplets and bubbles may, for many purposes be considered spherical. An idea of the size below which particles may be regarded as spherical is obtained by considering gravitational effects. Let 2a