CHAPTER 3: Droplet Mixing

Reactive inkjet printing involves bringing together small quantities of reagents to react in a localised space, and a requirement for the desired reactions to occur is that the reagents should mix sufficiently well and sufficiently quickly. The small size of inkjet droplets makes it difficult to observe mixing directly, and most studies of droplet mixing focus on millimetre-sized droplets. These studies indicate that mixing within impacting and/or coalescing droplets is actually rather poor. This is because at small scales, liquid flow is highly laminar, i.e. smooth and non-turbulent, and mixing therefore relies on molecular diffusion, which is a slow process. This chapter illustrates the roles of diffusion and advection in mixing under laminar flow conditions, and explores ways in which the large deformations in droplet shape during impact and coalescence can help speed up diffusive mixing by decreasing the distances over which diffusion must act and simultaneously expanding the area over which it can act. Observations in millimetre-sized droplets are interpreted in the context of inkjet-sized droplets, and two beneficial mechanisms in particular are identified: vortex ring generation during coalescence of a small droplet with a much larger one, and the temporary flattening of combined droplets during drop-on-drop impact of similar-sized droplets. Other transport mechanisms also arise as a result of differences in the material properties of the reagents, especially surface tension, and these are discussed in the context of the available literature.