For a droplet evaporating either in a flowing gas stream or on a heated substrate, internal mo- tions inside the droplet are present due to the external shear stress (Abramzon & Sirignano,
Chapter 2 35 1989; Law, 1976; Prakash & Sirignano, 1980) or due to temperature gradient within the drop- let (Diddens et al., 2017; Erbil, 2012; Hu & Larson, 2006; Mandal & Bakshi, 2012; Tam et al., 2009). In the convective regime, shear of the gas flow at the droplet surface drives the internal circulation in the liquid phase. Inhomogeneous temperature within the liquid bulk also generates the internally natural convections or Rayleigh flows. For a stagnant deposited droplet on a hot substrate, temperature difference over the liquid-vapour interface induces surface tension gradient resulting in thermal-capillary flows (or thermal Marangoni flows) at the interface. For droplet comprising binary liquid mixture, these motions (solutal Marangoni flows) are also created due to the interfacial concentration inhomogeneity. Enhancement in droplet evaporation rate was pronounced in the literature due to the effects of internal mo- tions in the droplet (Abramzon & Sirignano, 1989; Brignell, 1975; P. Chen et al., 2017; Law, 1976; Law & Law, 1982; Mandal & Bakshi, 2012; Prakash & Sirignano, 1978; Tam et al., 2009).
For droplet evaporating in a convective environment, studies have focused on the internal motions induced by the external shear flow that drives the motion at the droplet interface. The theoretical study of (Law, 1976) proposed the rapid internal mixing approach for droplet va- porisation for estimation of droplet lifetime which assumes a spatially uniform temperature field within the droplet. Good agreements have been obtained with experimental data which support the postulation of fast circulation rate inside the droplet. Prakash and Sirignano (1978) in their numerical study assuming quasi-steady gas phase found that the strength of the axisymmetric Hill's spherical vortex inside droplets is controlled by the external shear stress at the droplet interface. Time scale analysis in this study indicated that the droplet heat- ing follows a long unsteady stage during the vaporisation and argued that assumption of uni- form temperature was not so accurate even though the internal motion significantly enhances the heat transfer process. Later, Prakash and Sirignano (1980) coupled the gas-phase bounda-
Chapter 2 36 ry analysis using an integral approach with their previous liquid phase motion to analyse the vaporisation of three different fuel droplets. Their study confirmed the unsteady behaviour over a major duration of the droplet lifetime. Also, the temperature difference between the surface and interior was found to be higher for less volatile liquid droplets. It is clear that the use of non-uniform droplet temperature model provides more accurate characterisation of the droplet vaporisation process although the less rigorous rapid-mixing model (uniform liquid temperature) can still produce acceptable estimation of vaporisation time without the mecha- nistic details of the process.
Differences in temperature within the liquid bulk, which has been reported in a number of studies (Prakash & Sirignano, 1980; Volkov et al., 2017; Wong & Lin, 1992; J.-R. Yang &
Wong, 2002) can definitely result in the buoyant motions driven by liquid density difference (Rayleigh flow or natural convection). However, the internal Rayleigh flow is normally ig- nored for the droplet vaporising in a gaseous flow; this may be due to the dominance of the internal motions driven by shear flow. Therefore, additional efforts are required in comparing the motions induced by external shear flow and by the density difference.
Similar to internal circulation of an evaporating droplet in gaseous environment, the internal motion of a droplet deposited on substrate (a process driven by surface tension gradient) has also been investigated (P. Chen et al., 2017; Fanton & Cazabat, 1998; Girard et al., 2008; Hu
& Larson, 2005, 2006; Shi et al., 2017; Tam et al., 2009; Xu & Luo, 2007; Zhong et al., 2017). Xu and Luo (2007) visualised Marangoni flows in evaporating water droplets on glass surface with the aid of fluorescent tracers at room temperature. Girard et al. (2008) investi- gated the influence of Marangoni flows on the evaporation rate of a water droplet resting on heated aluminium substrate (up to 50 oC) and found that contribution of Marangoni convec- tion was negligible on the evaporation rate. A similar observation was also earlier reported by
Chapter 2 37 Hu and Larson (2005). However, a combined numerical and experimental study by Zhong et al. (2017) reported an increase in mass transfer coefficient with inclusion of Marangoni flows in a heptane/ether droplet. Diddens et al. (2017) also reported an enhancement of evaporation rate with the inclusion of Marangoni flows in water/glycerol and water/ethanol droplets. The recent study of P. Chen et al. (2017) examined the influence of both thermal and solutal Ma- rangoni flows on the evaporation rate of pure and binary mixture sessile droplet on heated substrate. They noted that the evaporation model of Hu and Larson (Hu & Larson, 2002) sig- nificantly under-predicts evaporation rate at temperatures beyond the ambient condition which was attributed purely due to the Marangoni effects. Empirical coefficients were added to the model of Hu and Larson (2002) to account for the evaporation enhancement due to Ma- rangoni flows.
In summary, a comprehensive review of the previous work presented in this chapter has identified a number of knowledge gaps which require additional efforts to advance under- standings in this research area. In line with the topics introduced in the literature review, ho- mogeneous and heterogeneous heat transfer modellings for feed vaporisation in a typical mul- tiphase system (FCC riser) are presented in Chapter 3; vaporisation of a suspended droplet in convective environment is discussed in Chapter 4, vaporisation study of sessile droplet on a heated solid sphere is presented in Chapter 5 and evaporation characteristics at the three phase contact line is reported in Appendix F.
Chapter 3 38