# Secondary Atomization of a Biodiesel Micro-Emulsion Fuel Droplet Colliding with a Heated Wall
## 1 Introduction  
In many types of internal combustion engines operating on liquid fuel, droplets of an atomized fuel flow collide with a wall. Diesel engines often have quite a small combustion chamber, which makes the collisions of fuel droplets with the walls inevitable. Moreover, the trend of miniaturization is now common for engine design in general. All of this makes it especially important to understand and reliably predict the interaction of single fuel droplets with a heated surface [1]. Several practical matters are usually discussed [1; 2; 3; 4] concerning different ways of droplet interaction with a wall in an engine. First, if droplets of atomized fuel are ignited without evaporating completely, the engine demonstrates lower combustion efficiency, while emitting unburnt hydrocarbons [2]. Second, the droplet-wall interaction may result in fuel sputtering, which in turn results in the formation of an air-fuel combustible mixture in the wall vicinity [3]. Third, in some engines, fuel evaporation may form gas-phase hot spots near the combustion chamber wall, which can lead to a destructive effect termed \"super knock\" [4]. Experimental research into the interaction of fuel droplets with a wall is also relevant because of the need to develop the existing mathematical models and create new ones to describe the processes in more detail. The dynamics of carbohydrate fuel (heptane, decane, Jet A-1, diesel) interaction with a heated stainless steel wall in film evaporation regime was studied in [5]. The authors focused on analyzing the maximum droplet spreading diameter at various temperatures below the boiling point. The analysis shows that the maximum spreading diameter is significantly affected not only by the Weber number (_We_) and surface temperature (\(T_{0}\)), but also by the dynamic viscosity of fuel. The experimental data obtained was used to build an empiric model predicting the maximum spreading diameter of a fuel droplet on a heated surface and accounting for the temperature of the said surface. [PERSON] et al. [6] discovered that a diesel droplet does not interact with a heated surface in the same way as a droplet of water [7], n-heptane [8], or ethanol [9]. In particular, the duration of diesel droplet contact with a heated stainless steel surface does not depend on the impact angle or impact velocity, though it is 30% higher than for [PERSON]'s free oscillation prediction. Moreover, [PERSON] et al. established that the droplet disintegration criterion for diesel also differs from that of the other above liquids. The threshold _We_ for a diesel droplet breakup is approximately 14. In addition to the fuel viscosity affecting the interaction outcome, another important factor is the fuel component composition, which in its turn may affect the viscosity of the entire system. The interaction dynamics of a two-component fuel droplet and heated surface was experimentally studied by [PERSON] et al. [10]. A mixture of \(n\)-hexane and \(n\)-decane was used because these fuel types have a significant difference in boiling temperatures \(T_{\rm b}\). It was established that interaction regimes differ significantly for two-component and single-component fuel droplets. The study demonstrated the regimes typical of both two- and single-component droplets; however, some regimes were only typical of one of the considered droplet types. The research also showed that an increase in the velocity of droplet impact with the surface led to lower surface temperatures, thus specifying the interaction regime. Another example of multi-component fuel droplet interaction with a heated wall is a series of experiments with biofuels--camelina-derived alternative jet fuels [11]. In this case, the fuel was a mix of Jet A-1 and camelina-derived biofuel. A typical Weber number (_We_) for droplets of this composition ranged from 28 to 886.