**2. Model**

standard diesel engines with minor tuning or no modification requirement in the ICE processes [3, 4]. According to Tier I and Tier II standards of the U.S.A. Environmental Protection Agency (EPA) (see [5] for details), biodiesel fuels produced within the last decade meet the minimum requirements of health risk [6]. Similarly, ethanol (or bio-ethanol) is commonly used as an alternative source of energy in the form of pure, or gasoline-blended, fuel in sparkling ignition (Otto cycle) engines [7]. Bioethanol is a very promising reactant for petrol engines and for biodiesel production industry, compared to methanol and fossil fuels. Lipids, such as fats or oils, react with ethanol to produce biodiesel. Also, it is renewable,

The delay in processes preceding the onset of combustion (mainly the spray formulation, and heating and evaporation of fuel droplets) in the internal combustion engines is crucial to the design and performance of these engines [9, 10]. The complexity of modeling evaporation processes should be taken into account as it involves detailed physics of heat transfer, mass transfer and fluid dynamics associated processes. Most of the studies on fuel droplet heating and evaporation analyses have been either based on considering individual components, described as 'discrete component' (DC) approach [11, 12], or on a probabilistic analysis of large numbers of hydrocarbons, described as 'continuous thermodynamics' [13–16] and 'distillation curve' [16–18] approaches. The DC approach is highly accurate and computationally efficient in the cases when a small number of hydrocarbons need to be taken into account. In the second approach, several simplifying assumptions are made; such as the assumption that hydrocarbon species inside droplets are mixed infinitely quickly, described as 'infinite diffusivity' approach, or they are not mixed at all, described

The DC model, based on the analytical solutions to the equations of heat and mass transfer and species diffusion [19], has been verified against numerical simulations and validated against experimental data in [20] (see [9, 21] for more details). Following [22–25], the droplets heating and evaporation processes are analyzed by application of several blends of diesel-

The DC model is used for this analysis and applied to a broad range of diesel-biodiesel fuel fractions and ethanol-gasoline fractions. The mixture of EU diesel fuel with 22 types of widely used fatty acid methyl ester (FAME) biodiesel fuels have been investigated. These are: tallow (TME), lard (LME), butter (BME), coconut (CME), palm kernel (PMK), palm (PME), safflower (SFE), peanut (PTE), cottonseed (CSE), corn (CNE), sunflower (SNE), soybean (SME), rapeseed (RME), linseed (LNE), tung (TGE), hemp-oil, produced from hemp seed oil in the Ukraine (HME1), hemp-oil, produced in European Union (HME2), canola (CAN), waste cooking-oil (WCO), yellow grease oil (YME), camelina (CML), and jatropha (JME). Droplets with four fractions of diesel-biodiesel blends have been investigated in the DC model. These are 5% biodiesel with 95% diesel fuels (B5), 20% biodiesel with 80% diesel fuels (B20), 50% biodiesel with 50% diesel fuels (B50), pure biodiesel (B100) and pure diesel fuels (PD). For the ethanol-gasoline blends, droplets with five fractions have been investigated in the DC model. These are 5% ethanol with 95% gasoline fuels (E5), 20% ethanol with 80% gasoline fuels (E20),

green, and not toxic [8].

60 Advances in Biofuels and Bioenergy

as 'single component' approach.

biodiesel fuels and ethanol-gasoline fuels.

The diesel-biodiesel blends are represented by a mixture of 22 types of biodiesel fuels with up to 22 species of methyl ester and diesel fuel, formed of 98 hydrocarbons represented by 9 groups (see [26] for more details). The ethanol-gasoline blends are represented by a mixture of ethanol and fuel used in advanced combustion engines, type C (FACE C) gasoline fuel, formed of 20 hydrocarbons, in 6 groups categorized according to their chemical structures and thermodynamic and transport properties (see [27] for more details). The thermodynamic and transport properties of diesel are inferred from [28], and those of biodiesel fuel are inferred from [26, 29] respectively; while properties of ethanol and gasoline fuel are taken from [27, 30] respectively. The contribution of species and average droplet temperatures are taken into account in the calculation of all fuel properties. All units used in our analyses are SI unless indicated otherwise.
