## 1 Introduction  
Despite relentless attempts to introduce electricity to the transport sector, internal combustion engines (ICE) remains the main vehicle propulsion in the upcoming decades. However, they will undergo further development of technologies for controlling soot and NO\({}_{\rm x}\) emissions [1]. Among the traditional ICEs, compression ignition (CI) engines are preferable to spark-ignition (SI) engines in view of thermal efficiency because of the high compression ratio, lean combustion, and low pumping loss. However, the drawback of CI engines is the high emissions of NO\({}_{\rm x}\) and soot owing to the diffusion combustion characteristics [2; 3; 4]. The simultaneous reduction of NO\({}_{\rm x}\) and soot emissions is really a challenge because these two pollutants have a trade-off relationship with each other [5]. Soot particulates are generally produced by inhomogeneous and locally fuel-rich regions of the diffusion flame, while NO\({}_{\rm x}\) is formed in the high-temperature region around the stoichiometric air-fuel reaction regions [6]. The reduction in the diffusion combustion phase has contributed to a significant reduction in soot emissions [7]. Numerous studies report the fact that it is very hard to improve the performance and emissions of CI engines by the change of the single-fuel property [8]. It is expected that dual-fuel mode offers a better way to control the combustion than the conventional diesel CI engine. This is due to the combustion characteristics of a fuel blend-air mixture that strongly depend on the fuel vaporization, the fuel-air mixing process, and the fuel chemical reactivity of each component [9; 10; 11]. In order to reduce \(\mathrm{NO_{x}}\) and soot emissions simultaneously, some advanced combustion technologies have been introduced, such as homogenous charge compression ignition (HCCI) and premixed charge compression ignition (PCCI). These technologies are intermediate between CI and SI combustion modes. Although they are attractive technologies in view of thermodynamics, it is challenging to control the ignition timing and heat-release characteristics [12]. Besides, the major drawback of the HCCI and PCCI combustion strategies is the high levels of HC and CO emissions. Subsequently, the concept of reactivity controlled compression ignition (RCCI) has been developed to overcome the problems encountered in HCCI and PCCI. In RCCI, high-octane fuel is injected into the intake manifold, while a high-octane fuel is directly injected into the combustion chamber for ignition. The combustion properties and ignition timing of the engine can be controlled by varying injection timing and adjusting the mixing ratio of the two fuels [13]. Another attempt to control the emission of ICEs is adopting the optimal fuel blends in different operating conditions of the engine. This is the concept of the hybrid fuel engine (HFE). This technology has been proved to be a feasible approach for improving the performance of traditional mono-fuel engines [14; 15]. With a large variety of properties, renewable fuels have high potential for use in the HFE. Many researchers have investigated various fuel blends in order to achieve low emissions and high thermal efficiency combustion [16; 17; 18; 19]. Among the fuels, dimethyl ether (DME) and biogas are very attractive because of their advantageous physical chemistry properties, and being renewable fuels [20; 21; 22]. In fact, DME is considered to be a clean alternative fuel [23] and has remarkable potential for application in ICEs [24; 25]. It can be produced from a variety of abundant renewable material sources or fossil fuels [26]. Likewise, it is an ideal diesel fuel substitution applied to CI engines because of its high cetane number [27]. Moreover, DME forms a liquid phase with moderate pressure (about 5 bar); therefore, it can be used in the existing infrastructures for transportation and storage of liquefied petroleum gas (LPG) [28]. DME contains about 35% oxygen.