Microfluidic applications have served as interface between the macro- and nano-world. Microscale systems offer many advantages such as minimal substances consumption, complex chemical waveforms, and significantly reduce analysis and experimentation time (for example, an important concept recently introduced was TAS, the Micro Total Analysis System for details see, Manz, 1990). The absence of inertial and turbulent effects in microfluidic devices offers new horizons for physical, chemical and biological applications. The short length scales gives high surface-to-volume ratios, small diffusion distances and easy temperature profiling where needed, giving the opportunity to manipulate substances in ways never imagined before. Drops or slugs and their application in micro and nano-scales are a very important field in present science. In medical applications for example: cell-based assays (Pihl, 2005), models for capillary blood vessels for red cells infected with malaria (Shelby, 2003), drug delivery targeted at specific sites in the body for a less invasive chemotherapy, miniature biosamples preparations on fully automated biochips, for DNA sampling and other genomic applications. On different chemical applications it has been used in two-phase chemical reactions (Tice, 2004; Hodges, 2004; Harries et. al., 2003; Burns and Ramshaw, 2001 and 2002), elucidation and optimization of nitration reaction was demonstrated by Dumman, who concluded that the capillary microreactor can be used for  quantitatively examining exothermic liquid-liquid reaction systems (Dumman et. al., 2003); fast or dangerous reactions, solvent extraction, substances separation and so on. At the microscales the problems associated to the scaling-up for large scale production by simply numbering-up are reduced; this means that several microreactors can be used to obtain the necessary products, instead of building complicated and expensive plants. Mathematical models describing the movement of drops, or in general, multiphase flows developed so far, are not able to predict or quantify properly all the important particularities of this complex systems (capillary microreactors). Hence a deeper knowledge of the physical problem, say hydrodynamics transport, is mandatory. This task requires powerful modeling techniques; therefore we initiated the hydrodynamic study of drops/slug movement through capillaries. We focused in the application of a slug flow microreactor model, to match the necessities and behavior described in (Kashid et. al., 2005 and 2006).