The present application relates to an improved apparatus for mixing intensification in multiphase systems, which can be operating in continuous or batch mode. In particular, it relates to a reactor, which can be assembled and disassembled easily for cleaning. The apparatus is based on oscillatory flow mixing (OFM) and comprises an oscillatory flow plate reactor (OFPR) provided with 2D Smooth Periodic Constrictions (2D-SPCs). The apparatus can be fully thermostatized and it is based on a modular system, in order to achieve most of the industrial application. The OFPR is suitable for multiphase applications such as screening reactions, bioprocess, gas-liquid absorption, liquid-liquid extraction, precipitation and crystallization. Regarding its size and geometry and the ability to operate at low flow rates, reagent requirements and waste are significantly reduced, as well as the manufacturing and operating costs, compared to the common reactor, such as continuous stirred tank reactor (CSTR) and the "conventional" OFR.