The present application relates to an improved apparatus for mixing intensification in multiphase systems, which can be operating in continuous or batch mode. The apparatus is based on oscillatory flow mixing (OFM) and comprises a novel oscillatory flow reactor (OFR) provided with Smooth Periodic Constrictions (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 new OFR 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 operating costs, compared to the common reactor, such as continuous stirred tank reactor (CSTR) and the "conventional" OFR. The disclosed apparatus fulfil some of the gaps observed in the "conventional" OFR as well as in meso-OFR known. Excellent heat and mass transfer is obtained. The scale-up is predictable.