In the mesoscale, mixing dynamics involving immiscible fluids is truly an outstanding problem in many fields, ranging from biology to geology, because of the multiscale nature which causes severe difficulties for conventional methods using partial differential equations. The existing macroscopic models incorporating the two microstructural mechanisms of breakup and coalescence do not have the necessary physical ingredients for feedback dynamics. We demonstrate here that the approach of dissipative particle dynamics (DPD) does include the feedback mechanism and thus can yield much deeper insight into the nature of immiscible mixing. We have employed the DPD method for simulating numerically the highly nonlinear aspects of the Rayleigh–Taylor (R–T) instability developed over the mesoscale for viscous, immiscible, elastically compressible fluids. In the initial stages, we encounter the spontaneous, vertical oscillations in the incipient period of mixing. The long-term dynamics are controlled by the initial breakup and the subsequent coalescence of the microstructures and the termination of the chaotic stage in the development of the R–T instability. In the regime with high capillary number, breakup plays a dominant role in the mixing whereas in the low capillary number regime, the flow decelerates and coalescence takes over and causes a more rapid turnover. The speed of mixing and the turnover depend on the immiscibility factor which results from microscopic interactions between the binary fluid components. Both the speed of mixing and the overturn dynamics depend not only on the mascrocopic fluid properties but also on the breakup and coalescent patterns, and most importantly on the nonlinear interactions between the microstructural dynamics and the large-scale flow.
Computer simulations of domain growth and phase separation in two-dimensional binary immiscible fluids using dissipative particle dynamics