Segregation, or un-mixing, of particles has been a topic of intense research and industrial frustration for many decades. When particles differ in almost any mechanical property, processing typically leads to pattern formation, layering, or complete separation of the materials and this non-homogeneity can cause dramatic revenue loss and product failure in industries such as pharmaceuticals, ceramics, and agriculture, to name but a few. In particular, particles of different size and density may segregate quite strongly in free-surface flows; the larger (lighter) particles often rise to the top, while the smaller (denser) particles sink to the bottom. In this paper, we show both experimentally and computationally that by introducing periodic flow inversions that occur at a frequency above some critical value, we can effectively eliminate both density and size segregation. The critical frequency is related to the inverse of the characteristic time of segregation and is shown to scale with the shear rate of the particle flow. This observation could lead to new designs for a vast array of particle processing applications and suggests a new way for researchers to think about segregation problems. We demonstrate this approach in several industrially-relevant devices, including chute flows and tumbling mixers.