The discovery of post-perovskite phase transition near the core-mantle boundary( CMB) has turned our heads to the potentially important role played by the increasing complexity of the physical properties in the lower-mantle models. In this study we have investigated the influences on lower mantle dynamics by the strongly depth-dependent coefficient of thermal expansion and radiative thermal conductivity together with the post-perovskite transition within the framework of isochemical models. We have carried out the simulations in both 2-D and 3-D Cartesian geometries. First, we review the basic connection between the temperature profile and the Clapeyron slope, calling attention to the special relationship between the temperature intercept of the post-perovskite phase change and the temperature at the core-mantle boundary. Double-crossing of the post-perovskite boundary takes place only, when the temperature of the CMB is greater than the temperature intercept of the phase change. We find that mantle plumes become multiscale in nature because of the combined effects exerted by variable mantle viscosity, strongly depth-dependent thermal expansivity, radiative thermal conductivity at the bottom of the mantle, the spinel to perovskite phase transition and the perovskite to post-perovskite phase change in the deep mantle. Both radiative thermal conductivity and strongly decreasing thermal expansivity in the lower mantle can help to induce partially layered convection with slabs stagnating in the transition zone. In our isochemical models a second low viscosity zone is created under the transition zone accompanied by intense shear heating. Secondary mantle plumes emerge from this region at the base of the transition zone. Large-scale upwellings in the lower mantle are induced mainly by both the style of lower-mantle stratification and the decrease in thermal expansivity. They control the location and the local dynamics of the upper-mantle plumes. In these models with variable thermal conductivity and viscosity, an increase in the temperature of the CMB causes a greater tendency for layered convection. From the same depth-dependent thermal expansivity, we can deduce the 3-D density anomalies from the seismic velocity anomalies inferred from seismic tomographic inversion. Using these density distributions, we can calculate the viscous responses of the Earth due to these density anomalies for a given viscosity structure. We then focus on the lateral viscosity variations of the deep mantle on the solution of the inverse problem involving the inferences of the viscosity from the long-wavelength geoid. Our solution for the large-scale lateral viscosity structure in the lowermost mantle shows that the region underneath hot spots have significantly higher viscosity in the deep mantle than the region below subduction regions. Recent inferences from firstprinciples calculations and laboratory experiments on analogue post-perovskite material also surmise the rheology of post-perovskite would be dominated by dislocation mechanism and be softer than perovskite. We put forth a hypothetical scenario in which the bottom portions of the superplumes in the deep mantle are stiffer than the adjacent post-perovskite mantle and are held fixed by the surrounding horizontal flow of post-perovskite.