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Liu, an environmental engineer and geochemist by training, dealt with the disconnect between these two approaches when he began working to describe water flow in realistic soils. After trying a few simulations using only the N-S equations, he saw that the results would never mimic reality.

“I then thought that the difference of fluid flow in porous media from that in pores is the additional friction force acting on fluids by the solid surfaces [at the boundaries], and we might add a force term in the N-S equation to correct for that,” he says.

He and his colleague Yilin Fang, a PNNL hydrologist, realized that another research group had borrowed a mathematical term from the N-S equations and added it to a Darcy equation. The other team had used the hybrid equation to describe water flow in a ground river channel and masses of porous rock.

“We then thought, ‘How about adding the Darcy term in the full Navier-Stokes equation?’ ” he says.

After thus turning the original idea around and cobbling together a new equation, Liu and Fang passed the problem to post-doctoral researcher Xiaofan Yang. Yang developed a unified multiscale model and tested it against an experiment using a soil core taken from Washington State’s Rattlesnake Mountain.

At PNNL’s Environmental Molecular Sciences Laboratory, Yang used the Chinook and Olympus supercomputers to demonstrate that the new equation shifted seamlessly and appropriately from one mode to another in the course of simulations. In regions with measurable pores, the inapplicable Darcy component of the equation became negligible, and the N-S core of the equation described the flow. In porous regions, the N-S terms in the equation took a back seat, and the model followed Darcy’s law.

And best of all, the approach eliminated the need to define the boundaries between pore regions and porous regions.

The team compared their model to water flowing through real soil. Using X-ray computed tomography, they mapped the pore regions and porous regions in the Rattlesnake Mountain soil core, which was 15 cm long and 2.5 cm in diameter. With that information in hand, they created a computer model of the core and ran a simulation of water being absorbed up into the dry soil. When they set the real soil core into a water tray, its rate of water uptake matched the water uptake in the simulation, validating the unified multiscale model.

Liu and colleagues look forward to future applications of their new approach. They are now applying their model to larger, more complex cases of soil-water interactions.

In the future, they will add the actions of prokaryotes to the simulation. “Current soil organic carbon decomposition models are empirical ones that ignore soil pore structure effects,” Liu says. “To simulate water flow in a realistic soil system will help us to understand how soil pore structures would affect the spatial distribution of moisture conditions, which in turn, affect soil microbial community activities.”

That simulation, in turn, will help fill in the picture of both how soil organic carbon is metabolized and decomposed, and how “greenhouse gases such as carbon dioxide, nitrous oxide and methane are produced at the mechanistic level, and eventually to develop mechanism-based models to describe these processes for better prediction of global climate change.”