Lava Flow Rheology: Modelling a Fluid That Can Stop Itself

Not a Newtonian fluid

Water is a Newtonian fluid: apply any shear stress, however small, and it flows. Lava, laden with crystals and dissolved gas bubbles even while molten, is not. Below a critical shear stress called the yield stress, it behaves like a solid; only once the applied stress exceeds that threshold does it start to deform and flow, and even then the relationship between stress and flow rate is not simply proportional. This behaviour is captured by the Bingham plastic model, the standard rheological description used in lava-flow modelling.

tau = tau_0 + mu_p * (du/dy)     for tau > tau_0   (flows)
du/dy = 0                        for tau <= tau_0  (locked, solid-like)

  tau    applied shear stress
  tau_0  yield stress (rises sharply as the flow cools and crystallises)
  mu_p   plastic viscosity
  du/dy  shear rate (velocity gradient across the flow)

Why a flow can stop on a slope

Because of the yield stress, a lava flow does not need a flat surface or an obstacle to stop — it can simply run out of driving stress. The stress driving the flow forward is proportional to the flow's thickness and the slope; as a flow thins out toward its margins, or as the slope shallows, or as cooling raises the yield stress, the driving stress eventually drops below the threshold and that section locks in place while thicker, hotter material elsewhere keeps advancing. This is why lava flows have sharp, well-defined fronts and margins rather than thinning out gradually to nothing the way a puddle of water would.

The thermal crust: insulation, not strength

Within seconds of exposure to air, the outer surface of a lava flow radiates heat fast enough to solidify into a dark, glassy crust. That crust is a poor thermal conductor, so it insulates the hot, still-liquid interior and dramatically slows the cooling of everything beneath it — a flow with an intact crust can travel far further than the same lava would if it stayed fully exposed. But the crust itself has almost no mechanical strength: it constantly buckles, cracks and tears as the liquid underneath keeps moving, producing the wrinkled, ropy surface of pāhoehoe or the jagged, broken-up surface of ʻaʻā depending on how fast that cracking happens.

Channels, lobes and levees

Once a flow finds a preferred path, usually a topographic low, the fastest-moving lava concentrates there, forming a central channel. At the channel's cooler, slower-moving edges, shear rate and temperature both drop, pushing local stress below the yield threshold and letting that material solidify in place — building solid levees along both banks that then confine and speed up the channel further, in a self-reinforcing feedback loop very similar to how a river builds its banks, except by freezing rather than erosion. Where the flow front breaks out from behind its crust, it typically advances not as a continuous sheet but as a sequence of small overlapping lobes, each one inflating, stalling and being overtaken by the next.

Simulating it on a 3D terrain

A cellular model of lava flow tracks, for every cell on a terrain grid, a thickness, a temperature and a derived local yield stress and viscosity. At each step, lava is redistributed from higher-stress cells to lower-stress neighbours following the Bingham relationship above, temperature drops according to radiative and convective cooling laws, and any cell whose driving stress falls below its yield stress is frozen for the rest of the run. Iterated over thousands of steps, this simple local rule set reproduces channels, levees, lobate margins and, eventually, a flow that visibly stalls exactly where the physics says it should.

Frequently asked questions

Try it live

Everything above runs in your browser — open Lava Flow Model and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.