Rheology and Ancient Warfare: Stuck in the Mud, Solids that Flow

November 14, 2017


Rheology is a useful tool not only for studying high tech materials but also for leveraging the seemingly mundane substances around us to our advantage.  The viscoelastic properties of mud have been applied for many applications over the years - over 3,000 years, to be precise.


A story involving rheological concepts used in battle stems from the combat advice of Deborah, a leader who guided the ancient Israelites to victory over the Canaanite general Sisera. Her strategy was simple and effective: fight in an open plain while a rainstorm approaches. In 1200 BC, the Canaanite army owned 900 iron chariots, a large and cutting-edge force compared to the weaker Israelite army. (1)  Once the rain came down, the Canaanite chariots were stuck in the mud, giving the advantage to the Israelites. (2)


Muddy materials are still of interest to rheologists today. Laponite and bentonite are mineral-based clays that are studied for applications for handling earth and for use in commercial products. (3) Aqueous suspensions of these synthetic clays are useful for understanding how natural muds and wetted soils flow. Additionally, Laponite suspensions are well known for their gel-like properties caused by electrostatic 3D ordering of the platelet nano-structures.  They have been shown to increase viscosity and shear modulus over time due to structural build-up, (3) and Laponite is added to other materials in order to thicken them through laponite-induced gelation. (3) Similarly, micron-scale natural mud displays shear-thickening and is known to possess a yield stress required to flow, (4) which necessitates a force to move the mud. This result is illustrated in day-to-day life when someone steps into mud and has to use extra force to remove their foot – or as the ancient story mentioned previously, to remove the wheels of a chariot.


However, Deborah is attributed for more than just use of rheological concepts of mud for military triumph. She is the historical figure whom the rheological Deborah number (D) is named for due to her poetic statement that “even the mountains will flow before the Lord.” (2)


In fact, rheologists interpret mechanical responses of solids as though they are just very high-friction heavy liquids. The foundational phrase “Panta rhei – everything flows” is the motto of the Society of Rheology. (5) Deborah’s statement fits this mindset, as given infinite time, mountains would flow.  The Deborah number is calculated as follows:


D = Time of Relaxation / Time of Observation                                    (6)



Relaxation time is the time required for the material’s structure to deform, move, or re-arrange. Molecules relax on a relatively short time scale, polymers on a slightly longer time scale, and covalently bonded gels on an even longer scale. But the total time that passes during the molecular shuffling is key to understanding flow. Ketchup may be considered to flow slowly by the hungry individual awaiting to apply it to their hamburger, but ketchup certainly flows more quickly than tar pitch. (7) In the first case, ketchup has a high Deborah number (observing it as a solid because it does not instantly flow out of the bottle), whereas in the latter situation of observing ketchup over 90 years, it certainly would flow and make a mess (low Deborah number). In this manner, fluidity is relative.


Rheological phenomena are prevalent in daily life through natural materials, regardless of philosophical consideration. To learn more about rheological applications, request a free consultation.



  1. Magill, N., Moose, F., Moose, C., Dictionary of World Biography: The Ancient World – Deborah, 2003.

  2. http://www.womeninthebible.net/women-bible-old-new-testaments/deborah-and-jael/

  3. Willenbacher, N., “Unusual Properties of Aqueous Dispersions of Laponite RD”, Journal of Colloid and Interface Science, 1996, 182, 501. 

  4. Van Kessel, T., and Blom, C, “Rheology of cohesive sediments: comparison between a natural and an artificial mud”, Journal of Hydraulic Research, 1998, 36, 4, 591.

  5. Society of Rheology: http://www.rheology.org/sor/ 

  6. Reiner, M., “The Deborah Number”, Physics Today, 1964, 62.  

  7. Pitch Drop Experiment: http://smp.uq.edu.au/content/pitch-drop-experiment  



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