Modeling dilatant behavior with a cornstarch and water suspension

Introduction

The initial goal of this project was to model deformation in the lower crust using a cheap and readily available analog material: cornstarch. However, it soon became apparent that while the material was messy enough, it posessed rather interesting properties that precluded it from approximating a Newtonian fluid. When approximately 1 part cornstarch is 'mixed' with approximately 1 part water, the resulting suspension behaves as a dilatant fluid, meaning its viscosity increases with increasing strain rate. This is also known as shear thickening. Dilantancy is the expansion of a granular mass caused by particles moving past each other. For example, when pushed slowly with an object, the material flows fluidly around it, deforming in a ductile manner.When the strain rate is increased (i. e. you push faster), material closest to the object becomes very hard and actually fractures in a brittle manner. The change in viscosity and subsequent change in deformation behavior in this material is rather abrupt, and several experiments where carried out in an attempt to characterize this transition. This project focused on defining this transition from ductile to brittle behavior in a dilatant fluid. Even though a cornstarch suspension may not be the best analog to model the lower crust, there are several other geologic systems which it may apply to, such as crystal-rich magmas and areas with high-pore fluid pressure in clay-rich sediments in active orogens.

Model description

Three different experiments where conducted:

EXPERIMENT (A): SETUP - A mixture of cornstarch and water was prepared to a consistancy where the material flowed readily as a fluid when not stressed and behaved brittly when stressed, which occured at 42.8% water content. The material was placed in a large rectangular flat-bottomed plastic bin, with centimeters marked off on the side. A standard mail scale was placed on its side on a table, with the bottom against the wall. The plastic bin was placed on top of rollers, on top of the table in order to minimize friction. One short side of the plastic bin was placed against the top of the scale.

PROCEDURE - A 'backstop,' in this case a ruler, was placed in the cornstarch suspension at the far end of the plastic bin and care was taken to keep the bottom of the backstop from touching the bottom of the plastic bin in order to minimize suction along the bottom. The backstop was then pushed through the material while keeping a constant reading on the scale. The backstop was pushed for 30 seconds, after which the distance it traveled was noted. This was repeated for varying scale readings.

EXPERIMENT (B): SETUP - This experiment is a reproduction of the one described in Smith (1997). The same mixture of cornstarch and water as in Experiment (A) was prepared in a smaller amount. The cornstarch was quickly shaped into a ball and placed in a smaller, flat-bottomed plastic bin, then allowed to flow on its own until a stable disk-shape was reached. A passive marker was placed in the center of the disk. A protractor was used to measure angle of inclination, and a ruler was taped to one side of the plastic bin to measure the distance the passive marker moved.

PROCEDURE - The plastic bin was tilted to a specified angle (alpha) and the cornstarch suspension allowed to flow down the incline for 30 seconds. At the end of 30 seconds, the distance the passive marker had moved was noted, and the experiment was repeated a a different angle of inclination. If part of the disk collapsed during a run and reached the end of the plastic bin before the disk, and interfered with its flow, the run was stopped and not recorded.

EXPERIMENT (C): SETUP - This experiment was an attempt to model the deformation of a dilatant material in an easily controlled environment. The 42.8% water and cornstarch material was prepared and placed in the large plastic bin of Experiment (A). A grid was drawn on the surface of the cornstarch mixture using a ruler that had been colored on one edge with a sharpie. The bin was placed on a table and three sides of the bin were held stable by heavy rocks. A digital camera was set up on a tripod to record the experiment, with photos taken approximately every 5 seconds.

PROCEDURE - A backstop was placed in the cornstarch suspension as in Experiment (A), but in the middle of one of the long sides of the bin in order to avoid edge effects. The backstop was the pushed at a constant velocity across the short width of the bin in one of three manners: 1) orthogonal followed by strike-slip convergence, 2) strike-slip followed by orthogonal convergence, and 3) oblique convergence.

Results

EXPERIMENT (A) - Stress was taken as measured on the mail scale. Strain rate was taken to be approximated by velocity in this case.

The scattered nature of the data is considered to be a result of the many sources for experimental error. At best, this graph shows a general linear relationship between strain rate and stress, but the transition from ductile to brittle behavior is not apparant. So, Experiment (B) was conducted to determine this transition. The graph below shows the results from this experiment. Line is a best fit least-squares power law line.

EXPERIMENT (B) - Stress was calculated using: stress = (w sin alpha)/ A, where w = weight of the material, alpha = angle of inclination, and A = area of the disk. Stress is shown in pascals (Pa). Average strain rate was calculated using: strain rate = velocity/h, where h = height of the disk. Average strain rate is in cm/s. A clearer approximation of the trransition from ductile to brittle behavior with strain rate can be seen from the graph of the results below. The material switches from ductile to brittle deformation at about 140 Pa and 0.1 ave. strain rate.

EXPERIMENT (C) - Below are links to three movies made of the experiment. The cornstarch suspension was thoroughly mixed between each run.

Strike-Slip Movie

Oblique Movie

Orthogonal Movie

Implications and applications

Due to its dilatant behavior, cornstarch suspended in water is not a good analog for modeling a Newtonian lower crust. However, workers have suggested that crystal-rich magmas behave in a dilatant manner (Smith, 1997; 2000), as evidenced by brittle fractures in igneous intrusions that are cross-cut by fluid flow of the same material. This implies that a cornstarch suspension could be a useful analog for modeling deformation and flow in crystal-rich magmas, and that this type of flow may be important in the modeling of all igneous intrusions as crystal content increases with time.

Dilatant microstructures in clays have been found along actively deforming decollement zones in Barbados. These structures are interpreted to have formed due to high pore-fluid pressures in the clay sediment, resulting in heterogeneous strain and two main fabrics. The dominant fabric is characterized by a strong preferred orientation of clay minerals, whereas the other struuctures that form are small pods of randomly oriented clay minerals. These areas are interpreted to have formed due to dilatant behavior of the clays while suspended in water in aareas of high pore-fluid pressure, much like the cornstarch suspended in water. So, the cornstarch material may be potentially used as an analogue for modeling dilatant behavior in major fault zones.

Aside from research-related uses, the corstarch material probably has the most potential to be used as a teaching tool to younger students, such as elementary and middle school. Its dilatant behavior is very strange to most people, and it can be used to demonstrate the properties of liquids and solids, and as an analogue for flowing molten rock.

Works cited

Smith, J. V., 1997, Shear thickening dilatancy in crystal-rich flows: Journal of Volcanology and Geothermal Research, 79, p. 1-8.

Smith, J. V., 2000, Textural evidence for dilatant (shear thickening) rheology of magma at high crystal concentrations, Journal of Volcanology and Geothermal Research, 99, p. 1-7.

Takizawa, S., aand Ogawa, Y., 1999, Dilatant clayey microstructure in the Barbados decollement zone: Journal of Structural Geology, 21, p. 117-122.

Casas, A. M., Gapais, D., Nalpas, T., Besnard, K., Roman-Berdeil, T., 2001, Analogue models of transpressive systems: Journal of Structural Geology, 23, p. 733-743.

Sokoutis, D., Bonini, M., Medvedev, S., Boccaletti, M., Talbot, C., and Koyi, H., Indentation of a continent with a buitl-in thickness change: experiment and nature: Tectonophysics, 320, p. 2433-270.