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Importance and methods to control, vary, and characterize mud strength for studying locomotion
Divya Ramesh, Gargi Sadalgekar, Qiyuan Fu, Zachary Souders, Jack Rao, Chen Li
TL;DR
Mud locomotion lacks the controlled, characterized substrates available for sand. The paper develops methods to prepare uniform clay mud with variable yield strength and track strength drift. Mud is weaker during penetration and sticks more during extraction than other flowable substrates, increasing locomotion difficulty.
Problem
Locomotion on and within muddy substrates remains poorly understood because methods for controlling, characterizing, and varying mud are lacking.
Method
The paper develops methods to prepare uniform mud with controlled, variable yield strength, characterize it, and track temporal drift.
Results
Mud is 1–2 orders of magnitude weaker than other flowable substrates during penetration and sticks more during extraction, inducing downward pulling force.
Takeaways & Limitations
Mud’s weaker penetration resistance and greater extraction stickiness make locomotion more challenging than on other flowable substrates.
Takeaways & Limitations
Characterizing muddy substrates also requires accounting for stickiness and how forces vary with wetness, beyond vertical penetration strength alone.
Abstract
from arXiv · showhide
Animals and robots encounter mud at the water-land interface. Like sand, mud can stay solid or flow like a fluid. Unlike sand, the yield strength of mud at which solid-fluid transitions occur depends on not only the amount of solid relative to fluid (water in mud, air in dry sand), but also how much coarse grains and fine clay are within the solid. Despite understanding of locomotion on/within dry sand dominated by coarse grains with repulsive normal forces and friction, little is known for mud dominated by fine clay with strong cohesion. Here, we developed methods to prepare uniform mud of controlled, variable yield strength and characterize and track its drift from water evaporation. Compared to other flowable substrates, mud strength measured by upward force during penetration is weaker and can vary more, and mud sticks more during extraction to pull downward, making it more challenging for locomotion.
1. Introduction
Flowable substrates span sandy and muddy regimes whose behavior depends on particle composition and wetness. Because muddy locomotion lacks the control and characterization available for sand, this paper develops controlled clay mud methods for studying solid–fluid transitions.
- Substrate classification: Fine clay fraction η and solid volume fraction ϕ describe granular composition and wetness, respectively.For dry sand, ϕ measures compaction because pore volume contains air rather than water.
- Substrate classification: Coarse-grained sandy substrates are dominated by repulsive frictional contacts, whereas fine-clay muddy substrates develop stronger cohesion from colloidal effects.Small amounts of water can add weak cohesion between coarse grains through surface tension.
- Research gap: Equivalent understanding of locomotion on and within muddy substrates is lacking because methods to control, characterize, and vary mud are limited.Existing locomotion research has focused extensively on sandy substrates, especially dry sand.
- Methodological challenge: Standard dry- and wet-sand preparation methods are unsuitable for sticky mud, and common fixed-depth force measurements are insensitive across much of its transition regime.These limitations motivate new preparation and strength-characterization tools for muddy substrates.
- Study approach: The study develops low-cost methods to control and vary muddy-substrate wetness, characterize yield strength, and track its temporal drift through solid–fluid transitions.The methods are intended to support systematic locomotion studies using uniform, variable-strength mud.
- Solid–fluid transitions: For a given fine clay, clay-mud yield strength increases monotonically with ϕ by up to several orders of magnitude.Clay mud has qualitatively similar rheology to mud containing both fine clay and coarse grains in the solid–fluid transition regime.
2. Materials and Methods
The study used Kaolin clay, defined mud wetness by solid volume fraction, and developed automated mixing and sealed storage methods to prepare uniform mud while limiting property drift.
- Materials: Kaolin clay was selected because it is inexpensive, widely used in previous mud studies, and supports comparison with prior results.Edgar Plastic Kaolin and Georgia Kaolin behaved qualitatively similarly but produced different quantitative results.
- Wetness specification: Solid volume fraction ϕ was used to specify mud solid concentration as solid-particle volume divided by total solid–water mixture volume.The study also defined solid weight fraction w and converted between ϕ and w using particle and water densities.
- Mud preparation: The mixer dispensed small powder amounts every 0.5 seconds because adding large amounts at once formed clumps and mixed poorly.The mixer operated slowly, between the third and fifth speed settings, to maintain uniform mixing.
- Storage and scaling: Multiple batches were combined in large testbeds, manually remixed, and immediately sealed to maintain consistency and limit evaporation-driven drift.A 1.02 m × 0.51 m × 0.16 m testbed containing 49.3 kg of ϕ = 34% mud required 14 batches.
- Storage and scaling: Mud was stored in an airtight container with plastic wrap, sealing strips, and latching straps whenever it was not used.These methods were tested by tracking mud-strength drift over multiple days.
2.4. Safety during mud preparation
Mud preparation required controls for airborne clay and crystalline silica, including local ventilation, containment, protective equipment, and exposure monitoring.
- Hazards: Kaolin particles can become airborne during preparation, and kaolin may contain crystalline silica that poses inhalation risks.The reported kaolin contained 0.5% crystalline silica by weight.
- Controls: A ventilation system with a small-particle filter and a nearby custom duct was used to remove dust around the mixer.The ventilation system was turned on before mixing and remained on for 2–3 hours afterward.
- Controls: A plastic tablecloth contained residual clay dust near the automated mixer, limiting its spread through the room.The containment measures complemented the ventilation system.
- Personal protection: Users were instructed to wear N95 masks and long-sleeve gloves while handling, weighing, and pouring clay powder.Clothing worn during mixing was also to be washed with water afterward.
- Exposure monitoring: Personal monitoring found crystalline-silica exposure below 6.9 μg/m3 and respirable-dust exposure of 0.047 mg/m3 during and after mixing.These measurements covered approximately 5 hours of mixing and 1 hour afterward.
- Exposure monitoring: Particle monitoring in the shared space found respirable-dust exposure well below OSHA’s 5 mg/m3 permissible exposure limit.The monitoring was performed for approximately 6 hours, more than 21 days after mixing.
- Exposure monitoring: Similar exposure tests should be repeated when the system is installed elsewhere.The reported measurements apply to the tested ventilation setup.
2.5. Determining wetness range of solid–fluid transition regime
The study estimated settling and fracture limits by incrementally varying solid volume fraction ϕ, then used controlled compositions and sealing methods to study mud strength and its drift.
- Transition limits: The solid–fluid transition regime lies between settling and fracture limits, denoted ϕs < ϕ < ϕf.Mud wetness was characterized by varying solid volume fraction ϕ.
- Settling limit: The settling limit was approximated by increasing ϕ in 1–2% increments and identifying the lowest concentration without visible settling after 5 minutes.The procedure began with fluid mud near ϕ = 5%, followed by mixing, settling, and visual inspection of the lower material.
- Measurement caveats: The settling and fracture limits were approximate because more accurate measurements required waiting substantially longer.The text gives 24 hours for settling and 1 hour for fracture-limit assessment as examples.
- Fracture limit: Georgia Kaolin mud was harder to fracture by horizontal dragging than Edgar Plastic Kaolin mud, so vertical penetration was more reliable.Georgia Kaolin had finer particles than Edgar Plastic Kaolin.
- Test compositions: Experiments used Edgar Plastic Kaolin at ϕ = 14%, 27%, 34%, and 39%, and Georgia Kaolin at ϕ = 27%, 34%, 39%, and 42%.Most compositions were within the transition regime; Georgia Kaolin at ϕ = 42% was above the fracture limit.
- Drift control: Airtight lids, plastic wrap, sealing strips, and latching straps were used to reduce evaporation and track strength drift over multiple days.These sealing methods were applied whenever the mud was not being used.
2.8. Mud container size to minimize boundary effect
Boundary effects can inflate measured penetration forces, so the study used a large, deep mud container and custom force-sensitive penetrometers that measured force across depth.
- Boundary effects: Measured force becomes larger than the infinite-container value when the probe approaches the container bottom or sidewalls.The experiments therefore positioned the probe away from boundaries.
- Container design: The test container measured 1.02 m × 0.51 m × 0.16 m, allowing sidewall effects to be avoided.The container was filled to 0.12 m, or three-quarters of its height, to reduce bottom effects.
- Container validation: No significant boundary effect was found for Edgar Plastic Kaolin mud at ϕ = 34% and ϕ = 39% when fill height exceeded 10 cm.A boundary effect was observed at a lower fill height of approximately 3 cm.
- Penetration measurement: Upward force on a horizontal disc increases with substrate strength and is proportional to intruder area.Moving the test location can resolve spatial variation at scales larger than the intruder.
- Instrument limitations: Commercial penetrometers were generally too insensitive for mud in the solid–fluid transition regime, which is 1–2 orders of magnitude weaker than soil and dry sand.Only the most expensive tested penetrometer measured the stronger ϕ = 39% mud, and it still lacked sensitivity across most of the regime.
- Instrument limitations: Commercial instruments also use fixed penetration depths and cannot measure how force changes with depth during intrusion and extraction.Depth-dependent forces matter because locomotion involves changing substrate challenges and extraction energy loss.
- Custom instruments: Two custom penetrometers were developed to measure mud force as a function of depth in the solid–fluid transition regime.The stationary device controls penetration speed automatically, whereas the portable manual device trades precision for mobility.
2.10. Stationary automatic penetrometer
The stationary automatic penetrometer uses controlled vertical motion, force sensing, and position measurement to characterize mud resistance as a function of depth.
- The penetrometer measures forces up to 49 N with 0.0011 mm position resolution and 10 μN force resolution.
- The penetrometer pushes an intruder disc into a substrate at constant speed while measuring vertical resistive force and displacement.
- A motor-driven threaded-rod system moves the disc vertically, while a single-axis load cell measures force along the vertical direction.
- The system records force and motor position to obtain force as a function of displacement, from which penetration depth is determined.
- Disc radius was reduced from 3 cm to 1 cm for stronger mud when the larger disc would exceed the force-sensor limit; forces were area-scaled for comparison.
2.11. Data processing for stationary automatic penetrometer
The stationary system processes synchronized force and position data into force–depth curves, using contact detection, interpolation, filtering, and controlled data alignment.
- Position and force recordings are synchronized by timestamps, and position data are interpolated to match the force-sampling frequency.
- A band-stop filter removes cyclic noise caused by small cyclic movement along the threaded rod.
- Mud-surface contact is identified when force exceeds 0.03 N, allowing disc depth to be offset to zero before plotting force against depth.
- The portable penetrometer retains the basic penetration-and-extraction mechanism but uses manual LEGO gearing and Hall-effect displacement sensing.
- Unresisted penetration could become too rapid at lower ϕ, so rotary damping or servo-motor resistance was added to keep the magnet detectable.
2.13. Data processing for portable manual penetrometer
Portable-penetrometer data are processed into comparable force–depth profiles by identifying contact, separating phases, cropping depth, and averaging trials; the portable and stationary systems are cross-checked.
- The analysis separates penetration and extraction phases using displacement and time data, then plots vertical force against depth.
- For stationary measurements, initial contact is defined by a force threshold above 0.3 N before force and displacement are cropped and replotted.
- Penetration data are cropped at 3 cm depth and interpolated so measurements can be averaged across trials, locations, and days.
- Portable-penetrometer characterization was compared with stationary-penetrometer characterization across mud strengths to verify force–depth profile accuracy.
- Spatial comparisons average three trials at each of four locations, then average those location means across each time interval.
2.15. Experiments to characterize dependence on mud strength wetness
The experiments characterize mud yield strength across clay volume fractions and track spatial uniformity and temporal drift over hours to many days, including drying-related changes.
- Yield strength was measured from vertical force versus depth for Georgia Kaolin mud spanning ϕ = 20%–42% across transition and fractured-solid regimes.
- Penetration was limited to 4 cm because deeper tests could exceed sensor range; three trials were collected for each volume fraction and the mud was remixed afterward.
- Long-term drift was tracked with portable-penetrometer tests for Georgia Kaolin mud at ϕ = 27%, 34%, 39%, and 42% over 24–114 days.
- Spatially distributed tests were reduced from 18 locations initially to 4 on subsequent days after the mud was found to be spatially uniform.
3. Results and Discussion
Mud strength varies strongly with wetness and drifts over time, while penetration and extraction produce qualitatively different forces. Custom penetrometers revealed that mud is weaker, stickier, and more locomotion-challenging than many comparable substrates.
- Vertical force vs. depth in mud is complex: During intrusion, vertical force was always upward, increased nonlinearly with depth, and plateaued, unlike the linear depth dependence observed in dry and wet sand.Force decreased substantially but remained upward when the intruder stopped, then diminished quickly when upward motion resumed.
- Vertical force vs. depth in mud is complex: During extraction, cohesive mud generated downward force that could persist after the intruder left the surface until sticking mud detached.For transition-regime mud at ϕ = 20–41%, the downward force increased in magnitude as the intruder became shallower; ϕ = 42% mud showed a nonmonotonic pattern.
- Controlled mud is spatially uniform: Mud preparation produced excellent spatial uniformity: penetration force at 0.64 cm averaged 14.3 ± 0.7 N across four locations, with 2–9% trial-to-trial variation.The four location means were 14.1 ± 0.6 N, 14.9 ± 0.3 N, 13.4 ± 0.3 N, and 14.7 ± 1.3 N.
- Strength drifts more over a long time but is much slower than without sealing: Within a day, yield strength changed by about 14% on average, but over multiple days it drifted by about 2 times.Measured increases were 31% over 27 days at ϕ = 27%, 184% over 114 days at ϕ = 34%, 138% over 106 days at ϕ = 39%, and 104% over 24 days at ϕ = 42%.
- Strength drifts more over a long time but is much slower than without sealing: Sealing slowed long-term drift substantially: prepared mud increased by 31–184% over 24–114 days, versus a 133-fold increase in seven days when left open to dry.Over the solid–fluid regime, mud yield strength could vary by 3 orders of magnitude with wetness, more than other flowable substrates usually varied.
- Mud is more challenging for locomotion than other flowable substrates: Mud in the solid–fluid transition regime was typically over an order of magnitude weaker than dry sand and snow, and two orders weaker than wet sand and soil.The same animal, robot, or vehicle would sink one to two orders of magnitude more in wetter mud and at least as much on drier mud; only dry mud far above fracture strength was stronger.
- Mud is more challenging for locomotion than other flowable substrates: Mud sticking creates large downward and backward pulling forces during extraction, increasing bogging risk and mechanical energy loss during locomotion.Despite the large downward extraction force, energy lost to mud was about the same as on sand, where downward force was negligible.
- Summary: Custom penetrometers measured force continuously with depth during both intrusion and extraction, covering weak transition-regime mud and stronger, drier mud.Their capabilities address the inadequacy of commercial fixed-depth penetrometers because mud’s force–depth relationship is nonlinear and varies with wetness.
Funding
The study received funding from the Burroughs Wellcome Fund, Johns Hopkins University, and the National Science Foundation.
- Funding came from the Burroughs Wellcome Fund Career Award at the Scientific Interface.
- Additional support came from a Johns Hopkins University Bridge Grant and an NSF Foundational Research in Engineering grant.
Data availability
Codes for real-time control and data acquisition of both penetrometers are publicly available through Figshare.
- Codes for the portable manual and stationary automatic penetrometers are available online.The repository is hosted on Figshare.
Supplementary figures
The supplementary figures document boundary effects, penetration-test processing, and iterative penetrometer design, while comparing force measurements across mud conditions and depths.
- Penetration-force comparisons used Edgar Plastic Kaolin mud at solid volume fractions of 34% and 39%, with separate trials shown for each treatment.
- Lower mud height produced a rapid end-of-penetration force increase that was absent at larger height, indicating a bottom boundary effect.The comparison used mud heights of approximately 10 and 3 cm.
- The supplementary processing figures show stationary automatic and portable manual penetrometer measurements, including displacement, depth, and force over time.Depth is offset to zero at initial mud contact, identified at a force of 0.03 N.
- The penetrometer designs were iteratively modified to increase depth, reduce wobble, prevent rack bending, improve support, and maintain disc perpendicularity.Later versions used longer rods, reinforced supports, metal gears, and added weights.
- Force data were normalized by the mean force at each depth for ϕ = 42%, with error bars representing ± s.d. across three trials.These tests used Georgia Kaolin clay mud.