A Lattice-Based Cellular Automata Modeling Approach for Granular Flow Lubrication

[+] Author and Article Information
Venkata K. Jasti, C. Fred Higgs

 Carnegie Mellon University, Mechanical Engineering Department, Pittsburgh, Pennsylvania 15213

J. Tribol 128(2), 358-364 (Dec 11, 2005) (7 pages) doi:10.1115/1.2164466 History: Received March 08, 2005; Revised December 11, 2005

Liquid lubricants break down at extreme temperatures and promote stiction in micro-/nanoscale environments. Consequently, using flows of solid granular particles as a “dry” lubrication mechanism in sliding contacts was proposed because of their ability to carry loads and accommodate surface velocities. Granular flows are highly complex flows that in many ways act similar to fluids, yet are difficult to predict because they are not well understood. Granular flows are composed of discrete particles that display liquid and solid lubricant behavior with time. This work describes the usefulness of employing lattice-based cellular automata (CA), a deterministic rule-based mathematics approach, as a tool for modeling granular flows in tribological contacts. In the past work, granular flows have been modeled using the granular kinetic lubrication (GKL) continuum modeling approach. While the CA modeling approach is constructed entirely from rules, results are in good agreement with results from the GKL model benchmark results. Velocity results of the CA model capture the well-known slip behavior of granular flows near boundaries. Solid fraction results capture the well-known granular flow characteristic of a highly concentrated center region. CA results for slip versus roughness also agree with GKL theory.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

Crystal growth of the snowflake simulation. (a) Image from the cellular automata simulation. (b) Photograph of a mature snowflake (59)

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Figure 2

Schematic of roughness factors

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Figure 3

Schematic of the Cellular Automata model

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Figure 4

Eight possible directions of motion

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Figure 5

Rule for boundary interaction

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Figure 6

Rule for interparticle interaction

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Figure 7

Velocity versus height from theoretical model

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Figure 8

Velocity versus height from CA model

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Figure 9

Solid fraction versus height from theoretical model

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Figure 10

Solid fraction versus height from CA model

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Figure 11

Roughness factor versus slip from GKL model and CA model




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