Statistical-mechanical theory of rheology: Lennard-Jones fluids
Bibliographic record
Abstract
The generalized Boltzmann equation for simple dense fluids gives rise to the stress tensor evolution equation as a constitutive equation of generalized hydrodynamics for fluids far removed from equilibrium. It is possible to derive a formula for the non-Newtonian shear viscosity of the simple fluid from the stress tensor evolution equation in a suitable flow configuration. The non-Newtonian viscosity formula derived is applied to calculate the non-Newtonian viscosity as a function of the shear rate by means of statistical mechanics in the case of the Lennard-Jones fluid. For that purpose we have used the density-fluctuation theory for the Newtonian viscosity, the modified free volume theory for the self-diffusion coefficient, and the generic van der Waals equation of state to compute the mean free volume appearing in the modified free volume theory. Monte Carlo simulations are used to calculate the pair-correlation function appearing in the generic van der Waals equation of state and shear viscosity formula. To validate the Newtonian viscosity formula obtained we first have examined the density and temperature dependences of the shear viscosity in both subcritical and supercritical regions and compared them with molecular-dynamic simulation results. With the Newtonian shear viscosity and thermodynamic quantities so computed we then have calculated the shear rate dependence of the non-Newtonian shear viscosity and compared it with molecular-dynamics simulation results. The non-Newtonian viscosity formula is a universal function of the product of reduced shear rate (gamma*) times reduced relaxation time (taue*) that is independent of the material parameters, suggesting a possibility of the existence of rheological corresponding states of reduced density, temperature, and shear rate. When the simulation data are reduced appropriately and plotted against taue*gamma* they are found clustered around the reduced (universal) non-Newtonian viscosity formula. Thus we now have a molecular theory of non-Newtonian shear viscosity for the Lennard-Jones fluid, which can be implemented with a Monte Carlo simulation method for the pair-correlation function.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".