Expert-Informed Squeeze Flow Analysis

• Expert-informed squeeze flow analysis is a physically rigorous method that integrates constitutive modeling, experimental constraints, and domain knowledge to study yield stress fluids.
• It employs advanced Bayesian calibration and uncertainty quantification to reconcile experimental data with model predictions, reducing bias inherent in traditional rheometric methods.
• This approach enhances process design in soft-matter engineering by accurately capturing complex behaviors such as thixotropy, pseudo-plug formation, and structural kinetics.

Expert-informed squeeze flow analysis refers to the rigorous, physically-informed, and uncertainty-quantified methodology for interpreting, modeling, and predicting the behavior of yield stress fluids, complex suspensions, or structured materials under squeeze-flow conditions, with explicit integration of domain knowledge and experimental constraints. Unlike approaches that rely solely on simple rheometric characterization or purely empirical constitutive fits, expert-informed analysis deploys advanced constitutive modeling, careful protocol design, and probabilistic calibration—often within Bayesian frameworks—to reconcile models with experimental squeeze-flow data even in the face of model bias, epistemic uncertainty, and microstructural complexity.

1. Fundamental Models and Governing Equations

Squeeze flow generally involves a soft material, typically a yield stress or viscoplastic/thixotropic fluid, compressed between parallel plates under prescribed loading or displacement. The axisymmetric, incompressible, low-Reynolds-number squeeze-flow regime is governed by:

• Continuity: $\nabla \cdot \mathbf{u} = 0$
• Momentum: $$\rho(D\mathbf{u}/Dt) = -\nabla p + \nabla \cdot \boldsymbol\tau$$

where the deviatoric stress $\boldsymbol\tau$ is provided by a constitutive law. Advanced expert-informed models account for microstructural structure parameters $\lambda(\mathbf{x},t)$ evolving according to breakdown/build-up kinetics:

$$\frac{D\lambda}{Dt} = -a\,\dot\gamma\,\lambda + b\,(1-\lambda)$$

The structural variable $\lambda$ then modulates rheological properties nonlinearly, as in the regularized, $\lambda$-dependent Herschel–Bulkley law:

$$\tau = \tau_y(\lambda)\big[1-e^{-m\dot\gamma}\big] + K\,\dot\gamma^{n(\lambda)}$$

with $\tau_y(\lambda)$ and $n(\lambda)$ varying linearly with $\lambda$ from "no structure" ($\lambda=0$) to "full structure" ($\lambda=1$) (Florides et al., 2023).

2. Bayesian and Uncertainty-Quantified Squeeze Flow Calibration

Expert-informed squeeze flow analysis systematically confronts the gap between canonical rheometric characterizations and the effective behavior observed during complex squeeze-flow experiments. In high-fidelity pipelines, Bayesian model calibration is employed:

• Parameter vector: $$\theta = [\eta_0,K,n,\tau_y; V, H_0, F; \sigma_\text{bias}]$$
• Expert-informed priors: Broad, physically justified bounds on rheological parameters (e.g., $\tau_y\in[1,200]$ Pa), not tied to bulk rheometry
• Likelihood: Measurement-model discrepancy is explicitly included (e.g., additive Gaussian-process bias on plate radius–time curves)
• Predictive analysis: Posterior distributions over parameters allow calculation of credible intervals on force, displacement, or sample radius trajectories

This approach reveals that priors strictly informed by classical rheometry (so-called "rheo-informed") often yield inappropriately high yield stress values ($\tau_y \approx 75$–$125$ Pa), inconsistent with squeeze-flow data, and generate poor posterior predictive performance. By contrast, expert-informed broad priors enable the Bayesian inference to discover much lower effective $\tau_y$ (e.g., $8.8\pm5.8$ Pa), with sharply improved fit to observed radius–time or height–time data and physically meaningful uncertainty quantification (Rinkens et al., 15 Jan 2026).

3. Constitutive Complexity: Thixotropy, Pseudo-Plugs, and Nonlocality

State-of-the-art analysis recognizes that complex fluids may exhibit thixotropy, structural rejuvenation, viscoelastic stresses, and nonlocality. For semisolid or thixotropic suspensions:

• Structural parameters evolve on the squeeze timescale.
• Constitutive exponents ($n$) vary—shear-thinning $(n\sim 0.2)$ at low structure, shear-thickening $(n\sim 1.4)$ at high structure.
• The material response during rapid initial loading stages ($t \lesssim 0.01$ s) is elastoviscoplastic, requiring distinct modeling from the pure viscoplasticity operative at longer times.

In Bingham or Herschel–Bulkley fluids, expert asymptotic expansion demonstrates that the so-called "plug" region (flat velocity profile at the gap center) is not truly unyielded, but weakly yielded at higher order—a "pseudo-plug"—because slow spatial variation of the plug speed induces extensional stress exceeding the local yield criterion (Muravleva, 2013, Muravleva, 2019).

4. Model Selection, Identifiability, and Data-Informed Decision Making

Expert-informed methodologies explicitly address the limitations of model transferability from idealized flows to complex squeeze scenarios. Bayesian evidence (model plausibility) and posterior predictive checks reveal when standard rheological models are unable to capture experimental squeeze-flow data—often due to non-universality of yield stress, missed structural effects, or inadequate accounting of spatial heterogeneity. Model selection penalizes unnecessary complexity but shows that, for squeeze flow, minimally sufficient models (e.g., biviscous power law) greatly outperform both naive Newtonian and "rheo-informed" variants when properly calibrated (Rinkens et al., 15 Jan 2026, Rinkens et al., 2023).

Typical protocol:

Workflow Step	Rheo-Informed Analysis	Expert-Informed Analysis
Constitutive priors	Derived from rheometer	Broad, physical bounds
Model fit to squeeze data	Poor	Accurate
Posterior $\tau_y$	High ($\sim$78 Pa)	Low ($\sim$9 Pa)
Predictive coverage	Underfit	Encompasses data
Model selection (plausibility)	Favors alternative	Favors credible model

The Bayesian framework robustly quantifies both parameter and model uncertainty, providing intervals for unobservable quantities (e.g., core plug radius, flow zone fraction) and highlighting cases where additional mechanism (e.g., viscoelasticity, structure kinetics) is required (Rinkens et al., 15 Jan 2026, Rinkens et al., 2023).

5. Algorithmic, Computational, and Experimental Guidelines

Expert-informed squeeze flow analysis requires:

• High-fidelity simulation: Typically Lagrangian or ALE finite element methods (e.g., 20×20 axisymmetric mesh, refined at rim), Newton–Raphson iterations, and regularization schemes (Papanastasiou parameter $m\sim 300$ s).
• Dual loading protocols: Early "burst" loads to trigger elastoviscoplastic response, followed by controlled displacement or force trajectories to sample full viscoplastic and structural-kinetic regimes.
• Parameter sweeps: Systematic exploration of Bingham number, Reynolds number, power-law exponents, and structure kinetics ($a$, $b$) to match observed height or radius evolution (Florides et al., 2023).
• Sensitivity checks: Mesh/time-step independence, quantification of solution bias, and friction/adhesion effects.

Experimental practices require precise measurement of normal force, gap/plate radius, and careful temperature control for isothermal material parameterization.

6. Context, Applications, and Extensions

Expert-informed squeeze flow analysis underpins precision rheometry, process design, soft-matter engineering (gels, suspensions), and operational interventions (e.g., squeeze cementing in well repair (Izadi et al., 2023)). In cementing or invasion scenarios, stochastic material gaps, yield-number control, and direct probabilistic assessment of flow/plug front penetration are crucial. Algorithmic solutions often require computationally intensive variational or augmented Lagrangian solvers to accurately resolve yielded and unyielded zones under gaps with significant stochastic heterogeneity.

A plausible implication is that transferability of classical rheometric parameters cannot be assumed for real flow scenarios; only quantitatively robust, expert-informed, uncertainty-calibrated squeeze flow analysis delivers physically meaningful predictions at the device, process, or operations scale.

7. Limitations and Research Trajectories

Despite its rigor, expert-informed squeeze flow analysis is constrained by:

• Neglect of inertia outside of high-frequency oscillatory regimes
• Potential nonlocality (microstructure, wall slip, boundary layer effects) not captured by mean-field constitutive models
• Computational cost of full Bayesian inversion and stochastic sampling, especially under high-dimensional uncertainty or in large-scale applications

Future developments target improved identification techniques (multimodal data fusion), advanced constitutive models with evolving structure and elasticity, and integration with in-situ imaging or velocimetry to directly inform and validate model predictions (Florides et al., 2023, Rinkens et al., 15 Jan 2026). The domain remains at the interface of computational mechanics, statistical inference, and advanced rheological experimentation.