Predicting thickness perception of liquid food products from their non-Newtonian rheology

The study addresses how the perceived thickness (a key mouthfeel attribute) of liquid foods relates to their underlying rheology. Prior attempts to link sensory thickness to simple rheological measures (e.g., viscosity at a single shear rate, linear viscoelastic moduli) or tribology often used oversimplified models of oral processing and neglected the non-Newtonian, shear-thinning nature of most foods, as well as complexities such as saliva interactions, wetting, deposition, and particle effects. There is an ongoing psychophysical debate whether perceived intensity follows a logarithmic (Weber–Fechner) or power-law (Stevens) relationship with the physical stimulus. For liquid food thickness, the relevant shear conditions in the mouth have been unclear, with many studies assuming a single characteristic shear rate. This work proposes and tests a physical, biophysically grounded model of dynamic squeeze flow between tongue and palate for non-Newtonian fluids, aiming to predict perceived thickness from measured rheology without adjustable parameters, and to evaluate whether perception follows a logarithmic or power-law dependence on the mechanical stimulus (shear stress on the tongue).

Prior research linked mouthfeel to rheological parameters (shear viscosity, G' and G'') and tribological properties, but oral processing involves complex hydrodynamics (shear, elongation, lubrication) and interactions with saliva, wetting, and deposition that simple models overlook. Many foods are shear-thinning rather than Newtonian, complicating correlations based on a fixed shear rate. Psychophysically, Weber–Fechner suggests perceived intensity scales with the logarithm of stimulus, whereas Stevens posits a power-law; evidence across senses has supported both, with recent Bayesian analyses favoring logarithmic scaling for some modalities. Earlier oral thickness models (e.g., DeMartine; Kokini) used static squeezing and simplified flow, potentially underestimating stresses and employing adjustable biophysical inputs. Additionally, for very viscous or semi-solid foods, power-law fits were reported, but for thin liquids the relevant shear-rate distribution during dynamic oral processing was not incorporated. This study builds on these gaps by integrating shear-thinning rheology into a dynamic squeeze-flow framework and testing it against sensory data across a broad stress range.

Materials: Three sets of samples were used. Sets 1 (custom-made) and 2 (commercial-like) comprised 14 bouillon soups varying in xanthan gum and starch content with salt; viscosities spanned ~1 mPa·s to ~1 Pa·s. Set 3 (from literature) comprised xanthan gum solutions with higher viscosities to extend the stress range while keeping elasticity negligible. Rheology: Shear flow curves (40 °C) were measured using an Anton Paar MCR302 cone-plate rheometer (50 mm, 1°) with humidity control. Samples exhibited shear thinning and were fit to a power-law constitutive equation: σ = κ γ̇^n, extracting consistency κ and index n for each sample (Table 1). Extensional rheology via filament stretching (plate–plate, 5 mm, MCR302 with high-speed imaging) confirmed negligible elastic/extensional contributions in the studied range. Wetting tests measured contact angles on paper; all bouillons showed similar partial wetting (θ ~ 30°) and pinned contact radius over 0–30 s. Sensory analysis: An experienced trained panel (11–14 members) evaluated thickness on a 16-point absolute category scale (0–15) using a modified Spectrum method. Samples were served blind, sequential monadic, randomized order per replicate, at ~40 °C. Two replicates per product; palate cleansers provided. Statistical analysis used PROC MIXED with Respondent and Product as fixed factors and their interaction random; least square means and multiple comparisons determined product differences. For set 3, literature scores were converted to the current scale via a specified transformation. Dynamic squeezing model: The oral cavity was modeled as two parallel rigid plates (palate and deformable tongue approximated as parallel plates due to soft lubrication and tongue deformability). A liquid layer of initial gap h0 ≈ V0/(πR^2) ≈ 2 mm (with tablespoon volume V0 ≈ 4 mL) is squeezed between tongue and palate over a circular contact of radius R ≈ 2.5 cm. Typical lingual normal force FN ≈ 500 mN and tongue speed V ≈ 15 cm/s are assumed constant based on literature; assessment time t ≈ 1.2 s. The shear-thinning rheology is incorporated into a lubrication analysis of dynamic squeeze flow, accounting for both sliding and squeezing contributions. The local shear stress on the tongue scales as σ ∝ κ V^n h^{-1} with an additional term from squeezing that depends on FN, h, R, and V, yielding a total stress expression that integrates the distribution of shear rates over the evaluation time rather than assuming a single characteristic shear rate. Under the approximation V ≫ squeezing velocity, the temporal evolution of the gap h(t) is obtained and used to compute the total stress experienced during assessment. With fixed biophysical parameters (R, h0, FN, V, t), the predicted stress depends only on measured κ and n for each sample. The predicted stress is then related to the panel’s mean thickness scores to test logarithmic (Weber–Fechner) vs power-law (Stevens) psychophysical relationships.

- All bouillons displayed pronounced shear-thinning, well described by σ = κ γ̇^n; κ and n varied with composition (xanthan gum and starch types/levels). Some samples exhibited very weak viscoelasticity; extensional measurements confirmed elasticity was negligible in the considered regime. - Biophysical and geometric parameters characterizing oral processing during thickness assessment were established: R ≈ 2.5 cm (from licking test), contact angle θ ≈ 30°, initial gap h0 ≈ 2 mm (from 4 mL volume), FN ≈ 500 mN, V ≈ 15 cm/s, t ≈ 1.2 s. - The dynamic squeeze-flow model predicts the shear stress on the tongue during evaluation without adjustable parameters, using measured κ and n. Calculated stress values for sets 1 and 2 spanned approximately 1–110 Pa. - For the bouillon datasets (sets 1 & 2), both logarithmic and power-law fits could describe the relation between mean perceived thickness (0–15 scale) and calculated stress. However, upon adding high-viscosity xanthan solutions (set 3) to extend the stress range, the logarithmic (Weber–Fechner) relationship consistently captured all data (sets 1–3) with the same fit parameters, while the power-law fit performed worse across the expanded range. - The results indicate that the human tongue behaves as a logarithmic sensor for thickness, analogous to other sensory modalities. Shear thinning critically influences perceived thickness because the dynamic process generates a spectrum of shear rates, leading to lower effective viscosities during squeezing and flow. - The model substantially improves over prior approaches by accounting for dynamic squeezing and integrating over the full stress/shear-rate history rather than correlating to viscosity at a single, arbitrary shear rate.

The study directly links non-Newtonian rheology and dynamic oral hydrodynamics to perceived thickness. By capturing the squeeze-flow mechanics and using realistic biophysical parameters, the model predicts the mechanical stimulus (shear stress on the tongue) that panelists experience and demonstrates that perceived thickness scales logarithmically with this stimulus. This resolves prior ambiguity arising from simplified static models and single-shear-rate correlations. The agreement across three sample sets—including highly viscous xanthan solutions—supports the Weber–Fechner law for oral thickness perception and suggests that during consumption of shear-thinning liquids, dynamic shear-thinning plays a central role in shaping mouthfeel. The stress range estimated by the model aligns with independent measurements of papillae deformation thresholds, reinforcing physiological plausibility. Practically, these insights allow formulation scientists to predict and design mouthfeel by targeting rheological parameters (κ, n) and considering how oral processing modifies local shear rates and stresses.

This work presents a physics-based, parameter-free framework that predicts the sensory thickness of liquid foods from their shear-thinning rheology via a dynamic squeeze-flow model of the tongue–palate interaction. The perceived thickness follows a logarithmic dependence on the calculated shear stress, consistent with the Weber–Fechner law and validated across low- to high-viscosity samples. The approach bridges rheology, biophysical oral mechanics, and sensory perception, enabling more accurate mouthfeel prediction and guiding formulation strategies via control of κ and n. Future research should extend the model to thicker and more complex systems (e.g., yield-stress fluids, strongly viscoelastic materials), incorporate saliva mixing, wetting and deposition dynamics in vivo, and evaluate interindividual variability and broader sensory attributes beyond thickness.

- Scope limited to (semi-)liquid, shear-thinning systems with negligible elasticity; the model has not yet been validated for yield-stress or strongly viscoelastic foods. - Biophysical parameters (FN, V, R, t, h0) were taken as fixed, literature-based averages; interindividual variability and dynamic changes during eating were not explicitly modeled. - Saliva interactions, bolus dilution, and in-mouth compositional changes were not incorporated beyond ensuring similar initial wetting; these factors may affect generalizability to other matrices. - Sensory data were obtained from a trained panel (11–14 participants) and focus on a single attribute (thickness); broader consumer populations and multi-attribute interactions were not assessed. - The parallel-plate approximation and lubrication assumptions neglect complex 3D tongue–palate geometries and potential transient elastic effects.