One-dimensional Differential Newtonian Analysis for Applications in Saliva Rheology

Abstract

Oral and systemic health starts with healthy saliva. Saliva's functionality is affected by its rheology. Thus, alterations in saliva rheology may cause or indicate unhealthy biological function. ``Sticky saliva'', a subjective pathological description used by health professionals to indicate abnormal saliva mechanics, is linked to oral health issues, like cavities and xerostomia, and may indicate systemic health conditions, such as multiple sclerosis and HIV. Therefore, quantifying saliva's ``stickiness" or its non-Newtonian behavior with physical science based metrics (i.e. viscosity, surface tension, elasticity) is critical for understanding the relationship between its mechanics and health outcomes.

Elongational flow is the main kinematic feature that distinguishes the coupling between the oral cavity and saliva mechanics. Therefore, our effort to quantify saliva stickiness pays special attention to its response to elongation. Capillary break-up rheometry (CBR) is a common technique for characterizing extensional flow properties. CBR is ideal for quantifying low-viscosity fluids, like saliva, because it does not require a force measurement. Instead, extensional flow properties are determined by monitoring the resulting midfilament evolution after an approximate axial step-strain is imposed on a fluid sample. The standard CBR analysis requires several approximations and corrections to maintain a purely kinematic approach. We have re-examined CBR foundations with a differential 1D Newtonian model to eliminate the large correction factors required when only measuring the midfilament thinning rate. Our analysis indicates filament free surface curvature gradients are the key measurement quantities required to accurately determine extensional properties when axial force is not measured. Thus, we present the development of a 1D differential Newtonian analysis that requires measurements of the fluid filament curvature and its gradients to determine the surface tension to viscosity ratio. We evaluate the performance of our 1D differential analysis with experimental CBR data and numerical data generated by a 1D Newtonian model.

We also explore methods to expand the measurement capabilities of current CBR set-ups with the 1D differential analysis. We simulate viscoelastic filament dynamics with a 1D Oldroyd-B model and evaluate the performance of the 1D differential method during the early viscous phase. We begin with the traditional but unrealistic CBR assumptions of long, unstable filaments with zero initial polymer stresses at the end of stretch (start of CBR measurement). The results suggest the 1D differential approach coupled with the standard viscoelastic CBR analysis can facilitate measurements of multiple rheological parameters from a single sample.

Finally, we investigate the performance of the 1D differential analysis during the stretching process. We first model the filament evolution during the axial step-strain to demonstrate the stretch history must be considered in the CBR analysis for viscoelastic fluids. We also model a stretch history that avoids filament break-up to extend the lower limit of the standard CBR method's viscosity range.