Optimal Capillary Rheometer Methods for Newtonian Fluids

Abstract

Human saliva performs multiple functions and is intimately tied to oral and systemic health. These functions are linked to salivary mechanics and therefore its rheology. The term ‘sticky saliva’ is used by health professionals to indicate abnormal salivary mechanics. These are in turn linked to oral health challenges like xerostomia and caries, which may indicate systemic issues. Changes in salivary rheology may therefore serve as indicators of systemic health disorders. In a combination of flows involving shear and elongation, elongational effects are dominant for such low-viscosity elastic liquids. Therefore, our efforts focus on characterizing low-viscosity elastic fluids in elongational flow. Capillary breakup rheometry (CBR) is a common technique for characterizing filament forming fluids. Properties are determined from kinematic measurements near the point of minimum filament radius. This technique is advantageous as it does not require force measurement and can handle small sample volumes. Traditional CBR analyses to determine the surface tension-to-viscosity ratio (termed ratio) require a slew of approximations, including reliance on filament breakup, to circumvent the measurement of force. The differential Newtonian analysis of McCarroll et al. (2016) eliminates most assumptions, including reliance on breakup. This analysis indicates that accurate determination of the filament free surface and evaluation of curvature gradients are key to characterizing extensional properties accurately from kinematics. The challenges associated with this analysis are twofold: accurate evaluation of higher-order gradients from pixelated images is required and determination of the ratio now relies on the choice of stretch history. We first examine the viability of finite difference stencils for higher-order derivatives of low-resolution data, with an emphasis on the evaluation of derivatives of the digitized free surface radius obtained from pixelated and denoised images. We investigate roundoff error estimates for low-resolution data, following which, procedures to obtain an optimal approximation to the derivative are made from estimates of truncation and roundoff error. We examine the efficacy of higher-order stencils in the determination of derivatives from numerical experiments on synthetic data. Our results indicate that higher-order stencils allow for larger grid spacing and reduction in error, especially for low-resolution data. We explore the effect of stretch speed on ratio measurement for viscous Newtonian fluids. The challenges in evaluating the ratio under limits of fast and slow stretch are examined by simulating the filament dynamics when stretched from rest with a 1-D slender filament model and evaluating the performance of the differential analysis under conditions of reduced spatial resolution. The analysis of McCarroll et al. (2016) provides a two orders of magnitude improvement when measurements are made away from breakup during stretch. The results suggest considering a ramp function to breakup with moderate stretch speeds. Current CBR analyses require the evaluation of spatial or temporal derivatives and/or rely on breakup. In addition, these analyses allow determination of only one dynamic parameter. By re-examining the effect of inertia and considering radius profiles during small oscillating extensions, we extend the lower limit of the standard CBR range (Rodd et al., 2005). Our analysis allows for simultaneous characterization of multiple parameters for a Newtonian fluid kinematically. We evaluate the performance of our analysis computationally to determine a regime for optimal measurement of parameters under conditions of full and reduced resolution. By accounting for inertia, these new oscillatory protocols can analyse two or more physical properties, most probably more accurately for low-viscosity fluids.