A method for evaluating time-resolved rheological functionalities of fluid foods

2.1 Materials

Three types of commercial food thickeners were used: starch-based (Tromeline, Nutri Co. Ltd, Japan), guar gum-based (Hightoromeal, Foodcare Co. Ltd, Japan), and xanthan gum-based (Softia S, Nutri Co. Ltd, Yotsukaichi). These thickeners are categorized as the first, second, and third-generation additives, respectively, and various improvements have been made with each generation (Moritaka & Nakazawa, 2009; Ueha et al., 2014; Waqas, Wiklund, Altskär, Ekberg, & Stading, 2017). Three concentrations of each thickener in pure water were used, as summarized in Table 1. The solution with the lowest concentration of the starch-based thickener was difficult in the USR measurement to capture the time variation of shear-thinning property with converting sufficient range of the shear rate due to the low viscosity. More than the specified amount was therefore added as shown in the parenthesis in Table 1. The specified amount was dissolved in 1 L of pure water with stirring with a spatula at room temperature of 25°C. Nine test solutions were degassed with a vacuum pump and then stored at room temperature for a day. As tracer particles for the UVP measurements, a small amount of styrene spherical particles (MCI GEL CHP20/P120, Mitsubishi Chemical Co. Ltd, Tokyo, Japan), with a mean diameter and density of 75–150 μm and 1.01 g/ml, were added to all the solutions. As 5 g of the tracer particles was added in 1 L of each solution, the volume fraction of the particles was φ = 0.05%. Based on the theoretical formula of the effective viscosity proposed by Einstein (1906), increase rate of the viscosity due to the volume fraction is roughly estimated by 2.5φ. In this experiment, the increase rate is estimated by 0.125%, and changes in the rheological properties can be sufficiently small to be ignored. For simplicity of notation, each solution is represented by a Greek numeral and an uppercase letter denoting the generation of the thickener and the concentration, respectively (see Table 1).

In the viscosity stability test, alpha-amylase (FUJIFILM Wako Pure Chemical Co. Ltd., Osaka, Japan) was used. First, 0.1 g of alpha-amylase powder was dissolved in 200 ml of pure water, then 2 ml of this amylase solution was added to 1 L of the thickened solution. The total amount of the amylase powder added was 1 ppm. This amount of amylase is almost as specified by the stability test method of thickeners determined by the Consumer Affairs Agency of Japan. The method of mixing the amylase solution and the thickened solution is specifically explained in Section 2.3.

2.2 Ultrasonic spinning rheometry

The experimental setup of USR is schematically shown in Figure 1. An acrylic cylindrical vessel (radius: R = 72.5 mm; thickness: 2 mm; and height: 60 mm) filled with a test fluid was installed in the center of a water bath for the UVP measurements and temperature control. The vessel was driven by a stepping motor as the velocity of the cylindrical wall takes a sine wave, u_wall(t) = U_wall sin(2πf_ot), U_wall = 2πf_oRΘ, where f_o and Θ represent the oscillation frequency and the rotation angle of the vessel, respectively. Oscillatory shear flow is induced by the motion of the cylindrical wall, and the flow propagates toward the central axis with an accompanying phase lag. For fluids with relatively low viscosity, the fluid cannot track the motion of the cylindrical wall immediately. There is a phase lag between the fluid near the wall and that near the central axis. For relatively high viscosity fluids, such as honey, the fluid can track the motion of the wall without a considerable phase lag. These phenomena suggest that the viscosity can be evaluated by observing the movement of the fluid. The spatiotemporal distribution of the azimuthal velocity u_θ (r, t) = (r/Δy)u_ξ was obtained using a UVP, which is also applicable for opaque fluids. Rheological properties, represented by viscoelasticity and effective viscosity, are estimated by substituting the velocity information into Navier–Stokes and constitutive equations. The theoretical background of USR has been explained in detail elsewhere (Tasaka et al., 2015; Yoshida et al., 2017).

An advantage of USR is the spatially local evaluation at each radial position in the vessel. Once the vessel is driven under the parameters (f_o, Θ) for more than the period of the oscillation, the spatial variations of the effective viscosity ${\mu }_{\mathrm{eff}}\left(r\right)$ and the effective shear rate ${\dot{\gamma }}_{\mathrm{eff}}\left(r\right)$ are obtained, where ${\dot{\gamma }}_{\mathrm{eff}}$ is ∼(10¹ s⁻¹) near the cylindrical wall and ∼(10⁻¹ s⁻¹) near the central axis. The viscosity curve ${\dot{\gamma }}_{\mathrm{eff}}-{\mu }_{\mathrm{eff}}$ can be obtained over this shear rate range immediately. Flow curve ${\dot{\gamma }}_{\mathrm{eff}}-{\tau }_{\mathrm{eff}}$ is also obtained by the integral operation on $d{\tau }_{\mathrm{eff}}={\mu }_{\mathrm{eff}}\left({\dot{\gamma }}_{\mathrm{eff}}\right)d{\dot{\gamma }}_{\mathrm{eff}}$ with a boundary condition of ${\tau }_{\mathrm{eff}}\left({\dot{\gamma }}_0\right)={\tau }_0={\mu }_{\mathrm{eff}}\left({\dot{\gamma }}_0\right){\dot{\gamma }}_0$, where τ_eff is the effective shear stress. In this paper, numerical integration is performed with ${\dot{\gamma }}_0=$3 s⁻¹, which is the minimum shear rate on the viscosity curve ${\dot{\gamma }}_{\mathrm{eff}}-{\mu }_{\mathrm{eff}}$ evaluated by USR. In this definition of differential viscosity, the power law exponent appearing in Section 3 never takes a negative value even in the limited range of the shear rate. USR can evaluate variations in the shear-rate-dependent viscosity/stress every few seconds. This local evaluation also makes it possible to evaluate the rheology of complex fluids, such as multiphase and gel–sol coexistent fluids containing dispersions with ∼(1 mm) size (Tasaka et al. 2021; Yoshida, Tasaka, & Fischer, 2019; Yoshida et al., 2017). With ordinary torque-type rheometers, these fluids cause shear-banding and wall-slip phenomena, adding bias errors to the torque measurement values, which then no longer reflect the original rheological properties.

Validation of the present USR has been conducted in studies (Ohie et al., 2022; Yoshida, Tasaka, & Murai, 2019a) with a standard torque-type rheometer (MCR 102, Anton Paar, Austria) with a plate–plate geometry. Using carboxymethyl cellulose aqueous solution, which is a representative shear-thinning fluid (Benchabane & Bekkour, 2008), Yoshida, Tasaka, and Murai (2019a) compared flow curves evaluated by USR and the torque-type rheometer. The results of both were in good agreement, indicating measurement accuracy of USR.

While USR has high applicability to complex fluids in nonequilibrium conditions, it is not always superior to torque-type rheometers in all respects. It also has a lowest limitation for viscosity evaluation, just as the limitation is specified even with a standard torque-type rheometer (Ewoldt, Johnston, & Caretta, 2015). The lowest limitation for the viscosity evaluation by USR is about 10 cSt under the experimental condition of f_o = 1.0 Hz. In the theory of USR, the oscillatory flow generated by the cylindrical wall is measured by UVP, and the viscosity at each radial position is evaluated by analyzing the velocity information. The thickness of the fluid layer moving on the cylindrical wall is about δ_v = (ν/2πf_o)^1/2, where ν is the kinematic viscosity (Ohie et al., 2022; Tasaka et al. 2021). Spatial resolution of UVP in the direction of measurement line is 0.74 mm. The viscosity therefore should be higher than ν = 10 mm²·s⁻¹ so that δ_v = (10 mm²/s /[2π × 1.0 Hz])^1/2 = 1.3 mm is thicker than the spatial resolution of UVP.

2.3 Experimental procedures

The shear-rate-dependent rheological properties of the original solutions were investigated by USR before the addition of amylase. The cylindrical vessel was filled with each of the 1 L solutions, and the temperature of the solution was controlled at 25°C by a thermostatic chamber. The USR measurements were conducted with the oscillation parameters: f_o = 1.0 Hz and Θ = π/2 rad to obtain the viscosity curves. Following the USR measurements of the original solutions, the stability after the addition of amylase was evaluated at the same temperature for the I, II-H, and III-H solutions. II and III solutions rarely react with amylase, so only the II-H and III-H solutions were evaluated as representative solutions. To allow the solution and the amylase to be mixed sufficiently, 200 ml of the solution was withdrawn from the vessel to a beaker and this solution was stirred quickly and thoroughly with 2 ml of the amylase solution with a spatula for approximately 10 s. The solution was put back in the vessel and the whole solution was similarly stirred. Immediately after that, the oscillation of the vessel and the UVP measurements were performed for the USR test in 20 min. The spatiotemporal velocity profile was extracted every 10 s, and a flow curve was obtained for each time point.

3.1 Rheological properties of the original solutions

The flow curves obtained by USR before adding the amylase are shown in Figure 2, where the axes represent the effective shear rate ${\dot{\gamma }}_{\mathrm{eff}}$ and effective shear stress τ_eff in logarithmic scale. For quantitatively characterizing shear-rate-dependence of the rheological properties, power law fitting ${\tau }_{\mathrm{eff}}=K{\dot{\gamma }}_{\mathrm{eff}}^n$ was applied to the flow curves, where K and n represent the consistency index and power law exponent, respectively. The conditions n < 1, n = 1, and 1 < n correspond to pseudoplastic, Newtonian, and dilatant fluids, respectively. The shear-thinning property becomes more dominant as the value of n decreases. The fitting based on the model was conducted against each flow curve in Figure 2 using the least square method. The fitting is in good agreement in the experimental results. The obtained parameters were plotted on the typical K-n space as shown in Figure 3, which was originally proposed for practically characterizing shear-rate-dependence of viscosity and elasticity (Wagner et al., 2017). The symbols of different concentrations are connected for better visibility. For the starch- and guar gum-based solutions, n takes almost the same value regardless of the concentration, meaning that there was little difference in the shear-thinning properties of these solutions before the addition of amylase. The guar gum-based thickener, classified as the second-generation thickener, had a better thickening effect per unit mass than the starch-based thickener, classified as the first-generation thickener, because the K value of the II-M (2.2 g per 100 ml) solution was larger than that of the I-M (4.7 g per 100 ml) solution. The plotted points for the xanthan gum solutions were located at the far lower of the graph compared with the starch and guar gum solutions. Therefore, the xanthan gum solution has remarkable shear-thinning property, which is tentatively a better condition for swallowing food (Nishinari et al., 2011; Nishinari, Turcanu, Nakauma, & Fang, 2019).

3.2 Stability of the rheological properties after addition of amylase

The temporal changes of the flow curves after being mixed with amylase are shown in Figure 4. The symbols represent the elapsed time after the addition. For the starch-based solutions, the flow curves lowered over time as shown in Figure 4a–c. Seven minutes after the addition of the amylase, the effective shear stress/viscosity of the starch-based solutions decreased to less than one hundredth of the original values. In contrast, the flow curves of the II-H and III-H solutions were maintained over 7 min, indicating that the second and third-generation thickeners were not affected by the amylase. Preliminary experiments indicated that the reaction proceeded uniformly in the vessel regardless of the radial position having a different shear rate amplitude. This is because the oscillatory shear flow in the vessel was under laminar conditions, where the stirring capacity was weaker than the turbulent conditions.

For quantitatively characterizing instantaneous shear-rate-dependence of the rheological properties, the power law fitting was applied to the flow curves, and the obtained parameters were plotted on the K-n space as shown in Figure 5. The shape of the symbols indicates the elapsed time after being mixed with the amylase, and the circles represent the time just before the addition. The symbols for different solutions with different concentrations are connected by lines for better visibility of the time variations. For the II-H and III-H solutions, the position of the plotted parameters does not change over time, indicating that mixing with amylase does not modify the rheological properties. The plot of the starch solutions (I), however, monotonically moved to the left with time elapsed. In addition, n approaches unity (Newtonian fluid) over time as an overall tendency. These indicate that the amylase changes the starch-based solutions to like pure water, increasing the risk of aspiration (Hasegawa et al., 2005; Kumagai et al., 2009; Nagatoshi et al., 2001; Tashiro et al., 2010).

3.3 Advantages of the functional evaluation via USR

Food materials are generally in heterogeneous and exhibit markedly different properties depending on timescale, and these represent a vast majority of the real foods (Nishinari et al., 2019; Wagner et al., 2017). The evaluation method base on USR will be applied to create a database of complex fluids, such as multiphase and gel–sol coexistent fluids represented by porridge and yogurt, in which USR has a great advantage over ordinary torque-type rheometers. A data set of the time-resolved rheological properties of swallowed foods can be constructed on the K-n space. In particular, porridge, which accounts for more than half of the calories in Japanese hospital food, loses its viscosity through hydrolysis. At what time the rheological properties of porridge decrease can be evaluated using the developed method. This method can assess how long the addition of a thickener can extend the time sustaining the original properties. In addition, in vivo measurements are required in parallel with these evaluations through the K-n diagram for elucidating the area where safe swallowing food is in. The last thing to emphasize is that a food bolus is subjected to not only shear but also extensional flows during swallowing process. Elongational and yielding properties also provide important insights on the dynamics of food bolus represented by cohesiveness (Hadde & Chen, 2019; Nishinari et al., 2019; Ross, Tyler, Borgognone, & Eriksen, 2019; Tobin et al., 2020). Combining extensional viscosity and yield stress measurements in addition to the evaluation by the present USR will lead better understanding bolus dynamics of heterogeneous foods in nonequilibrium conditions.