Methods

Firstly, the main chemical constituents of the pulp were determined. Moisture was quantified in a drying oven at 105 °C and the ash content, in a muffle furnace at 600 °C. Protein content was measured by using the Kjeldahl method [23].

Fiber content was measured by gravimetry according to the AOAC [23]. This method is based on treating a sample with acid and alkaline solutions at boiling temperature and taking the remaining insoluble matter after digestion as crude fiber.

Previously dried samples of açai pulp (obtained from moisture content analysis) were packed and sealed in filter bags (model F57 - Ankon Technology™), which consist of an inert and heat-resistant material properly developed for fiber determination. An empty bag was used as a blank. Firstly, the fat of the açai was extracted by manually soaking the bags in petroleum ether for 10 min. After the excess solvent was removed, the bags were placed in layers in a pile of stainless-steel plates, which was mechanically soaked for 30 min in H₂SO₄ solution (1.25% w/v) at the boiling temperature (~97 °C) using a fiber analysis vessel (Tecnal TE-149). Afterwards, the acid solution was dumped and the samples washed by soaking the bags for 5 min in boiling distilled water. The washing procedure was performed four times, dumping the previously used water and filling the bath with fresh water. After washing, the samples were soaked in boiling NaOH solution (1.25% w/v) for 30 min (~97 °C). Washing was repeated, and the bags were subsequently soaked manually in acetone for 5 min. Afterwards, the acetone was evaporated and the bags dried in an oven at 105 °C for approximately 4 h. Finally, the bags with the samples were burned in a muffle furnace at 600 °C in order to subtract the weight of the ashes.

Lipid content was determined according to Bligh and Dyer [24]. Digestible carbohydrates, which include mainly simple sugars and starch, and other compounds were calculated by subtracting all other components from the total mass to complete the analysis of açai composition. Analysis of each component was carried out in triplicate.

PSD analysis of açai pulp was carried out by applying the technique of laser-ray diffraction using a Mastersizer 2000 (Malvern™ Instruments) diffractometer set to the diffraction index of Fraunhoffer.

Before the runs, 20 ml of Calgon ((Na(PO₃)_n) at 25 g/l was diluted into 480 ml of distilled water, and this solution was used to calibrate the instrument’s optical device, generating a blank reference. Then, approximately 20 ml of the açai pulp was poured into this solution, which was sonicated for 30 s in order to avoid particle coalescence. The displacement of the tip of the ultrasonic probe was set to 13.0 μm. The sample was kept agitating by a mixer at 2200 rpm, coupled to the Martersizer. Subsequently, the laser-ray diffraction of the sample was measured, and the particle size distribution (PSD) was given by the instrument.

Results were expressed in terms of frequency and cumulative particle distribution. In the latter, the Rosin–Rammler–Bennet (RRB) model (Eq. 1) was fit to the experimental data. Moreover, the Sauter mean diameter (D_S), also known as surface-weighted mean-diameter, was calculated considering the model presented by Eq. 2a and 2b, which is used for PSD represented by RRB with m > 1. D_S is widely used in PSD characterization of food materials [25–27].

Rheological measurements were carried out with the Brookfield™ viscometer, model LVDV2T (low-viscosity digital viscometer) with a specific cylindrical compartment to contain the fluid (Small Sample Adapter from Brookfield™) and a thermostatic bath to control the temperature. Tests were performed with the aid of Rheocalc T software. The effects of shear rate, temperature, and shearing time were evaluated. Triplicate runs were performed at 10, 20, 30, 40, 50, 60, and 70 °C. The cone-plate Brookfield™ spindle SC4-21 was used in the tests performed with changing the shear rates, while the cone-plate spindle SC4-34 was used in the analyses carried out at a constant shear rate.

Before each experimental run, samples of açai pulp were thawed at room temperature (25 °C) 30 min before each rheological test. Subsequently, the thawed açai pulp was poured into beakers (50 ml volume) and smoothly homogenized with a lab spatula. Açai pulp was then poured into the viscometer compartment. New samples were used in each run.

Rheological measurements on a sample may be affected by the procedures applied before the fluid is loaded into the viscometer compartment [28]. Therefore, in order to standardize all the açai samples, a pre-shearing at 40 s⁻¹ for 30 s followed by a resting time of 3 min was applied to the fluid before rheological data were taken. This procedure was sufficient to 233 eliminate earlier shear effects. Then, rheological analyses were carried out according to the sections.

Shear stress and viscosity data recording was begun after the sample was maintained at a shear rate of 1.5 s⁻¹ for 20 s. After the first data point was collected, the shear rate was raised by 0.5 s⁻¹ every 5 s until it reached 5 s⁻¹ and was subsequently increased by 1.0 s⁻¹ every 5 s up to 40 s⁻¹. This step of shearing increase was named “UP.” Once the UP step was concluded, the backward shearing step (named “DOWN”) started by decreasing the shear rate from 40 s⁻¹ to 1.5 s⁻¹ following the same path as for UP but in reverse. These UP and DOWN loops were repeated four times on the same sample and were respectively named 1st UP, 1st DOWN, 2nd UP, 2nd DOWN, 3rd UP, 3rd DOWN, 4th UP, and 4th DOWN. The experimental design of these analyses is shown in Fig. 1. A 5th cycle was performed at 10, 40, and 70 °C; however, there was no considerable difference between this and the 4th cycle (data not shown). Therefore, four cycles were sufficient to consider a steady flow behavior in all the experimental runs.

Experimental design of tests to study the effect of shear rate on the rheological behavior of açai pulp

Such UP and DOWN loops are widely used to check the occurrence of thixotropy in fluids [7, 21, 29]. When shear stress data are plotted against the shear rate, a thixotropic fluid will present a hysteresis loop, the area of which may be calculated in order to estimate the degree of thixotropy [28].

The Herschel–Bulkley (Eq. 3) and Power-Law (Eq. 4) rheological models were fit to the experimental results of shear stress (σ) vs. shear rate (γ) over the entire shear rate range (1.5–40 s⁻¹) by non-linear curve fitting applying the method of Levenberg–Marquardt using the software Statistica™ 7.0. The parameters σ₀, k, and n were estimated considering a relative error of 10⁻⁶ as the convergence criterion. Models were assumed to be statistically significant when the value of probability (p value) calculated for each parameter was less than or equal to 5%.

Hysteresis loops between each UP and DOWN curve in each cycle were calculated from their graphical area. Additionally, the area between the first upward (1st UP) and the last downward curves (4th DOWN) was determined. Each area was calculated numerically by applying the trapezoidal rule.

In order to evaluate the time-dependent rheological behavior of açai pulp, viscosity and shear stress measurements were performed, maintaining a constant shear rate of 20 s⁻¹ for 30 min followed by 30 min of rest, and then a new shearing step at 20 s⁻¹ for an additional 10 min.

The Weltman (Eq. 5) and Hahn (Eq. 6) models, which have been used to represent thixotropic behavior in food fluids [20, 25], were fit to the experimental data achieved in the first 10 min of shearing. The equilibrium shear stresses (σ_e) were determined from the average of the last 5 σ values obtained in the first shearing step.

Activation energy for the effect of temperature on apparent pulp viscosity was calculated by the Arrhenius model (Eq. 7), considering the steady-state viscosities reached after the first 30 min of shearing: