Online measurement of floc size, viscosity, and consistency of cellulose microfibril suspensions with optical coherence tomography

The CMFs used in this study are manufactured mechanically from purified wood pulp (Celish® KY-100G, Daicel Chemical Industries, Japan). A polarized light microscope image and SEM image of the CMF are shown in Figs. 1a, b, respectively. The size distribution of the CMFs is quite wide, making it difficult to accurately and uniquely measure them. Tatsumi et al. (2002) reported an average length and diameter of 350 µm and 15 µm, respectively, for the fibrils, while Kose et al. (2015) obtained an average fibril width of 0.7 µm. Varanasi et al. (2013) analyzed a fine mass fraction of the CMFs and estimated their average width and length to be 70 nm and 9 μm, respectively. (Notice that the CMF batches used in these studies have been similar; according to Daicel Chemical Industries the manufacturing process of Celish® KY-100G has remained the same during the years.) For the flow experiments, the original CMF suspension was diluted by tap water¹ to mass consistencies of 0.4%, 1.0%, and 1.6%.

The measurement unit consisted of a 2.5 m long, optical-grade glass pipe with an inner diameter of D = 19 mm (Fig. 2a). Stable flow conditions in the pipe were induced by a low-pulsation, progressive cavity pump (Seepex MD series). The volume of the sample fluid in the loop, including the tank, was 13.5 l. The fluid temperature in the loop was set as 21 °C with a digital temperature controller (Model 9610, PolyScience). The volumetric flow rate in the loop was measured using a magnetic flow rate sensor (Sitrans F M MAGFLO). The measurements were conducted under stationary flow conditions at the flow rate range of 8 ml/s – 169 ml/s. To determine the wall shear stress at each flow rate, pressure drop was measured using a differential pressure sensor along the distance of Δl = 1.0 m. In addition to the OCT device, the setup included an ultrasound velocity profiling (UVP) unit (DOP2000, Signal-Processing S.A., Switzerland), measurements reported previously by Kataja et al. (2017) and Koponen et al. (2019). The measurement setup has been explained in more detail by Haavisto et al. (2017).

A commercial spectral domain OCT device (Telesto I SD-OCT, Thorlabs Inc.), operating at a 1325 nm center wavelength, was used to structural characterization and viscosity determination of the flowing CMF suspensions. The system has an inherent depth (radial direction, along the probing beam) resolution of approximately 7.5 µm in air and approximately 5.6 µm in water. The lateral (axial direction) resolution is approximately 15 µm. The maximum imaging depth range in air is 2.5 mm, with the A-scan consisting of 512 pixels; thus, the pixel resolution in air is approximately 4.9 µm.

The OCT device was set up to perform continuous A-scans through the pipe wall and the suspension, such that the OCT probing beam remained in the same location all the time. The floc structure of the CMF suspension flowing past the OCT probing beam, and its local velocity, was captured in the resulting OCT images. The axial pixel size of the captured data depends on the local flow velocity and the A-scan rate of the OCT device.

The A-scan rate was set between 28 and 91 kHz, depending on the flow rate, to avoid phase wrapping in the velocity measurements (Xia et al. 2017). The angle between the OCT probing beam and the flow direction (Doppler angle), used to calculate the axial velocities (Haavisto et al. 2017), was 86.5° ± 0.2°, as determined from B-scan images composed of 4096 A-scans in a lateral range of 5.00 mm.

The floc sizes were determined in the radial (normal to pipe wall) and the axial (along the pipe) directions. The floc size analysis was performed outside the wall depletion layer in the bulk region (see Fig. 2b), where the velocity profile is approximately linear and relatively shallow and the consistency is approximately constant. In the wall depletion region, consistency is an unknown function of the distance from the wall, whereas the steep velocity profile hinders simultaneous determination of the radial floc size and the velocity scaling of the axial floc size. For these reasons, floc analysis would not be reasonable there. The distances from the wall where the bulk region begins were estimated from the onset of the linear part of the flow velocity profile: 150 µm for 0.4% (see Fig. 2b), 100 µm for 1.0%, and 50 µm for 1.6% consistencies. Also, the maximum imaging depth was estimated based on the velocity profile as the point where it began to deviate from the assumed linear profile in the bulk region due to attenuation of the optical signal and decreased signal-to-noise ratio (SNR). The maximum imaging depths were 670 µm for 0.4%, 650 µm for 1.0% and 520 µm for 1.6% consistencies.

The floc size analysis followed for the most part the method introduced by Koponen et al. (2018). Initially, the depth-dependent decay of the OCT signal must be corrected. The decay is mainly caused by scattering and absorption of photons, fringe washout due to flowing scatterers (Yun et al. 2004), and inherent sensitivity decay of the system due to the finite pixel size of the spectrometer (Leitgeb et al. 2003). The depth-dependent decay was corrected by first calculating the average OCT signal as a function of depth and then scaling the pixel values at a given depth using the inverse of the average. This process ensures that the average OCT signal is equal in the corrected image at each depth.

To reduce granularity in the images, and to account for the different radial and axial resolutions of the OCT setup, the frames were resized to 11 µm × 11 µm pixels. The native radial pixel size of 4.9 µm (in air), the refractive index of water (n = 1.33), and the average axial velocity in the bulk region were taken into account in the scaling process. Unfortunately, the OCT velocity data used to calculate the flow velocity profile and the average axial velocity in the bulk region was only available as a separate set of measurements for a reduced number of flow rates. The average velocities in the floc measurement region, obtained from the available velocity profiles when plotted as a function of the flow rate, exhibited piecewise linear behavior, probably due to the combined effect of apparent wall slip and shear thinning. The velocities were fitted with piecewise linear functions (1, 2, and 3 line segments for 0.4%, 1.0%, and 1.6% consistencies, respectively) and interpolation was used to estimate the average axial velocities for all the flow rates. Figure 3 shows the average velocity as a function of flow rate for a 1.0% CMF suspension together with the fitted interpolation function. For improved axial scaling accuracy, both structural and velocity data should be recorded for all the measurements. However, an error in the axial scaling mostly affects the determined floc size, while the trend remains undisturbed.

To determine the floc sizes, the resized images were thresholded using Otsu’s method (N. Otsu 1979) instead of the median used by Koponen et al. (2018). The median thresholding assumes that half of the image consists of flocs and the other half of water. Such an assumption can lead to under- or overestimation of the area covered by the flocs, and furthermore, it can break down the flocs at high consistencies and combine them at low consistencies. Figure 4 shows resized images (upper row) and Otsu-thresholded images (lower row) for all the consistencies at the same flow rate of approximately 31 ml/s.

The radial and axial floc size distributions were calculated as run-length distributions, in which the run-lengths are the lengths of the longest possible continuous line segments that are completely inside the CMF phase and oriented in the radial and axial directions, respectively. The obtained distribution histogram of run-lengths was weighted by the length and normalized by a sum of length counts. Images were acquired at two different OCT A-scan acquisition rates, 28 kHz and 91 kHz. The SNR is reduced at the 91 kHz A-scan rate compared to the 28 kHz rate. This will cause discrepancies in thresholding and further in the floc sizes determined from the thresholded images. The discrepancy exhibits itself as an offset in the floc size values between the two A-scan acquisition rates, and it was compensated for by scaling the floc sizes acquired at 91 kHz, such that the floc size is approximately continuous as a function of wall shear stress (see Fig. 5).

Figure 6 shows the measured pressure loss in the pipe as a function of the mean velocity. The shape of the curves resembles that of shear thinning fluids. Notice, however, that the wall slip makes the behavior more complex, as the increasing wall depletion with increasing wall shear stress may lead to apparent shear thinning (Kataja et al. 2017). Local viscosity of the CMF suspension above the wall-depletion layer can be directly calculated from Eq. (2) by utilizing the wall shear stress (obtained from the measured pressure loss) and the shear rate calculated from the OCT velocity profile, as explained in the Introduction. Since the velocity profile above the wall-depletion layer is locally approximately linear, the shear rates can be determined by fitting a line on the linear part of the measured velocity profile (see the solid lines in Fig. 7). The dashed lines in Fig. 7 are extensions of the linear fits. The fits are located at different distances from the wall. At a consistency of 1.6%, the signal began to slightly decrease after a 300 µm distance from the wall and was more evident after 500 µm. This was due to strong scattering and attenuation of the signal, which led to low SNR and unreliable determination of the velocity. Interestingly, at consistencies of 0.4% and 1.0% the velocity profiles differed from the linear fits at the beginning of the bulk region, which can clearly be seen from the extensions of the fitted lines (dashed lines). Such a behavior, which was consistently observed with all flow rates, could be due to a shear banding process, in which a suspension has localized bands with different viscosities, and thus, shear rates due to a difference in the CMF structure, for instance in the fibril orientation or flocculation (Nechyporchuk et al. 2016). However, it is more likely that the CMF consistency was slightly higher in this region than in the interior parts of the pipe due to wall depletion, which pushed fibrils and flocs away from the wall. This finding is substantiated by the fact that the effect was stronger at lower consistencies, which also have a thicker wall-depletion layer (Koponen et al. 2019). At a consistency of 1.6%, due to the more crowded suspension, the migration of individual fibrils and flocs away from the wall is not as easy as with lower consistencies. Here collective compression of the suspension may be an important mechanism in the creation of the depletion layer which could explain why protuberance was not seen in the velocity profile.

Figure 8 shows the viscosity calculated from Eq. (2) as a function of shear rate obtained from the straight solid lines shown in Fig. 7. The solid lines show viscosities for the same CMFs determined with the UVP method in the whole pipe (Koponen et al. 2019). The OCT viscosities corresponded well with the UVP data. Thus, the actual viscous behavior of the CMF suspensions can be obtained accurately with OCT in the vicinity of the pipe wall.

For estimating yield stress, \(\tau_{y}\), the fit of the Herschel–Bulkley model \(\tau = \tau_{y} + K\dot{\gamma }^{n}\) with the shear stress–shear rate data failed, and the yield stress was estimated using the Casson model \(\tau^{0.5} = \tau_{{\text{y}}}^{0.5} + a\dot{\gamma }^{0.5}\) (Barnes et al. 1989). The obtained values for the yield stress were 0.5 Pa, 2 Pa, and 9 Pa, for 0.4%, 1.0% and 1.6% consistencies, respectively. Yield stress is here (just like the viscosity) smaller than in (Turpeinen et al. 2020); likely due to small differences in the used Celish batches and the different chemical composition of the used water (tap water vs. deionized water). Note that for the lowest shear rate, where the shear stress was 8.5 Pa, i.e. slightly below the estimated yield stress, the viscosity of the 1.6% consistency differed clearly from the general trend (see the filled data point in Fig. 8). Here, the fluctuations around the yield point through continuous break-up and recovery of the network structure combined with a limited measurement time led to large variations in the measured viscosity (Lauri et al. 2017). We have omitted this data point in Fig. 11.

Figure 9 shows the radial and the axial floc size distributions, which exhibit a roughly log-normal shape common to fibers and fibrils (Hourani 1988a, b; Koponen et al. 2018; Saarikoski et al. 2012) and many other flocculating particles (Coufort et al. 2008; Shin et al. 2015). At a consistency of 1.6%, and to some extent also at 1.0%, the measurement range was too short in the radial direction, which can be noted in the peaks at the highest floc size bins (see Fig. 9c, e). In the axial direction, the acquired image length was much longer, and therefore, we obtained undistorted distribution profiles. However, in order to evaluate and compare floc sizes, we limited the axial distributions to the same length as the radial distributions. For the average (length-weighted) floc size calculations, we omitted the peaks at the largest sizes and only used distributions up to the 450 µm for all the cases. Note that most CMF grades are finer than the CMF used here. Thus, their floc size is generally smaller and complete floc size distributions would be obtained.

Figure 10a shows the average axial and radial floc sizes as a function of shear stress. The floc size was systematically smaller in the radial direction when compared to the axial direction. This was the case also in a study by Koponen et al. (2018) of a finer, mechanically disintegrated CMF at a 0.5% consistency. The likely reason for this occurrence is that the laminar pipe flow does not experience elongational (axial) stresses and the flocs are mainly broken by radial shear stress. This could also explain why the radial floc size decreased monotonically with increasing shear stress at all three consistencies, while the axial floc size at a consistency of 0.4% remained almost constant and the floc sizes at consistencies of 1.0% and 1.6% began decreasing monotonically only when a certain shear stress level was exceeded.

Figure 10b shows the geometric floc size, defined as a square root of the product of the axial and radial floc sizes as a function of shear stress. The straight lines are power law fits \(L = G\tau^{ - \beta }\) to the data, where G and β are the fitting parameters. The red markers show data points that have been omitted from the fits (two outliers at a consistency of 0.4%, and the lowest shear stresses at consistencies of 1.0% and 1.6%). We can see that the power law index, β = − 0.18, was the same for all three consistencies. Thus, the floc rupture dynamics was independent of consistency with higher shear stresses. Finally, note that the floc size of 0.4% CMFs appeared to saturate at the highest shear stresses, but the number of data points was too small to draw any real conclusions.

The shear thinning behavior of CMF suspensions has been associated with decreasing floc size at an increasing shear rate or shear stress (Mohtaschemi et al. 2014b; Puisto et al. 2012a, b). However, there is a lack of experimental data to support this assumption. Figure 11 shows the viscosity and the geometric floc size as a function of shear stress. We can see that there is a clear similarity between the floc size and the viscosity. To our knowledge, this data is the most direct evidence to date of the relationship between the CMF suspension viscosity and floc size. Note that while a power law gives a good approximation of the viscous behavior of the CMFs (see Fig. 8), the viscous behavior is in reality more complex. At a consistency of 1.0%, and especially 1.6%, the viscosity-shear stress data consist of two groups separated by a transition region. Similar viscosity behavior has also been noted by Lauri et al. (2017) for a finer CMF at a 0.5% consistency. The most obvious reason for such an abrupt change in the rheological behavior of the CMF suspension would be a sudden structural change in the suspension, for example in the fibril orientation (Mykhaylyk et al. 2016) and/or flocculation (Bounoua et al. 2016). Indeed, the floc size at a consistency of 1.0% follows rather consistently the viscosity behavior. However, at a consistency of 1.6% the floc size cannot explain the abrupt drop in viscosity at the shear stress of 20 Pa. The changes in the floc aspect ratio (data not shown) were also too small to explain the observed behavior. It is possible that, for instance, concentration variations in the measurement region due to the wall depletion and subsequent compression of the 1.6% CMFs caused this to occur, but a clear explanation for the observed viscous behavior is currently lacking.

The change in the consistency can be qualitatively estimated based on the OCT amplitude signal. A quantitative analysis is possible by utilizing an attenuation coefficient, the slope of the decaying signal (Gong et al. 2020; Vermeer et al. 2013), and predefined suspension consistencies for calibration. Multiple different factors in a measured sample influence the amplitude of an OCT signal. A large difference in refractive indexes between a scatterer and surrounding media increases the reflectivity and leads to a higher signal amplitude. In addition, higher particle concentration or, in this case, higher fibril consistency results in increased signal amplitude. On the other hand, a dense packing of scatterers can lead to dependent scattering, which will decrease the backscattered light intensity, and thus, the signal amplitude (Almasian et al. 2015; Kalkman et al. 2010). Other influencing factors, in addition to those already mentioned in the Materials and methods section, include particle size, the scattering anisotropy of the suspension, multiple scattering, and the depth of field of the focusing optics (Almasian et al. 2015; Kholodnykh et al. 2003; Thrane et al. 2000; Yadlowsky et al. 1995). There have been studies to estimate the concentration of spherical particles in static (Hillman et al. 2006; Sugita et al. 2016) and flow (Wang and Wang 2011) conditions via statistical analyses of the OCT amplitude signal. Such studies typically used homogenous suspension with monodispersed particle size; however, due to the complex size and shape distribution of CMFs, the direct applicability of the proposed theoretical formalisms should first be verified with simulations.

Decay of the OCT signal can be used to estimate an attenuation coefficient, which includes the effects of both scattering and absorption. It has been demonstrated that in the single scattering regime, the OCT intensity signal can be estimated by a Beer’s law using a single exponential decay functionwhere z is the depth coordinate, I₀ is the incident intensity, and u_t is the attenuation coefficient (Faber et al. 2004; Schmitt et al. 1993; Smithies et al. 1998). A factor of two in the exponent accounts for the roundtrip attenuation. In the present study, an apparent attenuation coefficient was determined by fitting the single exponential function with two variables (attenuation and intensity) to the linear part (in a log scale) of the OCT intensity signal (see Fig. 12a). Due to nonhomogeneous suspension, the fitting was performed at the highest flow rates to ensure reasonable sample length, and thus, good averaging of the data. A linear relationship of the obtained apparent attenuation coefficients and the CMF consistency is shown in Fig. 12b. The term “apparent” is used here because the sensitivity decay of the OCT system was not considered in the calculation and the absolute intensity values are not known. Due to the unknown intensity range of the OCT signal, the absolute coefficient values are only relative. However, they are expected to be at the upper limit, and the actual attenuation coefficients would then be smaller. This is because the single scattering approximation and the linear relationship between the attenuation coefficient and the consistency typically applies only in the weakly scattering regime, u_t < 5–10 mm⁻¹ (Almasian et al. 2015; Faber et al. 2004; Kalkman et al. 2010). Nevertheless, the relative scattering coefficients are sufficient for monitoring consistency at the online conditions since the calibration slope (Fig. 12b) must always be determined in advance for each CMF suspension.