Rheological properties of corn stover slurries during fermentation by Clostridium thermocellum

Experiment 1: Rheology before and after fermentation

In this experiment, the rheological properties of unpretreated corn stover (with 0.2 mm maximum particle size) were examined without and with fermentation by C. thermocellum, a thermophilic, cellulolytic anaerobic bacterium. Steady shear flow sweeps were performed on slurries before and after fermentation. Slurries were prepared at four different insoluble solid concentrations \( c \) = 10, 12.5, 15, and 17.5 wt.%. These concentrations span the capability range of the rheometer and are representative of conditions anticipated in an industrial process. Fermentation was carried out using C. thermocellum. After reaction, the solids remaining in the reactor were reconstituted to the same four concentrations as the unfermented slurries to allow for a direct comparison of viscosity before and after fermentation.

As illustrated in Fig. 1, the slurries ranged from being a pourable liquid to being a clay-like paste, depending on the solids concentration and state of fermentation. These extremes posed challenges to collection of repeatable shear sweep data: Low-solids-concentration slurries were liquid-like, so they had to be well mixed and then immediately loaded onto the rheometer to mitigate particle settling. High-solids-concentration slurries had no visible free water; so, care had to be taken to load the appropriate amount of material into the rheometer to maintain good contact between the top plate and the material yet prevent the top plate from squeezing water out of the slurry.

Figure 1 reports viscosity and shear stress versus strain rate for flow sweep experiments, with power law fits displayed as dashed lines overlaid on the data. The black dotted lines represent the rheometer’s low-torque limit, 10 μNm, and the red dotted lines take into account manufacturing errors with 20 times this low-torque limit [9]. Viscosity is observed to decrease after fermentation and with lower solids concentration. For the range of strain rates considered, these corn stover slurries are well described by a power law constitutive model,

$$ \tau = m\dot{\gamma }^{n} $$

where \( \tau \) is the shear stress (Pa), \( \dot{\gamma } \) is the strain rate (1/s), \( m \) is the plastic viscosity (Pa s), and \( n \) is the power law index. Interestingly, all slurries have similar \( n \) values of 0.10, indicative of highly shear-thinning behavior. Figure 2 reports the plastic viscosity of both the unfermented and fermented material. Also shown are literature data: Viamajala et al. [38] report data for corn stover slurries milled to − 80 mesh (0.177 mm) size and treated with dilute acid (1.5% H₂SO4) at 25 °C and 190 °C. Dunaway et al. [6] provide data for before and after hydrolysis of a corn stover slurry with pretreatment via dilute acid (1.6% H₂SO4) at 190 °C, hydrolysis for 170 h by fungal cellulase (T. reesei), and 0.03 mm particle size (Berson, personal communication).

It may be observed that the plastic viscosity of our fermented 10 wt.% corn stover slurry is 40-fold lower than that of its unfermented counterpart. At higher solids concentrations (for instance 17.5 wt.%), this viscosity reduction is less pronounced (twofold decrease). Plastic viscosity is observed to increase with increasing solids concentrations but plateau for very high concentrations. This “stacking” stems from frictional forces (between granular particles) dominating once the solids concentration is so high that the slurry contains no free water [38].

Experiment 2: Rheology over the course of fermentation

In this experiment, flow sweeps and LAOS measurements were made on slurry samples drawn from the bioreactor during the course of fermentation to characterize the changes in rheology versus extent of fermentation. This section presents results of flow sweep tests, and the results of LAOS tests are presented in the next section. Duplicate fermentations for this experiment were carried out at an initial solids concentration of 8 wt.% (80 g/L), which is near the maximum allowable limit for batch cultures in light of initial mixing and sampling constraints in the laboratory bioreactor set-up employed. All slurry samples were concentrated twofold following fermentation and prior to rheological measurements to enable measuring viscosity above the low-torque limit of the rheometer. The solid concentrations referred to in this section are these twofold-concentrated values.

Figure 3 presents the changes in viscosity as fermentation proceeds for a corn stover slurry with an initial insoluble solids concentration of 16 wt.%. Data for two separate fermentation trials are overlaid along with their power law fits. Plastic viscosity is plotted on a linear scale (c) and a log scale (d) as a function of fractional conversion \( X \). Error bars represent 1 standard deviation. Data points for which error bars are not visible had standard deviations smaller than the symbols for the data. The solid concentrations at several fermentation time points are also indicated on Fig. 3a, b, with a lower solids concentration corresponding to a sample collected later in time. Consistent with the results presented in Fig. 1 (obtained at specified solids concentrations), results in Fig. 3a, b (at variable solids concentrations) exhibit several key features: shear-thinning behavior; viscosity well represented by a power law fit; and viscosity that decreases with decreasing solids concentration.

In Fig. 3c, d, plastic viscosity values are plotted versus fractional carbohydrate conversion on linear and log scales, respectively. The plastic viscosity falls from roughly 1920 to 1 Pa s over the course of the fermentation. Most of this nearly-2000-fold decrease takes place before 20% conversion, which corresponds to a fermentation time of approximately 2 days in these experiments. Interestingly, this 2000-fold decrease in viscosity is similar to that observed in Fig. 2 (therein considering a hypothetical fermentation run starting at 17.5 wt.% solids and reacting until a final concentration of 10 wt.% is reached). Here, the fermentation run started at 16 wt.% solids and ended at 10 wt.%; so, it is reasonable that the results of the two figures are in agreement.

The data were fit (via nonlinear least squares) with a double exponential curve, \( m\, = \, 1700{\text{e}}^{{ - 23{\text{X}}}} \, + \,220{\text{e}}^{{ - 9.5{\text{X}}}} \), which illustrates the initial rapid decay of viscosity in the first stages of conversion \( 0 \le X \le 0.2 \). The viscosity decreases eightfold (from 1920 to 250 Pa s) in the first 10% of conversion. A goodness-of-fit metric appropriate for a nonlinear regression such as this is the canonical angle \( \psi \), which is the angle between the vector of data \( \tilde{m}_{n} \) and the vector of model predictions, \( m_{n} \). This angle can be computed via \( \cos \psi \, = \,{{\left( { \mathop \sum \nolimits m_{n} \tilde{m}_{n} } \right)} \mathord{\left/ {\vphantom {{\left( { \mathop \sum \nolimits m_{n} \tilde{m}_{n} } \right)} {\left( {\sqrt {\mathop \sum \nolimits m_{n}^{2} } \sqrt {\mathop \sum \nolimits \tilde{m}_{n}^{2} } } \right)}}} \right. \kern-0pt} {\left( {\sqrt {\mathop \sum \nolimits m_{n}^{2} } \sqrt {\mathop \sum \nolimits \tilde{m}_{n}^{2} } } \right)}} \), where \( \psi = 0^{ \circ } \) would indicate a perfect fit and \( \psi = 90^{ \circ } \) would indicate that the model provides no explanation of the data. For these data and fit, the canonical angle is \( \psi = 12^{ \circ } \). This is a reasonable fit; by analogy with linear data y(x) =  x  +  N(0,σ²), the canonical angle depends linearly on the standard deviation σ (for \( \psi < 20^{ \circ } \)), and \( \psi = 12^{ \circ } \) corresponds to σ = 0.122 and a coefficient of determination of R² = 0.85.

LAOS experiments

Large amplitude oscillatory shear tests were conducted on the corn stover slurries sampled during Experiment 2 to further probe their rheological properties. In each LAOS experiment, stress is measured while the material is harmonically strained, \( \gamma \left( t \right) \, = \, \gamma_{0} { \sin }\left( {\omega t} \right) \). The stress response is plotted as stress versus strain (elastic Lissajous–Bowditch (ELB) curve) or stress versus strain rate (viscous Lissajous–Bowditch (VLB) curve). A perfectly elastic body would have a straight-line ELB curve and a circular VLB curve, and vice versa for a perfectly viscous fluid. Each subfigure in Fig. 4 contains a family of L–B (Lissajous–Bowditch) curves, with each curve centered around its frequency \( \omega \) (rad/s) and amplitude \( \gamma_{0} \) (%) in a Pipkin map [31]. LAOS data are typically filtered using a three-odd-term Fourier series [8]:

$$ \sigma \left( t \right)\, = \,\sigma^{\prime}\left( t \right)\, + \,\sigma^{\prime\prime}\left( t \right)\, = \,\mathop \sum \limits_{n = 1,3,5} \gamma_{0} G^{\prime}_{n} \sin n\omega t\, + \, \gamma_{0} G^{\prime\prime}_{n} \cos n\omega t$$

where \( \sigma^{\prime}\left( t \right) \) and \( \sigma^{\prime\prime}\left( t \right) \) represent the elastic and viscous stress contributions, and the \( G_{n}^{'} \left( {\gamma_{0} ,\omega } \right) \) and \( G_{n}^{''} \left( {\gamma_{0} ,\omega } \right) \) are the viscoelastic moduli.

Figure 4 shows ELB and VLB curves for corn stover slurries at time = 0 h (16 wt.% solids, \( X = 0 \), m = 1920 Pa) (a, b) and time = 44 h (13 wt.% solids, \( X = 0.14 \), m = 112 Pa) (c, d) after the start of fermentation. Each curve’s raw data and filtered data are plotted in black and in color, respectively. The maximum stress \( \tau_{ \hbox{max} } \) (Pa) is shown above each curve. The elastic stress \( \sigma^{\prime}\left( t \right) \) or viscous stress \( \sigma^{\prime\prime}\left( t \right) \) is plotted in dotted lines. In (a) and (b), the dotted line partitions the linear viscoelastic region and the nonlinear viscoelastic region. Also, the solid black line indicates the crossover line that delineates the predominantly elastic region (below) and the predominantly viscous region (above). Figure 4a, b show ELB and VLB curves, respectively, for a 16 wt.% solids “hour 0” slurry, which is essentially unfermented. These Pipkin maps show three distinct regions: linear viscoelastic (LVE); nonlinear viscoelastic (NLVE) yet still elastically dominated; and viscous dominated. The LVE region (defined herein as that for which the third- and fifth-order Fourier coefficients are less than 5% of the first-order coefficients) occurs for small strain amplitudes, with the cutoff amplitude depending on the frequency (as shown in Fig. 4) but being roughly \( \gamma_{0} \,\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{ < } \, 10\% \). In the LVE region, the narrowly elliptical shape of the ELB curves indicates that elastic behavior dominates at these low strain amplitudes.

In the NLVE region, the shapes of the L–B curves illustrate the complex rheology of the slurry. For example, the inward curvature of the viscous stress (dashed lines in the VLB curves) suggests that the deviations from linearity are due to shear-thinning, which reaffirms the results in Experiment 1. Also, in the NLVE region, both the ELB and VLB curves are tilted near the edges, as previously observed by [35] for pretreated, unfermented slurries at similar solids concentrations. For moderate strain amplitudes \( 10\% \,{ \lesssim }\,\gamma_{0} \,{ \lesssim }\,100{\text{\% }} \), the NLVE region is characterized by predominantly elastic behavior.

The transition from elastic to viscous behavior is given where the phase amplitude \( \tan \delta = G_{1}^{''} /G_{1}^{'} \) is unity. Figure 5b shows \( \tan \delta = 1 \) at roughly \( \gamma_{0} \approx 100\% \). It is interesting to note that the noisiest data occur on this elastic–viscous crossover boundary; this is not surprising given that for smaller strain amplitudes, the rotor is moving too little to disrupt the matrix of solids particles, whereas for much larger strain amplitudes, the matrix is disrupted so much that the displacements of individual particles are averaged out.

For high strain amplitudes and frequencies, the flow is dominated by viscous effects. In this region, some VLB curves are observed to self-intersect, which is indicative of a strong elastic nonlinearity caused by a viscoelastic stress overshoot, essentially meaning that the rate at which the slurry is unloading stress is faster than its rate of deformation [10]. Such nonlinearities are typically present due to reversible changes in the material’s disposition (with one possibility being that the slurry’s entrained water is being squeezed out upon deformation). At very high amplitudes and frequencies, the square-shaped elastic curves show that the slurry is plastically deforming.

Figure 4c, d shows the corresponding LAOS data for a 13 wt.% solids “hour 44” slurry. This 13 wt.% solids sample had visible free water, making data collection quite challenging. Most of the raw data were too noisy to be included in the Pipkin map, but with the available data, a few comparisons can be made. The LVE–NLVE transition occurs at a lower strain amplitude for the “hour 44” slurry, and this transition is due to its shear-thinning behavior, similar to the “hour 0” slurry. Overall, the shapes of the L–B curves are surprisingly similar for the “hour 0” and “hour 44” slurries, given that the steady shear viscosity has fallen by a factor of seventeen.

In Fig. 5a, the 16 wt.% “hour 0” slurry shows \( 0.30\, \le \,\phi \, \le \,0.83 \), with this upper limit of \( \phi = 0.83 \) being between Newtonian and perfectly plastic. The slurry transitions from exhibiting elastoplastic behavior (\( \phi \le \frac{\pi }{4} ) \) to exhibiting pseudoplasticity \( \left( {\phi \ge \frac{\pi }{4} } \right) \) at roughly \( \gamma_{0} \approx 100 \)%, which is consistent with the elastic–viscous crossover at \( \tan \delta = 1 \). In Fig. 5c, the 13 wt.% “hour 44” slurry’s perfect plastic dissipation ratios range from \( 0.32 \le \phi \le 0.87 \), which again is remarkably similar to the “hour 0” slurry. Like its unfermented counterpart, it did not exhibit perfect plastic yielding, but showed elastoviscoplastic deformation.

Feedstock preparation

Fermentation

Rheometry

Rheological measurements were carried out using a TA Instruments AR 2000ex rheometer with 40-mm diameter, cross-hatched parallel plates (TA Instruments, New Castle, DE). A 48-mm inner diameter, 6-mm high retaining collar, similar to that in [36], was fabricated and attached to the bottom plate to prevent material ejection. Strain-controlled shear data were collected by carrying out flow sweeps from \( \dot{\gamma } \) = 100 to 0.01 s⁻¹ using three points per decade, a gap height of 1.5 mm, and a sampling time of 15 s per data point. Each trial was replicated at least five times with a freshly loaded sample.

Strain-controlled LAOS measurements were performed with a test matrix of frequencies 1 ≤ \( \omega \) ≤ 50 rad/s and strain amplitudes 0.01 ≤ \( \gamma_{0 } \) ≤ 10 (unitless), with four points per decade. These ranges were chosen based on initial trials, because raw stress signals outside this range were unacceptably noisy. Raw data were post-processed with MITlaos [8] using a maximum Chebyshev harmonic of 5 to yield filtered LAOS data. Data were excluded from the study if the stress/strain signals were too noisy (typically at low frequencies and amplitudes) to enable a reliable Chebyshev fit.

Experiment 1: Rheology before and after fermentation

The milled feedstock was used to prepare corn stover slurries at 10, 12.5, 15, 17.5 wt.% insoluble solids concentrations. The viscosity of these unfermented slurries was measured via flow sweeps (as described in §4.3). The milled feedstock was also used to prepare a slurry at 10 wt.% (100 g/L) initial solids concentration for subsequent fermentation (as described in §4.3). This slurry was fermented for 188 h and harvested after gas production ceased; the final solids concentration was 5.9 wt.% (59 g/L). The whole reactor content was harvested by spinning down the broth at 10,000×g at 4 °C. A representative sample of this material was analyzed for residual carbohydrates and dry weight by further spinning down and drying the pellet at 60 °C, followed by determination of glucan, xylan, and arabinan content by QS. Another representative sample was spun down (to roughly 19 wt.% solids) and then re-suspended with water to make once-fermented slurries (at 10, 12.5, 15, 17.5 wt.% solids), which were then used for viscosity measurements.

Experiment 2: Rheology during the course of fermentation

The following experiment was performed in duplicate: The milled feedstock was used to prepare a corn stover slurry at 8 wt.% (80 g/L) initial solids concentration for subsequent fermentation. The fermenting slurry was sampled at 6–7 time points, including time t = 0. For each time point, a 130-mL sample was transferred to a beaker on a stir plate. Triplicate aliquots of 10 mL were taken for QS; the remainder was used immediately for rheological measurements and for determining the solids concentration. These aliquots were spun down at 7800×g, rinsed with an equal volume DI water once and spun down again, after which the residues were recovered and dried at 60 °C for at least 5 days, followed by determination of glucan, xylan, and arabinan content by QS. Rheological measurements included flow sweeps and LAOS.

Prior to rheological measurements, the harvested slurry samples were concentrated 2× by removing half the volume of water (by spinning down at 10,000×g at 4 °C). For example, an 8 wt.% sample was concentrated to 16 wt.%. This adjustment was necessary, because the fermentation required concentrations less than 10 wt.% but the rheological measurements required concentrations greater than 10 wt.%. Solid concentrations greater than 10 wt.% are prohibitive for fermentation due to difficulties in mixing and sampling at early time points. Solid concentrations less than 10 wt.% (for this particle size) would result in viscosity measurements below the rheometer’s low-torque limit. Hence, the effective solution for obtaining reliable rheological results during the course of fermentation was to remove half the water from the slurry samples.