We discuss the problem of the approximation of the solutions of the stationary Boltzmann equation, driven by diffuse boundary conditions at varying temperature, by means of stochastic particle systems. In particular we extend a previous results, by substituting the hypothesis of a cutoff on small and large velocities with the presence of an external field.
1.
Introduction
The plant Indigofera tinctoria L., often known as indigo, belongs to the legume family Fabaceae and is found in Africa and tropical Asia [1]. Indigo has been used to produce natural indigo dye for cotton textiles by traditional methods in small-scale industries in Thailand. Indigo plants are harvested for indigo dye production in the rainy season from August to October of each year in the northeast. The indigo biomass produced an average of 339 kg/ha [2] and indigo waste was separated from the water at 70–77% [3], or 237–261 kg/ha. The remaining indigo waste after the dye production procedure contains the stem and leaves [4]. The indigo waste consists of 19.8% CP, 46.6% NDF, 3,487.5 kcal/kg gross energy (GE), 5.4% condensed tannins, and 13.1% crude saponins [5]. In order to enhance the cost-effectiveness and environmental sustainability of indigo by-products, they might be used as a potential source of animal feed. Our previous studies found that the addition of dried indigo waste at 10% in a concentrate diet suitable for feeding to growing beef cattle while increasing levels of the dried indigo waste up to 30% resulted in a slightly lower feed intake, nutrient digestibility, rumen fermentation, and growth performance [5]. In addition, after the indigo dye production process, indigo waste quickly deteriorates after a few days, and sun-drying can be difficult during the rainy season.
Silage is the appropriate method for the controlled fermentation of crop residues with high moisture levels. It is now widely understood that the addition of silage additives improves silage quality, nutritive value, and degradability [6,7]. Chemical and biological treatments are usually utilized in silage additive studies, such as fermentable cellulase, sugar substrates, or Ca(OH)2 [8,9]. The inclusion of cellulase may enhance the breakdown of cell walls, thereby facilitating the release of fermentable substrate that can support the growth of lactic acid bacteria (LAB) [10,11]. In theory, enzymes' ability to release more substrate for LAB growth could increase lactic acid production, which would improve the quality of fermentation in the silage [11,12]. Adding molasses can provide a source of readily fermentable sugars for the growth of LAB to produce lactic acid [13]. Previous studies have reported that the addition of molasses and cellulase or combination ensiling of by-products improved the quality of silage, its nutritive value, in vitro degradability, and rumen fermentation patterns [14,15,16]. In addition, alkaline agents, especially Ca(OH)2 breaks down the ester bonds that connect lignin, hemicellulose, and cellulose, which improve the degradation and fermentation of silage [17]. Earlier studies found that treating the by-product with Ca(OH)2 has a positive effect on chemical compositions, in vitro gas production, digestibility of nutrients, and rumen metabolites in ruminants [7,9,18]. However, the indigo waste treated with the additives as ruminant feed has not been studied.
We hypothesize that the additives enhance the quality of silage, degradation, and fermentation characteristics. Therefore, our purpose of the study was to examine the impact of Ca(OH)2, molasses, cellulase, and their combinations on the silage quality, in vitro degradability, and rumen fermentation of indigo waste silage.
2.
Materials and methods
2.1. Ethics approval of research
The animal experimentation procedure was approved by the Animal Care and Use Committee of the Rajamangala University of Technology Isan (approval number 46/2565). The present investigation has substantiated that all met.
2.2. Treatment and fermentation preparation
The indigo waste (leaf and stem) was obtained after the dye was extracted from the indigo fabric community enterprise group in Baan Nohnrua, Pannanikom, Sakon Nakhon, Thailand. Indigo waste was chopped to a size of 1–2 cm. We conducted this study using a completely randomized design (CRD). The indigo waste was treated with eight treatments: 1) no additive (control), 2) calcium hydroxide (Ca(OH)2) at 2% fresh matter (FM), 3) molasses (MO) at 3% FM, 4) cellulase (CE) at 0.2 g/kg FM, 5) calcium hydroxide and molasses (Ca(OH)2:MO), 6) calcium hydroxide and cellulase (Ca(OH)2:CE), 7) molasses and cellulase (MO:CE), and 8) molasses, cellulase, and calcium hydroxide (MO:CE:Ca(OH)2). The CE enzyme (10,000 U/g, Sinobios IMP. & Exp. Co., Ltd, Shanghai, China). The additives were sprayed onto the indigo waste and then thoroughly combined. The indigo waste mixtures containing 500 g were packed into vacuum bags (Hiryu KN type, Asahi Kasei Pax Corp., Tokyo, Japan) with 32 bags (4 bags per treatment, 8 treatments), then sealed using a vacuum sealer (SQ-303, Asahi Kasei Pax Corp.). The silages were stored at room temperature and were then opened after a fermentation period of 30 days for silage quality, chemical analysis, and an in vitro investigation.
2.3. Fermentation end products and chemical composition of silages
A sample of silage (10 g of FM) was mixed with 90 mL of sterile distilled water and stored overnight at 4 ℃ [19]. The pH value was then measured with a portable pH meter (FiveGo, Mettler-Toledo GmbH, Greifensee, Switzerland). Measured the concentrations of lactic acid, acetic acid, propionic acid, and butyric acid by adding 480 μL of periodic acid (100 mM) and 300 μL of formic acid (10%) to 720 μL of standard as well as sample [20]. The mixture was then transferred to a gas chromatography machine (Nexis GC-2030, Shimadzu Co., Kyoto, Japan). The samples were evaluated for estimating the quantity of dry matter (DM), ash, and CP [21]. The NDF and acid detergent fiber (ADF) [22] were determined using a fiber analyzer (ANKOM 200, ANKOM Technology, NY, USA).
2.4. Animals and preparation of rumen inoculum
To supply the rumen fluid, two crossbred (Brahman x Thai native) beef cattle with a body weight (BW) of 200 ± 10 kg were used. Concentrate was added at a rate of 0.5% BW as DM, and rice straw was provided to the animal ad libitum. The cattle were fed twice daily, at 7:00 a.m. and 3:00 p.m., for 14 days. On day 15, 1000 mL of rumen fluid was collected from each animal using a stomach tube connected with a vacuum pump before the animal's morning feeding. The first 100 mL of rumen fluid were discarded in order to prevent saliva contamination. Rumen fluid was filtered through four layers of cheesecloth, placed in thermos flasks that had been pre-heated, and then transported to the laboratory.
Samples from each indigo waste silage were obtained, subjected to oven drying at 60 ℃ for a duration of 72 h, and crushed after passing through a 1 mm sieve. Samples of 0.5 g of each silage were weighed into 50 mL serum bottles. For a total of 36 bottles, there were four replicates of each treatment, 32 sample bottles, and 4 blank bottles. The ruminal fluid obtained from each animal was combined with an artificial saliva solution in a ratio of 2:1 (mL/mL) at a temperature of 39 ℃ while maintaining a constant flow of CO2 [23]. Each of the bottles contained 40 mL of rumen inoculum and was flushed with CO2. Aluminum caps and rubber stoppers have been used to cover the bottles. They were incubated at 39 ℃ and shaken at 60 rpm (Stuart orbital incubator S1600, Staffordshire, UK).
2.5. In vitro gas production and fermentation characteristics
The volume of gas produced was measured using a 25 mL calibrated glass syringe with an air connection at 0, 2, 4, 6, 8, 12, 24, 48, 72, and 96 hours. Each experimental run at each sample time contained four bottles containing only rumen inoculums. The average gas production quantities from these bottles were used as blanks. The net gas volume was calculated by subtracting the blank values from each value. The total amount of gas produced was put into the model of Orskov and McDonald [24] as follows: y = a + b [1 − e(-ct)]. In this context, let us define the following variables: a = the gas production from the immediately soluble fraction; b = the gas production from the insoluble fraction; c = the constant rate of gas production for the insoluble fraction; a + b = the potential extent of gas production; t = the incubation time; and y = the gas production at time "t".
Utilizing 32 bottles (4 bottles per treatment, 8 treatments), the IVDMD and IVOMD [25] were assessed after 24 hours of incubation. Using a second set of 32 bottles (4 bottles per treatment, 8 treatments), the pH, NH3-N [26] (Kjeltech Auto 1030 Analyzer, Tecator, Hoganiis, Sweden), and VFA [27] of ruminal fluid were assessed.
2.6. Statistical analysis
The data was evaluated for variances using an ANOVA procedure in SAS software [28], which uses a CRD. The following model was used to examine the data: Yij = µ + αi + εij, where Yi is the observation, µ is the overall mean, αi is the treatment effect, and εij is the residual error. Using Duncan's new multiple-range test, the mean difference between treatments was evaluated at p < 0.05.
3.
Results
3.1. Fermentation quality and chemical composition of silage
The pH of silage was lower for MO and MO:CE, whereas it was higher when adding only Ca(OH)2 to their combination when compared to the control (p < 0.01) (Table 1). The lactic acid content increased by 49.6, 44.9, and 72.2 g/kg DM for MO, CE, and MO:CE, respectively, when compared to the control (20.5 g/kg DM). The addition of Ca(OH)2:MO and Ca(OH)2:CE decreased the lactic acid content by 5.8 and 0.4 g/kg DM, respectively (p < 0.01). In addition, the acetic acid content of MO and MO:CE was lower than that of other treatments (p < 0.01). Adding Ca(OH)2:MO and Ca(OH)2:CE resulted in the lowest butyric acid concentration (p < 0.01). The CP content was increased in all additives (20.7–21.5% CP) than that of the control (19.5% CP) (p = 0.02) (Table 2). The NDF content decreased when adding Ca(OH)2:MO and Ca(OH)2:CE (60.7 and 59.4%, respectively) compared with the control (72.4%) (p < 0.01). The ash was higher for silage treated with Ca(OH)2, Ca(OH)2:MO, and MO:CE:Ca(OH)2, and highest for Ca(OH)2:CE (p < 0.01).
3.2. Gas kinetics, cumulative gas production, and in vitro degradability
All treatments did not change (p > 0.05) the cumulative gas at 96 h, the gas production from the immediately soluble fraction (a), the gas production from the insoluble fraction (b), or the potential extent of gas production (a + b) (Table 3). However, the constant rate of gas production for the insoluble fraction (c) was higher when MO was added (p = 0.03). The IVDMD was higher (p < 0.01) when MO, CE (33.7 and 32.4%, respectively), and the highest found in MO:CE (37.8%) in comparison to the control group (30.2%) (Table 4). The Ca(OH)2:MO treatment showed a significantly higher IVOMD (51.3%) compared to the control treatment (39.5%) (p = 0.03).
3.3. In vitro rumen fermentation characteristics
The ruminal pH was similar among treatments (p > 0.01) (Table 4). When adding Ca(OH)2, CE, Ca(OH)2:CE, or MO:CE, the ruminal NH3-N concentration was lower (28.0, 29.2, 26.9, and 28.6 mg/dL, respectively). The lowest concentration was found in Ca(OH)2:MO (24.5 mg/dL), compared to the control (32.7 mg/dL) (p < 0.01). The total VFA was increased for MO (92.9 mmol/l) when compared to the control (71.3 mmol/l) (p < 0.01) (Table 5). The proportions of propionic acid (C3) and butyric acid (C4) were increased, while acetic acid (C2) and C2:C3 were decreased using MO and CE treated indigo waste silage (p < 0.01).
4.
Discussion
4.1. Fermentation quality and chemical composition of silage
Lactic acid is the most efficient acid for lowering silage pH and preserving forage quality [29]. With the addition of MO and CE, lactic acid levels increased, and the maximum levels were found in MO:CE, resulting in a decrease in pH. Similarly, So et al. [8] reported that sugarcane bagasse fermenting with MO, CE, or their combination increased lactic acid and dropped the pH. The addition of molasses can offer a high quantity of soluble carbohydrate substrate for lactic acid bacteria (LAB) to produce lactic acid, thereby increasing the silage quality [13]. On the theory that exogenous enzymes can degrade cell walls and release soluble carbohydrates, lactic acid bacteria can then convert further into lactic acid [11]. In the present study, adding only Ca(OH)2 or a combination with molasses and cellulase lowered lactic acid while increasing the pH of silage. This result is consistent with Cook et al. [30], who showed that Ca(OH)2-treated corn silage reduced lactic acid and had a higher pH. These could explain the fact that the alkaline agents increased the pH, resulting in a lower lactic acid concentration when fermented with forage. Moreover, butyric acid was lowest (<0.3 g/kg DM) when adding Ca(OH)2:MO and Ca(OH)2:CE. Butyric acid shows clostridial metabolic activity, which results in substantial DM loss and insufficient energy recovery [31,32]. These results indicated that adding lime with molasses or cellulase prevented the growth of clostridia and improved the quality and palatability of silage.
All silage additives increased the CP content in the indigo waste silage. It is possible that MO, CE, or a combination stimulates fermentation to produce lactic acid, which speeds up the pH drop and inhibits CP degradation and harmful microorganisms [33]. In addition, previous studies suggested that Ca(OH)2-treated corn silage had a higher CP content when compared to untreated silage [34]. Some Clostridium species are capable of converting lactic acid to butyric acid and are also highly proteolytic. In the present study, adding Ca(OH)2 and its combination led to the lowest amount of butyric acid. This result might have inhibited clostridial growth and decreased the silage's proteolytic activity, which improved the CP content. The NDF content decreased when adding Ca(OH)2 with MO or CE to silage. The elimination of lignin and a portion of hemicellulose is referred to as alkali treatment [35]. MO is an easily accessible fermenting stimulant that supplies energy to microbes that hydrolyze plant cell walls [36], and CE may degrade the cellulose components effectively [37]. The lower NDF could be explained by the synergistic impact of Ca(OH)2 with MO or CE. Furthermore, the addition of Ca(OH)2 alone or combined with CE and MO improved the ash content of indigo waste silage. The increasing levels of ash found in alkali-treated forages demonstrated the additive's influence on adapting the mineral content of forages [38].
4.2. Gas kinetics, cumulative gas production, and in vitro degradability
The addition of MO enhances the constant rate of gas production for the insoluble fraction (c). This result was in agreement with So et al. [14], who reported that the addition of MO to sugarcane bagasse silage increases the c value in vitro gas production technique. It may be due to MO providing soluble carbohydrates for the growth of the bacterial population and also increasing quantities of fermentable substrates in the rumen. When comparing MO and CE to the control group, the IVDMD was higher, with the highest value observed in MO:CE in the silage. Similarly, So et al. [14] found that IVDMD was higher in silage treated with MO and CE together than in the control silage. At the time of ensiling, the CE had broken down the plant cell walls in the silage [15]. This makes it easier for microorganisms in the rumen to ferment the silage and improves degradation in the rumen [39,40]. Moreover, high-soluble carbohydrates are obtained by adding MO. These results indicated that the synergistic effect of MO:CE showed the highest efficiency of rumen degradation. The Ca(OH)2:MO-treated silage had a higher IVOMD. It could be plausible that the increase in protein content and a decrease in fiber level in Ca(OH)2:MO, while also providing more soluble carbohydrates, enhanced the ability of rumen microbes to efficiently degrade nutrients. Previous studies showed that Ca(OH)2 and MO increase the IVOMD of sugarcane bagasse and corn stover [7,41].
4.3. In vitro rumen fermentation characteristics
Not all the additives in an indigo waste silage alter the rumen pH. These results agree with Cherdthong et al. [42], who report that using MO or CE-treated rice straws has no effect on the rumen pH of beef cattle. However, So et al. [14] found that sugarcane bagasse fermented with molasses showed to lower in vitro rumen pH. The rumen pH in the present study for all additives ranges from 6.3–6.5, and the optimal pH range was 6.0–7.0 for the growth and activity of rumen microorganisms [43,44]. The NH3-N concentration in Ca(OH)2 and CE alone or in two additive combinations was lower than that of the control. The additives in indigo waste silage increase CP content. This makes it plausible that rumen microorganisms breaking down protein into NH3-N, which is linked to the supply of energy from soluble carbohydrates, could improve microbial protein synthesis and lower NH3-N. However, the addition of MO:CE:Ca(OH)2 in silage resulted in a higher ruminal NH3-N concentration than the control. The three additive combinations showed a lower constant rate of gas production for the insoluble fraction (c). This is possible due to rumen microbes lower degradation of nutrients, particularly carbohydrates, while protein is readily available to produce NH3-N, which then lowers microbial growth and also causes ruminal NH3-N accumulation. The influence of additives in silage on ruminal NH3-N may be confounding in our study. Satter and Slyter [45] showed that in vitro NH3-N concentrations of 20–50 mg/dL were optimal for rumen microbial growth. In the current study, the ruminal NH3-N concentrations (24.5–35.6 mg/dL) were within the normal range.
The enhanced production of VFA in the rumen is associated with the digestibility of nutrients and the rumen microbial population [46]. The higher rumen microbial population could enhance rumen VFA production [47]. The addition of MO to silage increases the total VFA concentration in the rumen. MO has high levels of soluble carbohydrates with higher fermentable forage, which may also increase the energy available for rumen microbial carbohydrate metabolisms, and may enhance VFA production. Ensiling indigo waste changes the VFA profile. Silages with MO and CE increase the proportions of propionic acid, while a decrease in acetic acid results in a lower C2:C3. A partial explanation for this phenomenon could be attributed to the high level of lactic acid in silages. MO in silage had a high population of lactic acid bacteria [15], resulting in a high lactic acid content, as found in our study. When feeding animals, rumen microorganisms rapidly ferment lactic acid to produce propionic acid. Adding cellulase enzyme to silage increases the water-soluble carbohydrate (WSC) by hydrolyzing the cellulose to glucose [48]. High glucose levels stimulate the growth of lactic acid bacteria (LAB), ultimately resulting in increased lactic acid production during ensiling, which is also converted to propionic acid in the rumen of ruminants [43]. In contrast, So et al. [14] reported that propionic acid in the rumen did not change when adding MO or CE to sugarcane bagasse silage in vitro. Moreover, adding MO and CE enhanced butyric acid and reduced acetic acid production in the present study. There exists a positive association between the production of butyrate and the levels of sugar and fermentable plant cell wall in forage [49]. This is possible due to silage with MO and CE, which may produce more WSC and higher degradability of fiber, resulting in higher butyric acid in the rumen. The process of converting two molecules of acetyl-CoA to butyrate additionally includes two steps that include the incorporation of hydrogen (H2) [50]. This reduces the influence of the lower H2 in the rumen and also inhibits methane production [51]. The alteration in rumen fermentation, characterized by rising propionic acid levels and reduced acetic acid levels, has been documented to have advantageous effects on ruminant productivity [52,53].
5.
Conclusions
Adding MO, CE, or their combination increased the lactic acid concentration and reduced the silage pH. The inclusion of Ca(OH)2 or their combination higher silage pH, and lowest acetic acid and butyric acid. Silage with all additives increases the CP content of silage, while a lower NDF content was found when adding Ca(OH)2 with MO or CE. Silages treated with MO, CE, and their combinations improved the IVDMD, while Ca(OH)2:MO increase IVOMD of indigo waste. Ensiled indigo waste by MO and CE showed lower acetic acid and higher propionic acid in the rumen. Based on our results, the addition of MO and CE for ensiled 30 days is recommended for indigo waste silage. Further assessments of the inclusion of additives in indigo waste silage will be conducted in an in vivo study.
Use of AI tools declaration
The authors declare that they have not used Artificial Intelligence (AI) tools in the creation of this article.
Acknowledgments
The authors are thankful the Department of Animal Science, Faculty of Natural Resources, Rajamangala University of Technology Isan, Sakon Nakhon Campus, and the Department of Animal Science, Faculty of Technology, Udon Thani Rajabhat University for the use of their research facilities. This research project is supported by Science Research and Innovation Fund. Contract No. FF66-P1-083.
Conflict of interest
The authors declare no conflicts of interest.
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