Drag reduction in turbulent flows by diutan gum: A very stable natural drag reducer

Drag reduction in turbulent flows by Diutan Gum: a very stable natural drag reducer

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Drag reduction in turbulent flows by Diutan Gum: a very stable natural drag reducer Walber R. dos Santos, Eduardo Spalenza Caser, Edson J. Soares, Renato N. Siqueira PII: DOI: Reference:

S0377-0257(19)30417-3 https://doi.org/10.1016/j.jnnfm.2019.104223 JNNFM 104223

To appear in:

Journal of Non-Newtonian Fluid Mechanics

Received date: Revised date: Accepted date:

16 April 2019 29 November 2019 7 December 2019

Please cite this article as: Walber R. dos Santos, Eduardo Spalenza Caser, Edson J. Soares, Renato N. Siqueira, Drag reduction in turbulent flows by Diutan Gum: a very stable natural drag reducer, Journal of Non-Newtonian Fluid Mechanics (2019), doi: https://doi.org/10.1016/j.jnnfm.2019.104223

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Highlights • We analyse the ability of Diutan gum (DG) to reduce drag in turbulent ows; • We show that DG is very stable and effcient; • The drag reduction ability of DG is compared with other polymers. • We carried out different viscosity tests to show that DG is a rigid material.

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Drag reduction in turbulent flows by Diutan Gum: a very stable natural drag reducer Walber R. dos Santosa , Eduardo Spalenza Casera , Edson J. Soaresa , Renato N. Siqueirab a Laboratory of Rheology, LABREO, Department of Mechanical Engineering, Federal University of Esp´ırito Santo, Avenida Fernando Ferrari, 514, Goiabeiras, 29075-910, ES, Brazil b Fluid Mechanics Research Laboratory, LPMF, Department of Mechanical Engineering, Federal Institute of Esp´ırito Santo - Campus S˜ ao Mateus, Rod. BR 101 norte, km 58, Litorˆ aneo, S˜ ao Mateus, ES, 29932-540, Brazil

Abstract We study the ability of diutan gum (DG), a polysaccharide that belongs to a class called sphingans, to improve drag reduction (DR) in turbulent flows. This new drag reducer is very stable. Its efficiency in terms of DR does not significantly fall, which means that the polymer degradation or de-aggregation is not important at all. The onset of DR is independent of Reynolds number and concentration, typical from rigid materials for which the DR mechanism is called Type-B. The efficiency of DG solutions was compared with those of xanthan gum (XG) (rigid polymer) and polyethilene oxide (PEO) (flexible polymer) solutions.

Email addresses: [email protected] (Edson J. Soares), +55 27 30392989 (Edson J. Soares)

Preprint submitted to Elsevier

December 12, 2019

1. Introduction Drag reduction (DR) by polymers has been studied since the pioneering work of Toms [1], who observed that a small quantity of polymethyl methacrylate (a synthetic flexible polymer) diluted in monochlorbenzene was able to significantly reduce the pressure drop in turbulent flows through straight tubes. The number of applications is very broad, including fire fighting [2], the transport of liquids in pipelines [3, 4, 5], agriculture [6] and medicine [7, 8, 9, 10, 11, 12]. The efficiency of a specific application depends on several distinct aspects of DR. Lumley [13] mentions a number of important features, as polymer’s concentration, molecular weight, temperature, molecular structure and length; polymeric flexibility and relaxation; Reynolds number; and quality of the solvent. Among these variables, concentration and molecular weight of the polymer are the most known. These two parameters work to increase DR until an ultimate asymptote is reached. Virk et al. [14] checked several concentrations and molecular weights of many kinds of polymers and found that DR is bounded by the so called maximum drag reduction asymptote (MDR). A great overview, where one can find the main aspects of some of the variables listed before, including the polymer concentration and molecular weight, can be found in Virk [15]. A great effort has been devoted to understand the mechanism of polymeric DR. There are two basic ideas. The first one comes from Lumley [13], who argues that polymers are stretched by the turbulent structures and, as a result, the extensional viscosity increases, which works to dissipate the small vortices. Many authors recently used this idea to construct their model, as Ryskin [16] and Benzi [17]. The second idea comes from Tabor and de 3

Gennes [18]. They consider that the polymers directly interact with the turbulent structures in a coil-stretch cycle and the turbulent kinetic energy is transformed by a counter-torque like mechanism into elastic energy, some vortices are destroyed and the elastic energy is released to the mean flow. This idea was recently followed by many authors in an attempt to further understand the mechanism of DR [19, 20, 21, 22, 23, 24, 25]. It is interesting to point that the most available theoretical works (based on [13] or [18]) consider that the polymers are stretched, i.e., the polymers are flexible. However, many drag reducers are rigid polymers. According to Virk et al. [26], drag reduction can be divided into two very distinct mechanisms: Type A and Type B. The former is associated with polymers that stay coiled at rest (flexible polymers). Such materials need a certain level of turbulence to stretch and start to reduce drag. In contrast, the second mechanism is related to polymers that stay extended at rest (rigid polymers). Consequently, the onset of the drag reduction is expected to occur earlier when the Type B mechanism is dominant. As suggested by Gasljevic et al. [27], in the case of Type B mechanism of drag reduction, since polymer molecules are fully stretched, when the fluid is at rest, a further increase in the level of turbulence does not result in a substantial change of molecular conformation. Andrade et al. [28] conducted some interesting tests with PEO (a flexible polymers). They tested a sample previously sheared at a laminar flow and observed that onset of DR was faster in comparison with a regular sample, without pre-shearing (see fig. 9 of [28]). They argued that, in the pre-sheared sample, the molecules were more stretched, which is in accordance with the idea of Type B mechanism of DR. The mechanism of DR

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for Xantham Gum solutions is clearly of Type B (see [29]). This mechanism is particularly important for our work because we believe that DG is also a rigid material, as we will show later. A huge obstacle to the attempts to develop new drag reducers is the mechanical molecular degradation. Flexible polymers strongly break under turbulent flows and, as consequence, the DR falls step by step until reaching an asymptotic value after a long enough time. This issue has received much attention and many important aspects have been studied, as the effect of concentration, molecular weight, Reynolds number, temperature and polymer conformation on polymer degradation [30, 31, 32, 33, 29, 34, 35, 36]. A good alternative to avoid mechanical degradation and stabilize DR is to use rigid drag reducers, as rigid polymers. When this kind of material is used, the DR is not necessarily constant, but it is, normally, more stable than flexible polymers, as largely observed for many different rigid materials, as XG [29, 37], Guar Gum [6, 38] and different mucilages [39, 40, 41, 42]. Another obstacle for a stable DR is the so called polymer de-aggregation, owing to ruptures of the intermolecular associations instead of to an intramolecular mechanical scission. Shetty and Solomon [43], using light scattering, provide evidence of the formation of aggregates in aqueous solutions of PEO, even in ultra-low concentrations. This polymer structure, containing more than one molecular chain, increases the drag reduction efficiency. In fact, we also believe that the aggregates play an important role in other kinds of polymers, especially in some rigid materials as XG [29, 44]. The main focus of this paper is to investigate the role played by diutan gum (DG) in drag reducing flows. As far as we know, this is the first

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study related to the ability of DG to reduce drag. DG is a polysaccharide belonging to a class called sphingans, produced by bacterias of the genus Sphingomonas, which was isolated from an algal sample by Peik et al. [45]. This group of polysaccharides generally has tetrasaccharide backbone structure [46, 47]. The sphingans gellan, welan, rhamsan and diutan are produced commercially for use in food, industrial, oilfield or personal care applications. The structure of the sphingans polysaccharide are similar, but variations in the composition and linkage produce unique rheological characteristics. Diutan consists of a repeat unit with L-rhamnose, D-glucose, D-glucuronic acid, D-glucose backbone and a two sugar L-rhamnose side-chains attached to the (1 → 4) linked glucose residue (see fig. 1 of [48]). In aqueous solutions, DG has double helix configuration, which is similar to that of XG. The main difference is that the configuration of the DG seems to be more regular than that of XG (see fig. 7 of [49]). 2. Rheological characterization of polymeric solutions We use in our DR tests DG solutions (provided by CP Kelco) with Mv = 5.0×106 g/mol, PEO with Mv = 5.0×106 g/mol and XG with Mv = 2.0×106 g/mol (PEO and XG were provided by Sigma Adrich). The rheological characterization shown here is mainly related to DG, since the rheological behaviour of PEO and XG is already properly known [29, 37, 44]. Our rheometry is mainly based on flow curves, measurements of the storage and loss moduli and first normal stress difference for a range of DG concentrations. We used the Haake Mars III rheometer, by ThermoScientific. This apparatus can provide reliable measurements above a minimum torque of 5.1×10−8 Nm. 6

The flow curves for a large range of DG concentrations (25 ppm ≤ c ≤

10000) with temperature fixed at 25 o C are shown in Fig. 1. DG is highly shear thinning, even for small concentrations (below 100 ppm). Such behaviour is similar to the observed for XG (see fig. 4 C of [29]), which depicts highly shear thinning behaviour even for solutions with small concentrations of the polymer. The viscosities of the DG solutions are well fitted by a Carreau-Yasuda (CY) like equation: η − η∞ 1 , = η0 − η∞ [1 + (λCY γ) ˙ a ]n/a

(1)

where η0 and η∞ are the viscosities in the zero-shear and infinite shear plateaus and 1/λCY and n are, respectively, a characteristic shear rate and the power-law index. The parameter a was introduced by [50]. In Table 1, the curve fitting parameters for DG are displayed. In addition, we also included the parameters for XG and PEO solutions used in our DR tests. Table 1: Carreau-Yasuda parameters for DG, XG and PEO solutions. Polymer DG DG DG DG DG DG DG DG DG DG DG DG DG

c [ppm] 25 50 75 100 200 400 800 1000 2000 4000 6000 8000 10000

η0 [Pa s] 0.040 0.055 0.060 0.080 0.180 0.380 1.600 5.500 10.00 26.00 45.00 90.00 190.00

η∞ [Pa s] 0.0011 0.0011 0.0012 0.0012 0.0014 0.0016 0.0018 0.0031 0.0039 0.0054 0.0061 0.0067 0.0086

λCY [s] 1.00 1.00 1.00 1.00 1.00 3.00 5.00 10.00 11.00 21.00 26.00 38.00 50.00

n 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.13 0.14 0.18 0.19 0.16 0.14

a 0.20 0.25 0.25 0.30 0.35 1.00 2.50 1.60 1.80 1.70 1.80 2.30 3.00

XG XG XG XG

50 100 200 800

0.050 0.073 0.098 0.598

0.0011 0.0012 0.0012 0.0018

25.00 30.00 35.00 40.00

0.35 0.40 0.40 0.45

0.20 0.25 1.20 0.33

PEO PEO PEO PEO

50 100 200 800

0.0050 0.0055 0.0065 0.030

0.0011 0.0011 0.0012 0.0024

2.00 2.20 2.40 2.80

0.40 0.45 0.40 0.55

0.30 0.20 0.25 0.30

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Based on the infinity shear-viscosity (η∞ ) and on the zero shear-viscosity (η0 ) obtained from the CY curve fittings (displayed in Table 1), we inferred the overlap concentration c∗ of DG. In Fig. 2, η∞ and η0 were displayed as a function of the concentration c. Supposedly, c∗ is the concentration for which η∞ or η0 is considerably increased. Using this technique we found c∗DG ≈ 91

ppm and c∗DG ≈ 114, based, respectively, in η∞ and η0 . The same procedure was used by [29] and [51] to estimate c∗ of XG. These authors used only η0 ,

but, as one can see, both characteristic viscosities can be used to estimate c∗ . They found very different values for c∗ . In fact, this procedure is not very precise, specially using η0 , which is not very well characterized for small concentrations. Hence, since we are comparing the data of DR obtained with DG with that with XG, we also inferred c∗ of XG using the same method to obtain c∗XG ≈ 181 ppm based on η∞ and c∗XG ≈ 196 ppm, based on η0

(different values of c∗ for XG are reported in the literature, like for instance 100 ppm by [52]. The overlap concentration of PEO was estimated by means of the relation c∗ [η] = k, where [η] is the intrinsic viscosity. Varius values of k have been proposed in the literature as k = 1 ([53]) and k = 0.77 ([54]). It depends on polymer-solvent system. For water PEO solutions, k = 1 has been used by different authors [55, 56, 57]. Using k = 1, we found c∗P EO = 3900 ppm. Our range of DG concentration used in the DR tests was 25 ≤ c ≤ 800. The comparison with XG and PEO was for the range 50 ≤ c ≤ 800. Hence, we worked with diluted and concentrated solutions of DG and XG and only diluted for that cases with PEO. Fig. 3 shows our measurements of the storage G0 (in the top) and loss G00 (in the middle) moduli for solutions of DG at different concentrations. In the

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bottom of this figure, the ratio G0 /G00 is shown. Clearly, G0 and G00 increase with concentration and frequency, specially the ratio G0 /G00 , the relative importance of the elastic modulus, which is a very known characteristic of viscoelastic materials. The behaviour of PEO, PAM and XG are similar. In fact, G0 /G00 of DG solutions have the same order of magnitude of XG for the same range of concentrations (see fig. 5 of [29]). We also measured the first normal stress difference N1 versus shear rate (Fig. 4). N1 is close to zero for solutions of DG with c ≤ 20, 000 ppm. Even for concentrations

significantly larger than the overlap concentration (c/c∗ ≥ 500), N1 starts

from high values at small shear rates (γ˙ ≈ 10−2 ) and reaches around zero at γ˙ ≈ 1. 3. Experimental apparatus and procedure Our tests of DR were carried out in two distinct experimental apparatus: a) a rheometer with cylindrical single / double gap device and b) a pipeline. We used the rheometer for preliminary tests, since the amount of material necessary for the experiments is very small and the measurements are very precise and fast, but the Reynolds number that can be achieved in these tests is not very high, much lower than the value found in practical applications. Since we are interested interested in demonstrating that DG is a good alternative drag reducer for long term applications, it is quite convenient to conduct tests at very high flow dynamic intensities, which is found in many real processes. Practical Reynolds numbers were obtained in our a pipe system. All solutions were obtained by gently spreading the polymer powders on the solvent surfaces. The dilution was simply by diffusion. This procedure 9

was adopted to avoid any polymer degradation or de-aggregation before the beginning of the test. For the tests carried out in the rheometer, the desired concentration were obtained from a concentrated sample (8000 ppm) diluted in deionized water. For the tests in the pipeline, since the amount of solution was quite large, we used simply filtered water. The solutions were prepared in recipients of 50 l. Each sequence of tests consumed 150 l and was carried out after 96 hours, the time for complete natural diffusion. The DR was calculated by Eq. (2), DR = 1 − fp /f0 .

(2)

Where fp and f0 are the friction factor of the polymeric solution and solvent, respectively, at the same Reynolds number. The two approaches (rotating apparatus and pipe system) are described in the sequence and the definition of other important parameters will be properly given with respect to each geometry. 3.1. Rotating apparatus The main details concerning our rotational apparatus and procedure were well discussed in our previous works [29, 57] (see Fig. 1 A and B in [57]). Hence, only the essential details are pointed here. The Reynolds number, Rer , and the friction factor, f , are defined for our rotating apparatus as follows:

¯ ωR ¯ ¯ ρ h ρhu Rer = = , η∞ η∞ f=

2τ 2τ =
. 2 ¯ 2 ρu ρ ωR 10

(3)

(4)

¯ Where η∞ is the solution’s viscosity at very high shear rate (see Table 1), ω R ¯ = (R2 + R3 )/2 is is a characteristic velocity, ω is the rotor angular velocity, R ¯ = Ri in the case of Taylor-Couette. the mean radius for the double gap and R ¯ is the given by ((R2 − R1 ) + (R4 − R3 ))/2 for the double The average gap h gap and by (Ra − Ri ) for the Taylor-Couette. It is worth noting that the viscosities of DG and XG solutions are highly shear thinning, even for low concentrations. Since the shear rates in the turbulent flows are very high, η∞ is the appropriate characteristic value of viscosity that must be used in the definition of Rer . 3.2. Pipe system Our pipe system was the same used in some of our previous works [34, 40, 42, 58] (see Fig. 1 in [34]). The polymer solutions, previously diluted, were deposited in the storage tank. The vessel is connected to a centrifugal pump, which is electronically controlled to keep the flow rate at a constant value. The path from the vessel to the test section was constructed to minimize any local material degradation or de-aggregation [34]. A magnetic flowmeter was placed at a point where the turbulent flow was fully developed. Static pressure transducers were placed on the right side of the flowmeter. After all the solution, initially in the pressure vessel, pass through the pipeline, with total length of 13.5 m, it is sent to the storage tank. The main section of test is 593 diameters long. The test temperature was kept constant at 25 o C. The flow rates, the values of the static pressures at the test section and the temperatures, at different points of the experiment, were collected simultaneously by a data acquisition system. When the total amount of solution, initially in the pressure vessel, had 11

passed through the pipeline, one round was finished. After that, the solution, now partially degraded or de-aggregated, returns from the storage tank to the pressure vessel by gravity, in a very slow motion, to avoid any uncontrolled polymer degradation or de-aggregation, and, finally, one cycle has been completed and the same solution is then used for the next cycle (similar procedure was used in [33, 59]). The value of the friction factor of the solution was calculated at each step and the test continued until no significant change in f was observed. In the majority of the cases, less than 25 steps were necessary to reach the steady state. For a given flow rate, the Darcy friction factor is calculated by   2D ∆P f= 2 . ρ¯ u L

(5)

Here, ∆P is the pressure drop between a pair of pressure transducers placed in the test section and L is the distance between them. D is the tube diameter, ρ is the density of the solution and u¯ is its mean velocity in the test section. The Reynolds number is defined, as usual, as

Re =

ρ¯ uD . η∞

(6)

Here, as previously pointed, η∞ is the solvent’s viscosity at high shear rate. It is worth pointing that the wall shear rate in our tests is very high. In most of our tests the flow rate was kept at 4 m3 /h. The diameter of the test section was 1.25 cm. Hence, the average velocity was around 9.1 m/s. For a laminar flow of a Newtonian fluid, the wall shear rate is 8¯ u/D. In such a flow, the shear rate would be 5,824 s−1 , which is virtually the infinity shear rate for the most concentrated solution (800 ppm) that we have used in our 12

tests (see the flow curves, Fig. 1). Since in our tests the flows are turbulent, the wall shear rate is significantly larger than 5,824 s−1 , which allow us to conclude that the infinity shear viscosity is, in fact, the best choice to define Reynolds number. 4. Results and discussion As commented before, our first data (Figs 5 and 6) were carried out in a rheometer with a double gap geometry, an apparatus quite adequate to gain an accurate and intuitive understanding of drag reducers, but limited to small Reynolds number. Fig. 5 displays the the wall shear stress divided by the shear rate (τw /γ) ˙ in terms of rotor angular velocity for DG concentrations ranging from 25 ppm to 200 ppm, in a temperature fixed at 25 o C. The term τw /γ, ˙ is definitely the solution’s viscosity for the range of angular velocity in which the flow is laminar and stable. When instabilities appear τw /γ˙ start to increase. The tests were carried out increasing the angular velocity from zero to 3000 rpm, state at which the flow is fully turbulent. The values of τw /γ˙ for DG solutions are compared with those from the deionized water (hollow black circles). For water, the flow becomes unstable for angular velocities larger than 500 rpm. After that, τw /γ˙ starts to increase, initially because of flow instabilities, and eventually, turbulence, at high rotor’s velocity. As expected, the transition between stable and unstable flow is shifted to the right by an increasing concentration, reaching 1000 rpm for c = 200 ppm. It is worth noting in Fig. 5 that there is not a practical DR for high concentrated solutions at small Re, because the significative increment in the viscosity. For 200 ppm (blue full triangles), for example, η∞ is around 60 % larger than the water’s 13

viscosity. For this case, an effective DR only occurs for angular velocity larger than 2000 rpm. In Fig. 6 the friction factor f is displayed for our double gap device √ √ in Prandtl von-K´arm´an coordinates (1/ f versus log(Rer f )) for concentrations of DG ranging from 2 ppm to 200 ppm. Rer varies from 350 at √ √ log(Rer f ) = 1.4 and reaches 1380 for log(Rer f ) = 1.9. We suppose that the transitional regime is narrow and the flow dynamics is mainly turbulent √ in this geometry (see discussion in [57]). The factor 1/ f is bounded by that for the water (hollow black circles) and the MDR asymptote (dashed line) √ √ (1/ f = 17.00log(Rer f ) − 11.55), an alternative Virk’s law for this rotating geometry proposed by Pereira and Soares [29]. For flexible polymers, the onset of DR, the value of Rer at which the friction factor departs from the Newtonian one, is clearly a decreasing function of concentration [15]. For rigid polymers, the onset is quite independent of c. It means that DR really exists, even for very small Rer . It seems that it is the case displayed in Fig. 6. √ The coefficient 1/ f is detached from the Newtonian for all the range of Rer analyzed, even for 5 ppm, the smallest concentration in which DR is observed here. Results reported by [29, 37, 60], using Xanthan Gum (XG), and by [51] using Scleroglucan (rigid-chain polymers), also indicate such an effect of the Reynolds number on the friction factor. The reason for these observations is related to the fact that rigid polymers are already extended on its equilibrium state at rest, which favours their interaction with the turbulent structures, reducing the drag. This is known as Type B mechanism of drag reduction, as discussed by Virk et al. [26]. Hence, what we see in Fig. 6 is a behaviour very similar to those of rigid polymers. Our next data will confirm

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that DG is really a rigid polymer. The next DR data were obtained in our pipe system for temperature fixed at 25 o C. Fig. 7 shows DR for DG in the range of concentrations 25 ppm ≤ c ≤ 800 ppm. These tests were conducted at fixed flow rate (4.0 m3 /h), instead of fixed Re. Such a value of flow rate is the maximum obtained in our apparatus. We chose it to obtain the most extreme condition for polymer degradation. Hence, since viscosity increases with c, the Reynolds numbers varies from a minimum Re = 44,000 (for 800 ppm) to a maximum Re = 83,000 (for 25 ppm). Some of the tests were carried out twice to show repeatability. We show here only the case for 200 ppm (purple squares). There is not a significant difference between them. We see that DG is a quite efficient drag reducer. The DR is 14 % for 25 ppm and 70 % for 800 ppm. It is worth noting that the DR is almost constant over the number of passes through the pipe system. This is very positive. Such a fact further suggests that DG is really a rigid material. A similar behaviour in terms of stability was found for aloe vera, another bio-polymer recently studied by our group using the same apparatus (see fig. 5 of [42]). The difference is that for aloe vera, the DR falls a little bit during the first passes through the system, whereas for DG the change of DR is insignificant. Soares at al. [42] argued that there is possibly polymer de-aggregation in aloe vera solutions, which would be the cause of fall in their efficiency. We will come back to this point later. The maximum value of DR in DG solutions is also clearly higher than that for aloe vera. For 800 ppm the DRasy is, respectively, 50 % and 70 % for aloe vera and DG (compare Fig. 7 of the present work and fig. 5 of [42]). We proved that DG is very stable even at very high Re (Fig. 7). However,

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25 passes in our system means in total only 65 s of residence time1 . Hence one question about the DG stability remains: what happens with the DG molecules after a very long residence time? Supposedly, the DG could start to break after a long period of stability caused, for example, by something like polymer weariness. As an attempt to answer this question we conducted the test displayed in Fig. 8, which shows a long term DR test for 100 ppm of DG in the Taylor-Couette device at a fixed Rer = 3560 (based on the gap). Such a long term test was conducted in our rotating apparatus because the polymers would be more susceptible to bio-degradation in our pipe line system. Moreover, the test control is easier on the rotating apparatus. The disadvantage, as mentioned before, is the small value of Reynolds number reached in this kind of geometry. If we use the general definition of Reynolds number, as discussed in [61], we will see that for the Taylor-Couette geometry the Reynolds number is, in fact, around 7120, twice the value computed by Eq. 3, nevertheless much smaller than that reached in our pipe system. Despite of that, flexible polymers, like PEO or PAM, would be strongly degraded in less than one hour with this level of Rer [29, 57]. This long term DR test was carried out for over 72 h, which implies a residence time around 4000 times larger than that for 25 passes in our pipe system. The molecules of DG does not break at all, which suggest that weariness does not play any role. In the next two figures we will discuss about the thermal stability of DG and XG. This is crucial for applications of drag reducers in cooling or heating 1

Our system has a straight horizontal pipe of 13.5 m and the tube diameter is 0.0165 m. For the tests in Fig. 7, the flow rate is fixed in 4 m3 /h.

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systems, for example. We carried out a sequence of tests with 100 ppm of DG and XG at Rer = 1040 in our rotating apparatus with the double gap device (Figs 9 and 10). The initial temperature was always Ti = 25 o C. At first, the samples were cooled from Ti to 5 o C at a cooling rate of 1o /min. After 10 min under this temperature, the sample was heated again to Ti , the test temperature. The triangles in both figures are the reference values of DR (tests with fresh solutions without cooling or heating). For both polymers, the cooling process had null effect on DR (see the squares symbols). In a second analysis, we investigate the effect of an increasing temperature on the DR efficiency. The samples were heated from the initial temperature Ti = 25 o C to Tf at a heating rate of 1o /min. After 10 min under Tf , the sample was cooled again to 25 o C, the test temperature. We tested top temperatures of 65 o C and 85 o C for both bio-polymers. Positively, the efficiency of DG was insensitive to the applied heating-cooling cycles, even for Tf = 85 o C. The values of DR for the DG solution were quite the same, around 0.2. Differently, the DR for XG was considerably reduced by the heating process. For Tf = 65 o C, DRmax , at the beginning of the test, fell from 0.21 (reference test - triangles) to 0.16 (circles). For Tf = 85 o C, DRmax was 0.09, significantly smaller than that of the reference test (57 % smaller than the DR of the reference test). This behaviour can be explained by the fact that the double helix structure of DG is not affected by temperature. Differently, the structure of XG is disordered when temperature is increased (see fig. 7 of Xu et al. [62]). As any bio-polymer, bio-degradation always plays a role. In Fig. 11 we took into account such effect in DG using a solution of 200 ppm in our

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pipe system. We have not taken into account the detailed bio-degradation mechanism as in [63, 64]. However, bacteria is probably one important cause, since the degradation was reduced by the use of bioside, as we will show later. The DR for the fresh solution was around 47 % after 25 passes through the system. After that, the solution rested into the reservoir tank. The test was repeated day by day until the fourth day, when DR dropped to 38 % (black cross). After one week, DR reached 32 % (orange down triangles). Three weeks later, almost a month from the test with the fresh solution, the DR was yet positive, around 10 %. Other bio-materials as Okra and aloe vera mucilages are less resistant to bio-degradation. We have previously conducted the same kind of test (similar dynamical condition and residence time) with these materials and they lost their ability to reduce drag in less than 10 days (see fig. 5 of [40] and fig. 9 of [42]). The bio-degradation can be avoided or, at least, minimized using biocides. We used sodium chloride (NaCl), a natural biocide, and potassium sorbate (C6 H7 KO2 ). We conducted a sequence of DR tests in our double gap device over 28 days comparing the DR efficiency for four different solvents with 100 ppm DG in Fig. 12. The solutions were exposed to the same condition of the test displayed in Fig. 11. The first solvent is pure deionized water (blue triangles), the second and the third are, respectively, deionized water with 3.5 % (red circles) and 10.0 % of NaCl (green diamonds). The last solvent is 0.05 % of C6 H7 KO2 in deionized water (grey triangles). The presence of salt and potassium sorbate reduces the DR efficiency and the stability of DG, which suggests that DG is a polyelectrolyte and its configuration is affected by the presence of ions, N a+ and Cl− for the case of salt in water. However, the reduction of DR is

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not very pronounced, different of what happens with XG, which has its DR efficiency dramatically reduced [35]). On the first day of test DRasy is 0.215 for pure water, 0.175 for water with 3.5 % of NaCl and 0.145 for the salt concentration equal 10 %. For the case of potassium sorbate, DRasy is 0.180 at the first day, quite close the DR for 3.5 % of NaCl. Fig. 12 also displays the 0 relative asymptotic drag reduction DRasy = DRasy /DRmax , where DRmax

is the maximum DR at the first day of test. Interesting that after 7 days of the first test, the DR efficiency for the solvent with 10 % on NaCl was not 0 at the first day was 0.81 and 0.79 in the considerably affected. Its DRasy 0 started seventh day. The case of pure water was very different. The DRasy 0 at 0.95 and reached 0.69 at the seventh day. After 28 days, DRasy for the

most concentrated salt solution was 0.51, substantially larger than that for pure water, 0.36. The absolute values of DR for solutions with NaCl were also larger than that for pure water. The biodegradation was better avoided 0 by Potassium sorbate, since its DRasy was 0.81 after 28 days. Hence, bio-

degradation can really be reduced, even using NaCl, a simple natural biocide, but this aspect of the problem must be better studied to find an optimum DR solution with maximum DR at the beginning (for fresh solution) with minimum bio-degradation. Our next tests were conducted to compare the ability of DG to reduce drag with other two very used water drag reducers: XG and PEO. The first is a rigid bio-polymer and the second is a flexible synthetic one. The main data were displayed in Fig. 13. We used solutions of 800 ppm at Re = 44, 000 and the tests were limited to 25 passes Np through the system. The DR for DG (red balls) was virtually constant, the DR0 at the last step was 0.98. For

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the case of XG, the DR started at 68 %, at first pass, and reached 58 % at Np =25, a relative drag reduction DR0 = DR(Np = 25)/DRmax =0.85. As expected, the loss of efficiency of PEO solutions was more pronounced. The DR started at 72 % and reached 42 % at Np =25, DR0 =0.59. The loss of efficiency is commonly related to polymer degradation, but also to polymer de-aggregation. A recent review focused on this issue is [65]. As we will show next, it is easier to relate the loss of DR to polymer degradation, because it can be inferred in terms of changes of viscosity. If degradation really occurs, the viscosity of the solution falls, but it seems that the same does not happen in the case of de-aggregation. Fig. 14 shows the specific viscosity µs = (µp −µ0 )/µ0 as a function of concentration for DG, XG and PEO. µs is simply a measure of how viscosity increases with addition of polymers. The terms µp and µ0 are, respectively, the viscosity of the polymeric solution and the solvent. We used a capillary viscosimeter (model Cannon-Fenske) in which the shear rate is determined by γ˙ = 4V/(πr3 t), where V is the sample’s volume, r is the capillary radius, and t is the time required for the sample to move between two fixed points. The viscosimeter used has r = 0.27 mm, V = 3 ml. For all solutions in Fig. 14, the range of test time was between 126 s and 151 s, which implies a range of shear rate of 1285 s−1 ≤ γ˙ ≤ 1552 s−1 . These values of γ˙ are quite close the infinity shear rate for solutions with c ≤ 50 ppm. Hence, the values of viscosities in Fig. 14 are virtually the infinity shear-viscosity. The full symbols in Fig. 14 are for fresh solutions, while the hollow ones are for samples of the solutions collect after the test displayed in Fig. 13. The difference between the fresh and old solutions (called before and after test in Fig. 14) of DG (red symbols)

20

and XG (blue symbols) is not very pronounced. The maximum difference between fresh and old solutions was for 50 ppm of DG, around 6 %. The case of PEO (green triangles) was totally different. µs for the old solution was significantly smaller, around 67 % for 50 ppm. We also show the flow curves for the fresh and old solutions with 800 ppm for the three polymers in Fig. 15. Again, for DG (red balls) and XG (blue triangles) there is not a significant difference between the fresh (full symbols) and old (hollow symbols) solutions. However, the flow curves for fresh and old PEO solutions (purple squares) are very different. In fact, the values of viscosity of PEO solutions after the DR test (hollow purple squares) were significantly smaller over all range of shear rates. Based only on the DR test in Fig. 13 and on the tests of viscosities for fresh and old solutions in Figs 14 and 15, we can say that the DR for DG does not fall over time because it is a rigid material, which is confirmed by the fact that the viscosity of its polymeric solutions does not change at all. The case of PEO is also clear. If the PEO viscosity falls, it means that its molecular weight certainly also falls and that is the main cause of the decrease in DR values, as largely reported [29, 34, 57, 66, 67]. What is not so clear, at a first glance, is the case of XG. The DR for this polymer falls over time, but the viscosity of its solution does not significantly change. Such persistent viscosity confirms that XG is really a rigid polymer. Its molecule does not mechanically breaks by the turbulent flow. Hence, if the molecules do not break, why does DR falls? We argued in many previous woks [29, 34, 40, 42, 68] that the fall of efficiency observed in bio-drag reducers, which includes XG, is possibly related to de-aggregation instead of degradation. What we

21

are showing here is that, possibly, the de-aggregation is not linked to viscosity, i.e., different from polymer degradation, the polymer de-aggregation is not sufficient to reduce viscosity. Finally, in Figs 16 and 17 we compare the DR induced by DG with PEO and XG, respectively, for three different concentrations, 50 ppm, 100 ppm and 200 ppm. For all concentrations, at the beginning, the DR of PEO solutions is larger than that observed for DG, but after few passes through the system, around five, the PEO solutions loose efficiency, mainly because of mechanical degradation, and their DR becomes smaller than that of DG, which is almost constant during all the test. For 200 ppm, for example, the DRasy of the DG is 48 % (purple hollow squares in Fig. 16). In this case the DR0 at the last pass is around 0.94. For 200 ppm of PEO the DR is 18 % (purple full squares in Fig. 16), which implies a DR0 = 0.25. XG also loses efficiency, as it is shown in Fig. 17 (as argued before, possibly by deaggregation, a mechanism different from mechanical degradation). The DR induced by DG is always larger than that from XG. For 200 ppm, the DR of the XG starts from 43 % and reaches 27 %, with DR0 = 0.62 (full purple squares), much smaller than that from DG. The DR0 at the last pass for DG is also larger than 0.90 for the other two concentrations, while is always around 0.60 for XG. 5. Concluding Remarks We investigated the ability of DG to reduce drag in turbulent flows. This new drag reducer is a polysaccharide from the class called sphingans, having a molecular structure formed by a tetrasaccharide backbone. In water solution, the DG molecule has a double helix configuration, similar to that of XG, but 22

more regular. Our data has proved that DG gum is a rigid material. The onset of DR was independent of Rer and c, which characterizes the Type B DR mechanism. The DR efficiency for DG is significantly larger than those for PEO or XG, mainly because PEO strongly degrades and XG, possibly, de-aggregates step by step during the DR test. In fact, it is very impressive that the DR for DG does not fall at all, even after heating-cooling cycles or for long term tests, which means that molecular scission or de-aggregation do not play any role for this new drag reducer. The measurements of viscosity before and after the DR test confirm such a fact. The viscosities of DG and XG were almost the same, while that of PEO significantly decreased, indicating molecular degradation. 6. Acknowledgements This research was partially funded by grants from Brazilian Research Council (CNPq). References [1] B. A. Toms. Some observations on the flow of linear polymer solutions through straight tubes at large Reynolds numbers. Proceedings of the International Congress of Rheology, Holland, North-Holland, Amsterdam, Section II, pages 135–141, 1948. [2] A. G. Fabula. Fire-fighting benefits of polymeric friction reduction. Trans ASME J Basic Engng, pages 93–453, 1971. [3] E. D. Burger and L. G. Chorn. Studies of drag reduction conducted over

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Figure 1: Flow curves for DG solutions for the range of concentrations 25 ppm ≤ c ≤ 10,000 ppm. The symbols are the experimental data and the lines are Carreau-Yassuda curve fittings.

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Figure 2: Overlap concentration of DG.

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Figure 3: Small amplitude oscillatory analysis: a) storage modulus G’; b) Loss modulus G”; c) The ratio G’/G”.

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Figure 4: First normal stress difference versus shear rate for three concentrated DG solution

.

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Figure 5: Ratio between wall shear stress and shear rate for the range of concentrations 2 ppm ≤ c ≤ 200 ppm.

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Figure 6: Friction factor in the double gap geometry in Prandtl-von K´ arm´ an coordinates for the range of concentrations 2 ppm ≤ c ≤ 200 ppm. Re varies from 350 r √ at log(Re f ) = 1.4 and reaches 1380 for water and 810 for 200 ppm of DG at √r log(Rer f ) = 1.9.

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Figure 7: DR versus the number of passes through the pipe system for the range of concentrations 25 ppm ≤ c ≤ 800 ppm at fixed flow rate.

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Figure 8: DR versus time for 100 ppm of DG in a Taylor-Coutte device: a long term DR test.

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Figure 9: DR versus time for 100 ppm of DG in a Taylor-Coutte device: Heating and cooling cycles.

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Figure 10: DR versus time for 100 ppm of XG in a Taylor-Coutte device: Heating and cooling cycles.

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Figure 11: DR versus the number of passes through the pipe system for a solution of 200 ppm of DG: bio-degradation over 28 days.

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Figure 12: DR versus time in the double gap device for a solution of 100 ppm of DG: the effect of salt to avoid bio-degradation over 28 days.

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Figure 13: DR versus the number of passes through the pipe system: comparison between DG, XG and PEO.

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Figure 14: Specific viscosities of DG, XG and PEO. Full symbols are the data for fresh solutions and hollow symbols are the data for solutions used in the DR test displayed in Fig. 13.

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Figure 15: Flow curves for 800 ppm of DG, XG and PEO. Full symbols are the data for fresh solutions and hollow symbols are the data for solutions used in the DR test displayed in Fig. 13.

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Figure 16: DR versus the number of passes through the pipe system: comparison between DG and PEO.

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Figure 17: DR versus the number of passes through the pipe system: comparison between DG and XG.

49