236 Journal of Chemical Engineering of Japan This article is published under a CC-BY license.

Journal of Chemical Engineering of Japan, Vol. 50, No. 4, pp. 236–243, 2017

Experimental Studies and Modeling of Devolatilization of Highly Viscous Solution in High-Speed Disperser

Shugang Ma1,2, Yuyun Bao1, Zhengming Gao1 and Ziqi Cai1

1 State Key Laboratory of Chemical Resource Engineering, School of Chemical Engineering, Beijing University of Chemical Technology, Mailbox 230, Beijing 100029, China

2 Petrochemical Research Institute, PetroChina Company Limited, Beijing 102206, China

Keywords: Polymer Devolatilization, High-Speed Disperser, Highly Viscous Solution, Acetone Removal Rate, Semi-Empirical Modeling

A novel high-speed disperser equipped with a rotor of simple structure is proposed to intensify the process of polymer devolatilization, which is almost indispensable in polymer manufacturing. Experiments on the rate of acetone removal from highly viscous acetone–syrup solution were conducted under di�erent operating conditions. The results indicated that, as the absolute pressure decreased, the acetone removal rate increased gradually and the removal of acetone was derived successively from di�usion and foam devolatilization. Meanwhile, the acetone removal rate increased with in-creasing rotor rotational speed and initial acetone concentration, but decreased with increasing inlet �ow rate. Besides, based on our previous work on the dimension and �ow characteristics of highly viscous liquid �laments, a semi-empiri-cal model of devolatilization was established to describe the process of di�usion devolatilization. A comparison between the experimental data and modeling results showed that the semi-empirical model was able to provide reasonable esti-mates of the acetone removal rate in di�usion devolatilization.

Introduction

In most polymer processing operations, residual volatiles (unreacted monomers, solvents, impurities, and reaction by-products) in concentrations ranging from several ppm to several tens of percent (Gestring and Mewes, 2002) almost invariably remain in the polymer products (Ye et al., 2005). In general, these volatiles can adversely affect the physical/chemical properties and application performance of poly-mers. The removal of residual volatiles from polymers is necessary and is usually achieved by a process called poly-mer devolatilization (Tukachinsky et al., 1993) to ensure the quality of the polymer products, meet environmental requirements (Francoeur et al., 2014), and eliminate health hazards.

Polymer devolatilization processes include mainly dif-fusion devolatilization for concentrated polymer solutions and foam devolatilization for polymer solutions with high concentrations of volatiles (Han and Han, 1986). Many mathematical models describing the above two devolatiliza-tion processes can be found in the literature. Ravindranath and Mashelkar (1988) developed an unsteady state diffu-sion model for polymer devolatilization in the presence of a stripping agent, while Blanks et al. (1981) modeled the diffusion devolatilization process in a styrene-polystyrene system under depolymerization conditions. Roberts (1970) presented a polymer devolatilization model based on the

classical penetration theory. This model accounted for the creation and renewal of exposed surface in single screw extruders, but slightly over estimated the expected values of diffusivities. Combining the penetration theory with a ma-terial balance on the volatile component, Secor (1986) de-veloped a mass transfer model for the removal of a volatile species in a twin-screw extruder, assuming that the diffusion coefficient was constant and the foaming was negligible. However, the model predicted a process screw length about 14% below the experimental value.

The diffusion devolatilization models mentioned above mainly assume that volatiles are removed from the polymer solutions by diffusion of the dissolved volatiles in the poly-mer through the interface between the polymer solution and the gas, and finally into the continuous gas phase. However, the foam devolatilization models usually hold the view that volatiles are removed from the polymer solutions by a series of complicated bubble behaviors and transfer mechanisms in devolatilization (Yang et al., 1997). So far, the mecha-nisms of foam devolatilization have been studied in various devolatilizers, such as the falling-strand devolatilizer (Al-balak et al., 1990) and screw extruder (Tukachinsky et al., 1994). Biesenberger and Lee (1986, 1987) and Lee and Bie-senberger (1989) systematically investigated the process of foam devolatilization in rotating machinery, and proposed a mathematical model and explanations for the experimental results. Yang et al. (1998) studied the foam devolatiliza-tion in an extruder, defined an adjustable parameter (the number of stripper bubbles) as a function of important process parameters, and developed a model for the design of the devolatilization section in the extruder. In fact, in the foam devolatilization, different bubble behaviors such as the

Received on January 8, 2016; accepted on September 3, 2016DOI: 10.1252/jcej.16we004Correspondence concerning this article should be addressed to Z. Cai (E-mail address: caiziqi@mail.buct.edu.cn).

Research Paper

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nucleation, growth, movement, deformation, concentration and coalescence, and collapse of bubbles affect the mass transfer in different ways, so it is difficult to fully describe the complex foaming process at present.

Since the devolatilization process accounts for 60–70% of the energy consumption in the production of polymers (Li et al., 2010b), developing high-efficiency devolatilizers for devolatilization intensification is necessary. In general, de-volatilizers can be classified into two broad categories—the still and the rotating devolatilizer—in polymer devolatiliza-tion. The still devolatilizers, including flash tank (Meister and Platt, 1989) and falling strand devolatilizer (Yarin et al., 1999; Rieckmann et al., 2011), usually have a simple struc-ture and enhance the removal of volatiles by flash evapora-tion and increasing the mass transfer interface, especially for polymer solutions with high concentrations of volatiles and low viscosities. The rotating devolatilizers, which mainly include wiped thin-film evaporator (Feres, 1987; Parrillo and Singh, 2005), screw extruder (Biesenberger and Kessi-dis, 1982; Collins et al., 1985; Foster and Lindt, 1989; Wang, 2001, 2007) and disc reactor (Woo et al., 2001), are usually applied to highly viscous polymer solutions, creating and renewing the mass transfer interface by rotation, extrusion, and shearing in the promotion of the volatile removal. How-ever, such traditional devolatilizers have weaknesses, such as large unit size, high energy consumption, and low mass transfer efficiency. In recent years, as a typical device for process intensification, the rotating packed bed (RPB) has gained increasing attention in polymer devolatilization on account of its small physical size, low energy consumption, and high mass transfer rate (Chu et al., 2014a, 2014b). Liu et al. (2008) used an RPB to remove free formaldehyde from a urea-formaldehyde resin, with water vapor and air as strip-ping gas, reaching removal efficiencies of 60% and 58%, re-spectively. Li et al. (2009, 2010b) employed a syrup/acetone system to simulate the process of polymer devolatilization in an RPB, where the acetone removal efficiency increased by about 67% over that of a flash tank, and the volatile removal efficiency in a real polymer solution (polyacrylonitrile with acrylonitrile monomers) could exceed 99% after the solution had been devolatilized twice by the proposed RPB.

In the present work, a high-speed disperser (Gao et al., 2015) with a simple rotor structure was utilized for the de-volatilization experiments. A solution of highly viscous syrup and acetone was employed to simulate a system of

polymer and volatile. The devolatilization experiments were conducted to study the effects of absolute pressure, rotor ro-tational speed, initial acetone concentration, and inlet flow rate on the removal rate of acetone from the highly viscous acetone–syrup solution. Moreover, based on our previous work (Gao et al., 2016) on the dimension and flow char-acteristics of highly viscous liquid filaments dispersed by the same rotor in a high-speed disperser, a semi-empirical model of devolatilization was put forward to describe the diffusion devolatilization process under the experimental absolute pressure, so as to understand the diffusion de-volatilization mechanism in depth and provide a theoreti-cal foundation for the application and optimization of this high-speed disperser.

1.　Experimental

1.1　Experimental setupThe apparatuses for the current devolatilization experi-

ments are schematically depicted in Figure 1(a). Syrup and acetone are mixed to form a homogeneous acetone–syrup solution in an airtight mixing tank equipped with com-bined impellers (a double helical ribbon impeller and mul-tiple narrow blade axial-flow impellers). The highly viscous acetone–syrup solution is conveyed into the high-speed disperser by a gear pump, and the vacuum in the high-speed disperser is generated by a vacuum pump. The ab-solute pressure in the high-speed disperser is adjusted by a valve between the high-speed disperser and atmosphere, and measured by a digital display resistance vacuum gauge (Guoguang ZDZ-52). Figure 1(b) shows a diagram of the rotor in the high-speed disperser. There are 180 vertical blades (each 2 mm in width and 50 mm in height) distrib-uted uniformly along the circumference of the rotor, whose external diameter and wall thickness are 219 mm and 4 mm, respectively. After entering the rotor, the highly viscous ace-tone–syrup solution is dispersed by the centrifugal force and the shearing of the blades, and a large amount of thin liquid filaments with high specific surface area per unit volume is generated in the cavity zone.

1.2　Experimental conditions and data processingIn the devolatilization experiments, the viscosity of the

acetone–syrup solution was measured by a rheometer (HAKKE RS150L). The rotor rotational speed and inlet flow

Fig. 1　(a) Schematic of experimental setup and (b) rotor

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rate were changed by the frequency converter connected to the motor. The experiments were conducted at a constant temperature of 25°C, and the detailed operating conditions are listed in Table 1.

The removal rate of acetone from the highly viscous ac-etone–syrup solution, here denoted by E, was adopted to evaluate the efficiency of the high-speed disperser during the devolatilization experiments.

−= ×0 f

0100%C CE C (1)

Here, C0 and Cf are the acetone concentrations in the initial and devolatilized acetone–syrup solution, respectively. The syrup and acetone are considered to be well mixed when the difference in acetone concentration between six sam-pling locations (distributed across different positions of the mixing tank in Figure 1(a)) is within the range of ±1%, and then the mean acetone concentration is taken as C0. Three samples are successively taken from the devolatil-ized acetone–syrup solution, and the acetone concentrations are measured. Similarly, the mean acetone concentration is taken as Cf.

The acetone concentrations in the initial and the devola-tilized acetone–syrup solution were measured by a UV-VIS spectrophotometer (LabTech BlueStar A) at 241 nm. Each sample of acetone–syrup solution was diluted by an equiva-lent mass of deionized water, and the relationship between the acetone concentration C and the acetone absorbance A is shown in Figure 2.

According to the plot in Figure 2, the acetone concentra-

tion C can be calculated by the following equation based on the acetone absorbance A at 241 nm.

= × + =20.373 0.007 0.997C A R (2)

1.3　Experimental results and discussionAs a complicated mass transfer process, polymer devola-

tilization is affected by various factors. For the devolatiliza-tion experiments in this work, the absolute pressure, rotor rotational speed, initial acetone concentration, and inlet flow rate affect the acetone removal rate in various ways, and interactive relationships can even exist among the above four variables. Therefore, the variable-controlling approach was adopted to separately study the effect of each of the above four variables on the acetone removal rate.

1.3.1　Effect of absolute pressure　The effect of absolute pressure on acetone removal rate is illustrated in Figure 3. Because of the relatively large range of absolute pressures in the experiments, two different devolatilization modes (diffu-sion and foam devolatilization) both exist in acetone remov-al. At high absolute pressures (P≥9 kPa), the removal of ac-etone is mainly attributed to diffusion devolatilization, and very few bubbles are generated after the acetone–syrup solu-tion enters the high-speed disperser (Figure 4(a)). Under the mechanism of diffusion devolatilization, the acetone removal rate increases with decreasing absolute pressure, as shown in Figure 3. The equilibrium concentration of ac-etone Ce in the dilute acetone–syrup solution can be calcu-lated from the acetone partial pressure PA in the continuous gas phase and Henry’s law constant H.

= Ae

PC H (3)

The decrease of absolute pressure in the high-speed dis-perser brings about a reduction of acetone partial pressure PA, leading to the increase of acetone mass transfer driving force (C−Ce), and thus promotes the removal of acetone. However, at low absolute pressures (P≤7 kPa), the removal of acetone mainly bases on foam devolatilization, and more and more bubbles exist in the highly viscous solution with the decrease of absolute pressure (Figures 4(b)–(d)). Appar-

Table 1　 Detailed operating conditions in devolatilization experi-ments

Variables Values

Absolute pressure P [kPa] 1, 3, 5, 7, 9, 11, 13, 15Rotor rotational speed N [rpm] 100, 300, 500, 700, 900, 1,100,

1,300, 1,500, 1,700Initial acetone concentration C0

[kmol/m3]0.117, 0.183, 0.343, 0.466, 0.552

Inlet flow rate Q [L/h] 156, 248, 288, 319, 380

Fig. 2 Relationship between concentration C and absorbance A of acetone at 241 nm

Fig. 3　Effect of absolute pressure on acetone removal rate

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ently, the presence of numerous bubbles enlarges the inter-facial area for acetone mass transfer. Besides, the formation, growth, coalescence, and collapse of bubbles contribute to the effective separation of acetone from the highly viscous solution by releasing the acetone into the gas phase con-necting with the vacuum pump, which greatly enhances the acetone removal compared with the diffusion-controlled process. Normally, the mass transfer driving force in foam devolatilization can be described by the following expres-sion.

−= eSH P P (4)

Here, SH and Pe are the superheat degree and equilibrium partial pressure of the volatile component. As shown in Fig-ure 3, the decrease of absolute pressure P in the high-speed disperser gives rise to the increase of SH, intensifies the foaming process by improving the growth rate and rupture probability of bubbles in the acetone–syrup solution, and further increases the acetone removal rate by enhancing the foam devolatilization.

1.3.2　Effect of rotor rotational speed　Figure 5 shows the effect of rotor rotational speed on the acetone removal rate in foam devolatilization. The acetone removal rate in-creases gradually as the rotational speed increases, but the growth slows down at high rotational speeds. After enter-ing the high-speed disperser, the acetone–syrup solution is dispersed into a large amount of liquid filaments in the order of millimeter/sub-millimeter by the high-speed rotating rotor, and a mass of bubbles come into being in the liquid filaments at sufficiently high superheat degree. First of all, as mentioned in our previous work (Gao et al., 2016), higher rotational speeds can generate thinner liquid filaments, thereby facilitating the movement of bubbles from the interior of the liquid filaments to the gas-liquid interface and the removal of acetone by bubble collapse. Furthermore,

the higher shear stress and turbulence caused by a higher ro-tational speed can further facilitate the nucleation of bubbles (Wong and Park, 2012), and then promote foam devolatil-ization. Finally, in spite of its modest contribution to acetone removal, diffusion devolatilization often coexists with foam devolatilization; thus, the mass transfer resistance for ac-etone removal by diffusion through the gas-liquid interface can be reduced by the thinner liquid filaments. However, with the increase of rotational speed, the mean residence time of liquid filaments in the cavity zone decreases (Gao et al., 2016). With the decrease in residence time of liquid filaments in the cavity zone, there is insufficient time for the mass transfer, so the increase of acetone removal rate slows down with further increases of rotational speed.

1.3.3　Effect of initial acetone concentration　Figure 6 indicates the effect of initial acetone concentration on ac-etone removal rate in foam devolatilization. The acetone removal rate increases with the increase of initial acetone concentration. In accordance with Henry’s law, a higher concentration of acetone in the acetone–syrup solution cor-responds to a higher acetone equilibrium partial pressure Pe, and the superheat degree SH (Eq. (4)) for foam devolatiliza-tion increases accordingly on the condition that the ambient absolute pressure remains unchanged, thus intensifying the foaming phenomenon and removal of acetone by accelerat-

Fig. 5　Effect of rotor rotational speed on acetone removal rate

Fig. 6　Effect of initial acetone concentration on acetone removal rate

Fig. 4 Images of (a) diffusion devolatilization (P=9 kPa) and (b), (c), and (d) foam devolatilization (P=7 kPa, 5 kPa, and 1 kPa, respectively)

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ing the nucleation, growth, and rupture of bubbles.1.3.4　Effect of inlet flow rate　The effect of inlet flow

rate on the acetone removal rate in foam devolatilization is shown in Figure 7. The acetone removal rate decreases with the increase of inlet flow rate. At a fixed rotor rotational speed, the increase of inlet flow rate may generate liquid filaments with larger diameters, limiting the movement of bubbles from the liquid filament interior to the gas–liquid interface and the subsequent removal of acetone by bubble collapse. Meanwhile, the increase in liquid filament diam-eter can also increase the mass transfer resistance for the ac-etone removal by diffusion through the gas-liquid interface. Furthermore, Figure 7 also shows that, as the inlet flow rate increases, the drop in acetone removal rate is much larger at low rotor rotational speeds than at high rotor rotational speeds. That is, the acetone removal rate is more sensitive to the inlet flow rate at a lower rotor rotational speed than at a higher rotor rotational speed.

1.3.5　Comparison of acetone removal rates between high-speed disperser and flash tank　The flash tank has been widely utilized to accomplish the polymer devola-tilization commercially since it has the characteristics of simple structure and low equipment cost. In order to show the devolatilization efficiency of the high-speed disperser, a flash devolatilization experiment was conducted and the comparison of acetone removal rates is listed in Table 2. According to the results in Table 2, it is found that the mean acetone removal rates at 300 rpm and 1,500 rpm in the high-speed disperser increase by about 35% and 66% respectively compared with that in the flash tank, indicating that the

high-speed disperser can promote the volatile removal and enhance the polymer devolatilization.

2.　Semi-Empirical Model of Di�usion Devolatilization

2.1　Modeling of di�usion devolatilizationIn our experiments, we found that at high absolute pres-

sures (P≥9 kPa), the removal of acetone mainly depends on diffusion devolatilization. The acetone inside the liquid filaments passes through the mass transfer interface between the solution and continuous gas phase, and then is stripped by means of vacuum. The highly viscous acetone–syrup so-lution can be split into large amounts of arc-shaped liquid filaments by the high-speed rotating rotor, and in the con-tinuous operation, the liquid filaments move forward along the direction of their extension (Gao et al., 2016), so it is reasonable to consider that no backmixing of materials ex-ists in a single liquid filament. Meanwhile, without regard to the interaction between liquid filaments in the cavity zone, it can be assumed that the acetone concentration distribu-tions along all the liquid filaments are consistent with one another.

In diffusion devolatilization, ignoring the existence of rare bubbles and assuming that the diffusive mass transfer mainly happens on the cylindrical surface of the liquid fila-ments in contact with the gas phase, the mass balance of ac-etone can be carried out in a small volume element of liquid filament with a diameter of d and a length of dl (Figure 8).

− ⋅ ⋅ ⋅ ⋅=s Ad dQ C π d l N (5)

Here, −Qs·dC is the change in the number of moles of ac-etone per unit time getting through the volume element, and π ·d ·dl ·NA is the number of moles of acetone transferred by the diffusive mass transfer through the external surface of the volume element per unit time. The volume flow rate Qs along each liquid filament can be expressed as Eq. (6).

= 2s e4

πQ d v (6)

Here, ve is the velocity along the direction of liquid filament extension and can be calculated according to Eqs. (4)–(6) in our previous work (Gao et al., 2016). Also, an expression for the liquid filament diameter d as a function of the angular velocity ω0 of the rotor and the polar radius r in the cavity zone was proposed in our previous work (Gao et al., 2016).

− −= +0.960 1.84100.631 0.086d ω r (7)

On the basis of the penetration theory, the average molar transfer rate of acetone per unit interfacial area per unit time can be given by Eq. (8).

−=A e( )DN C Cπt (8)

The same composition of acetone–syrup solution was em-ployed by Li et al. (2010a) in their devolatilization system. In the current work, the acetone diffusion coefficient in the

Fig. 7　Effect of inlet flow rate on acetone removal rate

Table 2　Acetone removal rates in the flash tank and high-speed disperser (C0=0.343 kmol/m3, Q=156 L/h)

Absolute pressure P [kPa]

Removal rate EFlash [%]

Removal rate EN=300 rpm [%]

Removal rate EN=1,500 rpm [%]

3 18.5 24.6 29.05 12.4 18.7 21.67 9.8 10.7 12.9

11 2.7 3.8 6.213 0.9 1.8 3.8

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highly viscous acetone–syrup solution is assumed to be con-stant and can be calculated according to the following equa-tion on the acetone diffusion coefficient in their study.

− −= × 16 3.2916 1.2422576.8987 10D T μ (9)

Substituting Eqs. (6) and (8) and the expression dl=ve·dt into Eq. (5) and integrating the resulting expression, we ob-tain Eq. (10).

−− =

f

0 0e

1 4d dC τ

C

DC tC C d πt (10)

Therefore, the acetone concentration Cf in the devolatilized acetone–syrup solution can be calculated as follows.

−− −

=f e

0 e

8expC C DτC C d π (11)

Here, τ is the mean residence time of liquid filaments in the cavity zone. τ can also be calculated according to our previ-ous work (Gao et al., 2016).

−= 105.985τ ω (12)

Along with the liquid filament diameter in Eq. (7) and the acetone diffusion coefficient in Eq. (9), the removal rate of acetone (Eq. (1)) under diffusion devolatilization can ulti-mately be obtained according to Eq. (11).

2.2　Experiments vs. modelingThe Henry’s law constant is an important parameter as-

sociated with the thermodynamic limitations of polymer devolatilization. In the modeling, the equilibrium concen-tration of acetone Ce in the acetone–syrup solution in Eq. (11) was calculated from the Henry’s law constant (Eq. (3)), which was obtained by regression analysis of the experimen-tal data of diffusion devolatilization.

⋅= 344.61(kPa m )/kmolH (13)

Therefore, the calculated values of acetone removal rate in the diffusion devolatilization are available.

Figure 9 compares the calculated and the experimental results of the removal rate of acetone in diffusion devolatil-ization. With relative errors in the range of ±30%, the diffu-sion devolatilization model in the current work is acceptable to characterize the process of diffusion devolatilization.

Conclusions

The effectiveness of a high-speed disperser for polymer devolatilization was experimentally investigated. Using a highly viscous acetone–syrup solution to simulate an indus-trial system of polymer solution with volatile components, we measured the acetone removal rate under various op-erating conditions. The experimental results revealed that the acetone removal rate increased with the reduction of absolute pressure, and foam devolatilization played a more important role in enhancing the removal of volatile compo-nents than diffusion devolatilization. As the rotor rotational speed increased, a lower mass transfer resistance and stron-ger promotion of bubble nucleation were generated by the dispersion effect of the rotor in the foam devolatilization, thereby increasing the acetone removal rate. Moreover, the acetone removal rate increased with increasing initial ac-etone concentration and decreasing inlet flow rate. Accord-ing to the law of mass conservation and penetration theory, a semi-empirical model of diffusion devolatilization was developed to analyze the process of diffusion devolatiliza-tion, and the maximum relative error between the calculated and experimental removal rates of acetone was in the range of ±30%.

However, the above work, including the experiments and modeling, is just a preliminary study on the devolatiliza-tion process in the high-speed disperser. To thoroughly understand the diffusion or foam devolatilization process, we need to measure the Henry’s law constant and diffusion coefficient experimentally, and establish a mechanism of devolatilization in future studies. In addition, the simple rotor structure should be further optimized to accomplish efficient devolatilization.

Acknowledgement

The financial support from the National Natural Science Foundation of China (Nos. 21676007 and 21506005) is gratefully acknowledged.

Fig. 8　Schematic diagram of diffusion devolatilization modeling

Fig. 9 Comparison of calculated and experimental results of acetone removal rate in diffusion devolatilization

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Nomenclature

A = acetone absorbance at 241 nm [—]C = acetone concentration, defined by Eq. (2) [kmol/m3]Ce = equilibrium concentration of acetone, defined

by Eq. (3) [kmol/m3]Cf = acetone concentration in devolatilized acetone–

syrup solution [kmol/m3]C0 = initial acetone concentration [kmol/m3]D = acetone diffusion coefficient, defined by Eq. (9) [m2/s]d = diameter of the volume element of liquid filament,

defined by Eq. (7) [mm]E = removal rate of acetone, defined by Eq. (1) [—]H = Henry’s law constant [(kPa·m3)/kmol]N = rotor rotational speed [rpm]NA = average molar transfer rate of acetone, defined

by Eq. (8) [kmol/(m2·s)]P = absolute pressure [kPa]PA = acetone partial pressure [kPa]Pe = equilibrium partial pressure of acetone [kPa]Q = inlet flow rate [L/h]Qs = volume flow rate along each liquid filament, defined

by Eq. (6) [m3/s]r = polar radius in the cavity zone [m]SH = superheat degree, defined by Eq. (4) [kPa]T = absolute temperature [K]ve = velocity along the direction of liquid filament

extension [m/s]μ = viscosity of acetone–syrup solution [Pa·s]τ = mean residence time of liquid filaments in the cavity

zone, defined by Eq. (12) [s]ω0 = angular velocity of rotor [1/s]

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