Development of model for studies on momentum transfer in electrochemical cells with entry region coil as turbulence promoter
 51 Downloads
Abstract
Entry region swirl promoters gain importance in industry because of its effectiveness in augmentation of mass and heat transfer augmentation. Design of equipment needs momentum transfer data along with mass or heat transfer data. Hence an experimental investigation was carried out with coaxially placed entry region spiral coil as turbulence promoters on momentum transfer in forced convection flow of electrolyte in circular conduits. Aqueous solution of sodium hydroxide and 0.01 M equimolal Ferriferro cyanide system was chosen for the study. The study covered parameters like effect of pitch of the coil, effect of length of the coil, diameter of the coil, diameter of the coil wire, diameter of the annular rod. The promoter is measured by limiting current technique using diffusion controlled electrochemical reactions. The study comprises of evaluation of momentum transfer rates at the outer wall of the electrochemical cell. Pressure drop measurements were also made to obtain the energy consumption pattern. Within the range of variables covered. The results are correlated by the momentum transfer similarity function. Momentum transfer coefficients were evaluated from measured limiting currents. Effect of each parameter was studied in terms of friction factor. A model was developed for momentum transfer. The experimental data on momentum transfer was modeled in terms of momentum transfer function and Reynolds number, geometric parameters.
Nomenclature
 _{A}
Area of electrode (m^{2})
 ^{C}
Constants of correlations of equations
 _{C}
Concentration of electrolyte (kgmole/ m^{3})
 _{CL}
Length of the conduit (m)
 d
Diameter of the conduit (m)
 _{de}
Equivalent diameter of the conduit (dd_{i}) (m)
 _{D}
Diffusion coefficient (m^{2}/s)
 ^{Dc}
Diametre of the coil (m)
 ^{Dw}
Diametre of the coil wire (m)
 ^{Di}
Diametre of the annular rod (m)
 _{De}
Eddy diffusivity (m^{2}/s)
 _{F}
Faraday’s constant = 96,540 (coulombs/gmole)
 I_{L}
Limiting current density (amp)
 k_{L}
Mass transfer coefficient (m/s)
 L_{c}
Length of the coil (m)
 N
Mass flux
 P_{c}
Pitch of the coil (m/turn)
 R
Radius of the conduit (m)
 u_{i}
Velocity at the interface (m/s)
 u_{b}
Average velocity (m/s)
 u^{∗}
Friction velocity(\( \sqrt{\tau_0/\rho } \))
 u_{i}^{+}
Dimensionless velocity (u/u^{∗})
 u_{b}^{+}
Dimensionless bulk velocity
 \( {u}_m^{+} \)
Average fluid velocity (m/s)
 ^{V}
Superficial velocity (m/s)
 y
Coordinate distance normal to wall (m)
 y_{1}
Distance from wall at which u = u_{b}
 \( {y}_1^{+} \)
dimensionless distance (yu^{*}/ν)
Dimensionless
 f
Friction factor
 \( {\operatorname{Re}}_m^{+} \)
Roughness Reynolds number for homogeneous flow
 R (h^{+})
Roughness Momentum Transfer
 St
Stanton number
 Sc
Schmidt number
 Φ
Ratio between total of molecular and eddy viscosity and total of molecular and eddy diffusivity (ν_{ t }/D_{ t } )
 Ф_{1}
P_{c}/d_{e}
 Ф_{2}
L_{c}/d_{e}
 Ф_{3}
D_{c}/d_{e}
 Ф_{4}
D_{W}/d_{e}
 Ф_{5}
D_{i}/d_{e}
 n
Numbers of ions transferred
 η
Performance factor
Greek symbols
 τ
Shear stress (kg/ms^{2})
 μ
Viscosity of the fluid (poise)
 ρ
Density of the fluid (kg/m^{3})
 τ_{0}
Wall shear stress (kg/ms^{2}, f/2. ρ.ub^{2})
 υ
Kinematics viscosity
 υ_{e}
Eddy kinematics viscosity
Subscripts
 b
Buffer
 i
Interface
 o
Wall
 p
Based on particle diameter
 t
Total of molecular and eddy
 v
Viscous
 Vb
Viscous buffer region
1 Introduction
Augmentation of heat and mass transfer processes are never ending quest for an engineer or technologist. Augmentation of a transfer processes offer the following advantages. Increased throughputs for a particular size of an equipment or reduced size of equipment for a particular flow rate. The other advantages are less floor area, ease in handling of raw material and utilities. These factors leads to the reduction unit product cost. Hence the augmentation technique found attractive for researchers. To arrive at this above objective, several strategies have been followed. Efforts have been continued with the investigation being directed towards achieving energy efficient mass transfer cells with assembly of the coils. The earliest augmentative technique is surface roughness [1] several works were reported in literature. Use of baffles [2] and surface alternations also come under this section. Works like spheres [3], fins [4], bluff bodies [5] and stream lined bodies [6] placed across the flow were also extensively found in literature. Flow through ducts and arched channels [7], jets [8] were also encountered. Investigations on insert promoters in heat and mass transfer operations were reported extensively. The work reported was on concentric rod placed in the circular conduit, since then heat and mass transfer studies with coaxially placed turbulence promoters were reported extensively. The investigation on coaxially placed promoters like twisted tapes [9], tapes wound on a rod [10], spiral coils [11], string of spheres [12] and cones [13], discs [14], orifices [15], circular rings places on a rod [16] were also studied. But works found in literature seemed to increase friction there by higher operating costs. This is particularly true for string of spheres, string of cone, string of discs [14], and flow past cylindrical rod [17], across stream lined bodies [18], and many devices like axially displaced promoters, and surface modifiers.
In the present study an effort is made in acquiring higher augmentation rate with lower frictional losses. It will lead to the construction of energy efficient transfer operation. Several researchers employed swirl flow for the augmentation of their process. Therefore an attempt is made to employ swirl motion in achieving this objective swirl flow devices were incorporated in circular conduits and found their effectiveness on heat and mass transfer processes. Among the swirl generating devices twisted tapes [19], tapes wound on a rod [10], spiral coils [11], spiral coils placed on central rod of an annular conduits [20] and tangential entry of fluid are prominent. Among the coaxially placed promoters, Entry region swirl generating promoters received the attention of several researchers. Nageswara Rao V [21] employed tape, tapedisc assembly as turbulence promoters in their study. Murali Mohan et al. [22] used entry region coil and coildisc assembly as turbulence promoters in circular conduits generated useful data for the augmentation. Present investigation is directed towards achieving energy efficient transfer process. To that effect, it envisaged to obtain mass transfer data at the inner wall of annular conduits along the length of the column. Subsequently, local mass transfer data were obtained and the results were reported. These results could be adopted for enhancing mass transfer processes like electro dialysis [23], ultra filtration [24], reverse osmosis [25] and several other processes and reported increased transfer rates. The electrochemical processes like electro winning [26], electro refining [27], electro milling [28] and electro organic synthesis [29] could employ swirl generating promoters to obtain higher transfer rates. Swirl flows have wide range of applications in various engineering areas such as chemical processes like mechanical mixing and separation devices, combustion chambers, turbo machinery, rocketry, etc. It can be effectively used in heat and mass transfer enhancements. In view of these observations, the present research work is momentum transfer data are experimentally obtained in the presence of electrochemical cells with entry region coil as turbulence promoter. It deals with the presence of the momentum transfer rate at the wall through limiting current technique.
 1.
To obtain limiting currents data on the outer wall of an annular conduits with entry region coil as turbulence promoters.
 2.
To study the effect of geometric parameters on mass transfer namely  pitch of the coil (P_{c}), length of the coil (L_{c}), diameter of the coil (D_{c}), diameter of the coil wire (D_{w}), and diameter of the annular rod (D_{i}) on the outer wall momentum transfer coefficients.
 3.
To generate pressure drop data with insert promoters and to identify the effect of geometric parameters such as pitch of the coil (P_{c}), length of the coil (L_{c}), diameter of the coil (D_{c}), diameter of the coil wire (D_{w}), and diameter of the annular rod (D_{i}).
 4.
To develop generalized correlations for momentum transfer in homogeneous flow.
 1.
Momentum transfer coefficient is increases with increasing in velocity.
 2.
Friction factor values are increasing with increase in pitch of the coil.
 3.
Momentum transfer is increasing monotonously with increase in length of the coil.
 4.
The effect of momentum transfer coefficient on the diameter of the coil has marginal effect on friction factor in the present study.
 5.Correlations were developed based on semi theoretical considerations. Wall similarity concept is used in the development of correlations. The following Correlation developed for momentum transfer is presented as:

Homogeneous flow
$$ R\left({h}^{+}\right)=18648\kern0.24em {\left[{\operatorname{Re}}_m^{+}\right]}^{1}\kern0.24em {(Fr)}^{0.495}\kern0.24em {\left(\frac{D_W}{d_e}\right)}^{0.77}\kern0.24em {\left(\frac{D_i}{d_e}\right)}^{0.175} $$(1) 
This equation is useful for the design and development of energy efficient transfer processes.
2 Experimentation
The recirculation tank was a cylindrical copper vessel of 100 l capacity with a drain pipe and a gate valve (V_{1}) for periodical cleaning of the tank. A copper coiled tube (H) provided with perforations. The perforations were meant for bubble of nitrogen through the electrolyte. The bubbling of nitrogen through the electrolyte expels the dissolved oxygen present if any. The tank was connected to the pump with a 0.025 m diameter copper pipe on the suction line of the centrifugal pump. The suction line was also provided with a gate valve (V_{2}). The discharge line from the pump divided into 2 lines. One line served as a bypass and a controlled by valve (V_{3}) is incorporated in it. The other line was connected to the entrance calming section (A). A control valve (V_{4}) and a rotameter were also incorporated in the line. The control valve was used to regulate the flow of electrolyte. The rotameter served as flow measuring device. The rotameter has a range of 0 to 347 × 10^{−6} m^{3}/s. The entrance calming section was circular copper pipe of 0.046 m ID provided with a flange and closed at the bottom with a gland nut (G_{1}). To an extent of 0.1 m of entrance calming was filled with capillary tube to damp the flow fluctuations and to facilitate steady flow of the electrolyte through the test section.
Range of variables covered in the present study
Variables  Minimum  Maximum 

Pitch of the coil (P_{c}), m/turn  0.016  0.046 
Length of the coil (L_{c}), m  0.05  0.16 
Diameter of the coil (D_{c}), m  0.031  0.038 
Diameter of the coil wire (D_{w}), m  0.006  0.008 
Diameter of the annular rod (D_{i}), m  0.0127  0.0254 
Reynolds number, Re  1200  14,500 
Schmidt number, Sc  789  1132 
Details of the coil assembly promoter covered in the present study
Pitch of the Coil (P_{ c }), m: 0.016, 0.026, 0.036, 0.046 
Length of the Coil (L_{ c }), m: 0.05, 0.09, 0.12, 0.16 
Diameter of the Coil (D_{ c }), m: 0.031, 0.034, 0.038 
Diameter of the coil wire (D_{ w }), m: 0.006, 0.007, 0.008 
Eighty liters of equimolal solution of 0.01 N Potassium ferricyanide and 0.01 N Potassium ferrocyanide with 0.5 N Sodium hydroxide as electrolyte was prepared used as the system. The electrolyte was analyzed for ferrocyanide ion concentration by volumetric titration method using standard potassium permanganate solution [1] and for ferricyanide ion using idometric method [2]. The viscosity of the solutions at different temperatures were measured with Ostwald Viscometer and densities were measured using specific gravity bottle. The point electrodes in the test section were polished using four zero emery to get a smooth surface followed by degreasing with trichloroethylene solution. The size of the electrode was measured with a traveling microscope. After fixing the promoter in position, blank runs i.e. were conducted with sodium hydroxide electrolyte alone to ensure that the limiting currents obtained were due to diffusion of reacting ions (Ferricyanide ion) only. Subsequently, known quantities of potassium ferricyanide and potassium ferrocyanide were added to get the concentration of electrolyte was maintained at equimolal 0.01 M Ferriferrocyanide couple was maintained.
The coils of known geometry were fitted at the entrance of the test section by means of flanged joint and the annular rods were fixed by means of gland nuts. The experiments were repeated by replacing the coil and /or annular rod. The electrolyte was pumped at a desired flow rate (through the test section) by operating the control and bypass valves. After the steady state was attained, potential was applied across the test electrode and wall electrode in small increments of potential (100 mV) and the corresponding current values were measured for each increment. As the area of the wall electrode was relatively large in relation to the area of the test electrode, nearly constant potential was obtained at the test electrode. Since the potential values are not of criteria in the present study, the limiting currents only were obtained from the current and potential data.
Pressure drop measurements for each flow rate were made simultaneously by using a U – tube manometer with Carbon tetrachloride as manometer liquid.
3 Results and discussions
Experiments were conducted with entry region coil promoter assembly in a homogeneous flow of electrolyte. It deals with 7500 local limiting current data obtained at the outer wall of an annular conduit fitted with an entry region spiral coil as a turbulence promoter. Local limiting currents at the outer wall of an annulus were measured along the length of the column. Cathodic reduction of ferricyanide ion was chosen as the system for the present study.
3.1 Studies on homogeneous flow with entry region coil in annular conduits
The experimental measurements consists of the flow rate of an electrolyte (Q), limiting current (i_{L}). From the measured current potential data, limiting currents were identified. The concentration of reacting ion (C_{o}) was estimated by isometric. Physical properties of the solution namely density (ρ), viscosity (μ) were measured by suitable method. The values of Diffusivities (D_{L}) were estimated by the method mentioned in experimental procedure. Diameter of the test section (d) and dimensions of the promoter assembly viz., pitch of the coil (P_{c}), length of the coil (L_{c}), diameter of the coil (D_{c})_{,} diameter of the wire of the coil (D_{W})_{,} diameter of the annular rod (d_{i}) and temperature (T), were measured with suitable instruments.
3.2 Momentum transfer
Based on friction factor versus Reynolds number data one can analyze the energy losses. The information is highly useful in the design and development of energy efficient electrochemical cells. The frictional losses are directly related to the flow condition prevailed in the column. These friction factor data would be useful in the analysis of mass transfer data which is analyzed in terms of geometric parameters of the promoters.
3.3 Effect of pitch of the coil
It is further observed that at any velocity within the range of variables covered in the present study, friction values are increasing with increase in pitch of the coil. The increase would continue up to certain pitch, on further increase in pitch would result in decrease in pitch because of the reduction in number of turns and thereby blockage or due to the reduction in cross flow element. Such pitch may be called a critical pitch. Similar observations were also made in mass transfer and by several other works [11, 20, 30, 31, and]. The early observation of this critical pitch is seen in mass transfer which may be an indication that the energy spent in the generation of turbulence is not fully utilized to augment mass transfer.
3.4 Effect of length of the coil
3.5 Effect of coil diameter
3.6 Effect of the diameter of the coil wire diameter
3.7 Energy enhancements over the data of smooth pipe flow
3.8 Performance of the entry region coil promoter
4 Development of generalized correlations
4.1 Momentum transfer
In view of these large deviations, an alternative approach has been attempted by the use of the wall similarity concept proposed by Webb, R, L et al. [1], Dippery and Saborsky [32], Nikuradse, J [33] and Deissler R G [34]. The similar concept assumes velocity distribution is expected to experience the effect of viscosity at the surface. When an object is placed across the flow in a circular conduit, drag is generated and the drag enhances turbulence. Thus generated turbulence exerts tractive force at the wall and makes the boundary layers thinner. The flow is divided into 2 regions namely inner region and outer region. The inner region constituted with boundary layer whose thickness is δ at y^{+}, where δ is small. The velocity distribution depends on y^{+}, τ_{0}, μ.
Combination of Eqs. 11 and 12 gives the velocity distribution equation for the turbulent dominated part of the wall region
The above equation presents modified velocity profile for the case of out turbulent region in the presence of promoters. Assuming that Eq. 14 holds good for the entire cross section of the circular conduit, the friction factor for the turbulent flow with entry region coil inside the annular conduit can be given by integration of Eq. 13. The generated roughness function R(h^{+}) is given by the following equation
Here, C_{1} is proportionality constant and b_{1} is an exponent, Re_{m}^{+} is roughness Reynolds number defined by the following equations for entry region coil with annular conduits in homogeneous flow. The analysis could also be useful for fluidized beds with modification of particle Reynolds number defined in following text.
4.2 Homogeneous flow
Multiple regression analysis was conducted with relevant geometric groups also resulted very high deviations. An attempt is made to include Froude group,
The effect of Froude group is prominently appearing when ever vortex or swirl generating type of flow appears. The regression analysis was conducted with R (h^{+}) and with 2 dimensionless numbers namely Reynolds number and Froude group.
5 Comparison of correlation
5.1 Efficiency of the promoter
6 Conclusions
 1.
Friction factor values are increasing with increase in pitch of the coil.
 2.
Larger the length of the coil greater the frictional values.
 3.
Diameter of the coil has marginal effect on friction factor in the present study.
 4.
Greater the coil wire diameter larger the friction factors.
 5.
The energy factor values are decreasing with Reynolds number.
 6.
The Performance of the coils are increasing linearly with Re. The promoter producing higher turbulence is also augmenting better and the efficiencies are increasing steeply indicating higher augmentation at lower flow rates.
 7.A Model developed for momentum transfer in homogeneous flow is as follows:$$ R\left({h}^{+}\right)=18648\;{\left[{\operatorname{Re}}_m^{+}\right]}^{1}{(Fr)}^{0.495}\;{\left(\frac{D_W}{d_e}\right)}^{0.77}{\left(\frac{D_i}{d_e}\right)}^{0.175}\kern0.6em $$
Notes
References
 1.Webb RL, Eckert ERG, Goldstein RJ (1971) Heat transfer and friction in tubes with repeatedrib roughness. Int J of Heat and Mass Transf 14(4):601–617CrossRefGoogle Scholar
 2.Zheng M, Li J, Mackley MR (2007) The development of asymmetry for oscillatory flow within a tube containing sharp edge periodic baffles. Phys Fluids 19(11):114101–114115CrossRefMATHGoogle Scholar
 3.Hong SW, Bergles AE (1976) Augmentation of laminar flow heat transfer in tubes by means of twistedtape inserts. J Heat Transf 98(2):251–256CrossRefGoogle Scholar
 4.Hwa Won Ryu, Young Soon Hyeon, Dong II Lee, Ho Nam Chang, O Ok Park (1991) Pressure drop and mass transfer around perforated turbulence promoters placed in a circular tube. Int J of Heat and Mass Transf 34(8):1909–1916Google Scholar
 5.Ravi T, Srinivasa Rao B, Gopala Krishna P, Venkateswarlu P (1996) Ionic mass transfer studies in fluidized beds with coaxially placed discs on a rod as internal. Chem Eng Process 35(3):187–193CrossRefGoogle Scholar
 6.Dawson DA, Trass O (1972) Mass transfer at rough surfaces. Int J of Heat and Mass Transf 15(7):1317–1336CrossRefGoogle Scholar
 7.Niu JL, Zhang LZ (2002) Heat transfer and friction coefficients in corrugated ducts confined by sinusoidal and arc curves. Int J of Heat and Mass Transf 45(3):571–578CrossRefMATHGoogle Scholar
 8.Prasad VSRK (1994) Studies on ionic mass transfer with impinging jet in closed cylindrical cells. Ph.D. thesis. In: Andhra university. Visakhapatnam, IndiaGoogle Scholar
 9.Naphon P (2006) Heat transfer and pressure drop in the horizontal double pipes with and without twisted tape insert. Int Comm in Heat and Mass Transf 33(2):166–175CrossRefGoogle Scholar
 10.Sujatha V (1991) Studies on ionic mass transfer with coaxially placed helical tapes on a rod in homogeneous fluid and fluidized beds. Thesis, Andhra University, Visakhapatnam, India, Ph. DGoogle Scholar
 11.Rajendra Prasad P (1993) Studies on ionic mass transfer with coaxially placed spiral coils as turbulence promoter in homogenous flow and in fluidized beds. Andhra University, Visakhapatnam, India, Ph. D ThesisGoogle Scholar
 12.Sitaraman TS (1977) Augmentation of mass transfer with coaxial string of spheres as internals in tubes and fluidized beds. Ph.D. In: Thesis. University of Madras, IndiaGoogle Scholar
 13.Sarveswara Rao S (1983) Studies on ionic mass transfer with coaxially placed cones on a rod in homogeneous fluid and fluidized beds. Ph.D. In: Thesis. Andhra University, Visakhapatnam IndiaGoogle Scholar
 14.Venkateswarlu P (1987) Studies on ionic mass transfer with coaxially placed discs on a rod as turbulence promoter. Ph.D. thesis. In: Andhra university. Visakhapatnam, IndiaGoogle Scholar
 15.Kumari S (2003) Studies on mass transfer using coaxial orifice turbulence promoters. Andhra University, Visakhapatnam, India, M. Tech ThesisGoogle Scholar
 16.Changal Raju D (1984) Augmentation of mass transfer at the outer wall of concentric annuli in presence of fluidizing solidseffect of wires wound on central rod. Ph. D. Thesis, Andhra University, Visakhapatnam, IndiaGoogle Scholar
 17.Bhaskar Sarma C (1978) Ionic mass transfer at circular and elliptical cylinders in cross flow of homogeneous fluid and in fluidized solids. Ph. D. Thesis, Andhra University, Visakhapatnam, IndiaGoogle Scholar
 18.Evans LB (1962) The effect of axial turbulence promoters on heat transfer. Ph.D. In: Thesis. University of Michigan, MichiganGoogle Scholar
 19.Bhatia et al (1967) Studies on spiral coils, twisted tapes as turbulence promoters in their heat transfer and pressure drop. J Inst of Engg India 48(1):34–35Google Scholar
 20.Changal Raju D (1984) Augmentation of mass transfer at the outer wall of concentric annuli in absence and presence of fluidizing solids effect of wires wound on central rod. Ph.D. thesis. In: Andhra university. Visakhapatnam, IndiaGoogle Scholar
 21.Nageswara Rao V (2004) Studies on ionic mass and momentum transfer with coaxially placed twisted tape disc assembly as turbulence promoter in circular conduits. Ph.D. thesis. In: Andhra university. Visakhapatnam, IndiaGoogle Scholar
 22.Murali Mohan V (2008) Studies on mass and momentum transfer with coaxially placed entryregion coil, disc and coildisc assembly as turbulence promoters in circular conduits. Ph.D. thesis. In: Andhra university. Visakhapatnam, IndiaGoogle Scholar
 23.Grigorchuk OV, Vasil'eva VI, Shaposhnik VA (2005) Local characteristics of mass transfer under electrodialysis demineralization. Desali 184(1–3):431–438Google Scholar
 24.Venkateswarlu P, Jaya Raj N, Subba Rao D, Subbaiah T (2002) Mass transfer conditions on a perforated electrode support vibrating in an electrolytic cell. Chem Engg and Proces 41(4):349–356CrossRefGoogle Scholar
 25.Prabhakar S, Ramani MPS (1994) A new concept of mass transfer coefficient in reverse osmosis practical applications. J Membr Sci 86(12):145–154CrossRefGoogle Scholar
 26.Subbaiah T, Das SC (1994) Effect of some common impurities on mass transfer coefficient and deposit quality during copper electro winning. Hydrometal 36(3):271–283CrossRefGoogle Scholar
 27.Subbarao D, Venkateswarlu P (2004) Ionic mass transfer studies in an open cell in the presence of circular cylindrical promoters. Chem Engg and Proces 43(1):35–41CrossRefGoogle Scholar
 28.Gomaa H, Al Taweel AM, Landau L (2004) Mass transfer enhancement at vibration electrodes. Chem Engg J 97(23):141–149CrossRefGoogle Scholar
 29.Zaki MM, Nirdosh SN (2007) Mass transfer characteristics of reciprocating screen stack electrochemical reactor in relation to heavy metal removal from dilute solutions. Chem Engg J 126(23):67–77CrossRefGoogle Scholar
 30.Chiou JP (1987) Experimental investigation of the augmentation of forced convection heat transfer in a circular tube using spiral spring inserts. Trans ASME 109:300–307CrossRefGoogle Scholar
 31.Rajendra Prasad P, Sujatha V, Sarma CB, Raju GJVJ (2004) Studies on ionic mass transfer with coaxially placed spiral coils as turbulence promoter in homogenous flow and in fluidized beds. Chem Engg and Proces J 43:1055–1062CrossRefGoogle Scholar
 32.Dipprey DF, Sabersky RH (1963) Heat and momentum transfer in smooth and rough tubes at variousprandtl numbers. Int J of Heat and Mass Trans 6(5):329–332Google Scholar
 33.Nikuradse J (1933) Laws of flow in rough pipes. VDI Forsch, 361Google Scholar
 34.Deissler RG (1955) Analysis of turbulent heat transfer, mass transfer and friction in smooth tubes at high Prandtl and Schmidt. Nat Adv Comm Aeronaut, Washington, DC TN1210Google Scholar
Copyright information
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.