Journal ofImaging Scienceand Technology

Vol. 50, No. 4July/August

2006

Society for Imaging Science and Technology

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Journal of Imaging Science and Technology® 50(4): 375–385, 2006.© Society for Imaging Science and Technology 2006

Variations of Airflow and Electric Fields in a CoronaDevice During Charging of a Moving Dielectric Substrate

Parsa Zamankhan and Goodarz AhmadiDepartment of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam,

New York 13699-5725E-mail: ahmadi@clarkson.edu

Fa-Gung Fan

J.C. Wilson Center for Research and Technology, Xerox Corporation, Webster, New York 14580

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bstract. The steady state airflow and electric field distributions incorona device (corotron) during charging of a moving dielectric

ubstrate (photoreceptor) for different operating conditions are stud-ed. The set of two-way, fully coupled electrohydrodynamics govern-ng equations is used in the analysis and parametric studies areerformed. The effects of wire voltage, photoreceptor speed, andevice-substrate gap size on photoreceptor charging, airflow,harge density, and electrical potential are studied. It is shown thathe charging is strongly affected by the wire voltage and the sub-trate speed. The results also show the importance of corona windffect on the flow structure in the device. © 2006 Society for Imag-

ng Science and Technology.DOI: 10.2352/J.ImagingSci.Technol.�2006�50:4�375��

NTRODUCTIONorotrons are devices that are essential for the operation of

lectrophotographic machines and xerography process.1

hey are used for charging the photoreceptor and the paperurfaces to desired voltage levels for the purpose of tonerransfer. A typical corotron is a long rectangle box with all itsides grounded except the side facing the photoreceptor. Oner several thin wires located inside the corotron serve as theorona generating elements. During the operation of aimple direct current (dc) corotron, a high voltage is appliedo the wires. Corona discharge occurs when the intensity ofhe electric field near the wire exceeds the threshold of airreakdown. The gas molecules near the wire in a regionalled “ionized sheath” are ionized. The wire then attractshe opposite polarity ions and repels the same polarity ones.

unipolar charge current is then generated from the wire tohe shield and the substrate.

The amount of surface charge received by the movingubstrate (photoreceptor) depends on the corotron size, wireoltage, gap size, and substrate speed, among others. Tochieve a proper value of surface charge, detailed knowledgef the electrical quantities is necessary. While electricaluantities control the charging processes, understanding air-ow condition is also very important. This is because theirflow in and around a corona device has major impacts on

eceived May 12, 2005; accepted for publication Dec. 12, 2005.

i062-3701/2006/50�4�/375/11/$20.00.

he device contamination (e.g., due to particles, dust) andhe emission of corona effluents (e.g., ozone, NOx).

Corona discharges in wire-plate and wire-shield geom-tries, including the electrostatic precipitator and high volt-ge dc transmission lines, were studied numerically and ex-erimentally by several authors.2–16 Most earlier studies were

ocused on the electrical quantities.2–11 A few also addressedhe hydrodynamical flow properties12–14 of these devices.

ore recently the electrical and hydrodynamical coupling ofhe electrohydrodynamic (EHD) flows has received increas-ngly more attention.15,16

Various numerical methods have been used in modelinglectrohydrodynamics in the past. In Refs. 2 and 13 finiteifference methods were used, while finite element methodsere employed in the work of Refs. 3 and 4 and Refs. 15 and6. A combination of finite element and finite differencepproach was used in Refs. 5 and 14. Earlier, the method ofharacteristic was used in Refs. 6–8 and finite volume meth-ds were implemented in Refs. 9 and 10 for solving thelectrostatics equations.

While there are many numerical and experimental stud-es of electrostatic precipitators and high voltage dc trans-

ission lines, there is very little work on corotron charginggainst a moving dielectric substrate. The recent work ofeng et al.17 for a steady state electric field in a corotron is anxception. They, however, ignored the airflow and simulatedhe corona charging with a finite element method. Fengt al.17 also favorably compared their numerical and experi-ental results.

In this paper, the steady state electric and airflow fieldsn a corotron with a moving photoreceptor are analyzed.he fully coupled electrohydrodynamic governing equationsre solved with a finite element method through FIDAP™Ref. 18) commercial software code. For different operatingonditions, the electrical and hydrodynamical field quanti-ies in and around the corotron are evaluated. For the casehere the airflow is absent, the simulation results are com-ared with those of Feng et al.17 and good agreement isbserved. A series of coupled flow and electric fields analyseshow that the corona discharge creates strong corona wind

n the corotron. The results also show that the wire voltage,

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Zamankhan, Ahmadi, and Fan: Variations of airflow and electric fields in a corona device

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he gap size, and the substrate speed have profound effectsn the airflow field in the corotron.

OVERNING EQUATIONSn this section the governing equations of coupled electro-ydrodynamic flow in a corotron are presented. The speedf the photoreceptor in high-speed electrophotographic ma-hines typically travels around 0.5 m/s or less. Corona air-ow due to the wire discharge produces a velocity that couldeach up to about 2 m/s in some regions inside of theorotron. The corresponding Reynolds number based on theidth of the corotron is typically much smaller than the

ritical Reynolds number for turbulence in a cavity flow;herefore, the air flow in the device is assumed to be inaminar flow regime. In this study it is also assumed that theolarity of the wire is positive and the discharge is uniformlong the wire so the negative corona instabilities are notnduced into the flow. Since the dimension of a corotronlong its wire direction is much larger than its cross section,two-dimensional model is considered to be sufficient in

he analysis. For constant material properties, the governingquations for a steady state two-dimensional electrohydro-ynamic flow are given as

Gauss’ law

�2V = −q

�0

, �1�

onservation of charge:

� · �uq� = D�2q + b � · �q � V� , �2�

lectric field-electrical potential relation:

E = − �V , �3�

ontinuity: t

76

� · u = 0, �4�

onservation of momentum:

u · �u = −1

�� p + ��2u + qE . �5�

n Eqs. (1)–(5), V is the electrical potential, E is the electriceld vector, q is the space charge density, D is ion diffusivity

n the air, b is the ion mobility, which is the ratio of the ionelocity in the field direction to the magnitude of the electriceld, �0 is the air permittivity, p is the fluid pressure, u is theuid velocity vector, � is the fluid density, and � is the kine-atic viscosity. It should be emphasized that the conserva-

ion of charge given by Eq. (2) includes the charge transporty ion mobility as well as the convective transport by airflownd the molecular diffusion.

EOMETRYigure 1 shows schematically the cross section of a corotrononsisting of a single thin wire, three grounded shield platesnd a moving substrate (photoreceptor). The relevant di-ensions are also shown in this figure. The modeled com-

utational domain includes the surrounding region exterioro the device so that more realistic boundary conditions cane prescribed.

As noted above, when a high voltage is applied to theire and the intensity of the electric field near the wire ex-

eeds the air breakdown threshold, the air molecules near tohe wire are ionized, and a corona current from the wirenitiates. Part of the current is directed toward the photore-eptor and charges up its surface. That is during the timender the corotron, charges are accumulated on substrateurface due to exposure to the charge flow. As charge buildsp on a surface segment, it will increasingly repel the ions so

he charging rate decreases as the surface segment moves

Figure 1. Schematic of cross sectionof the corotron and the computationaldomain.

oward the corotron exit.

J. Imaging Sci. Technol. 50�4�/Jul.-Aug. 2006

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Zamankhan, Ahmadi, and Fan: Variations of airflow and electric fields in a corona device

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Due to the movement of the ions (corona wind), the airxperiences an effective electrical body force. This electricalody force in addition to the viscous forces induced by theoving photoreceptor creates a rather complex flow pattern

n the corotron. Understanding the flow structure under dif-erent operating condition is important for contaminantransport and control and for increasing the performancend the life of corotron devices.

In the performed simulations a permittivity of �0

8.85�10−12 C2 /N m2, an ion mobility of b=210−4 m2 /V s, an ion diffusivity of D=5.32�10−6 m2 /s,

nd an air viscosity of �=1.84�10−5 N s/m2 are assumed.

OUNDARY CONDITIONSor the corotron geometry shown in Fig. 1, the hydrody-amical boundary conditions are

at the shields �wall�: u = 0, �6�

at the wire surface: u = 0, �7�

along A-B and E-F:�ux

�x= 0, �8�

along B-C and D-E:�uy

�y= 0, �9�

at the substrate ux = substrate speed, uy = 0. �10�

lectrical boundary conditions used are

at the wire surface: V = V0, �11�

at the shields: V = 0,�q

�n= 0, �12�

along A-B, B-C, D-E, and E-F:�V

�n= 0,

�q

�n= 0,

�13�

at the substrate:�q

�n= 0. �14�

n Eqs. (12)–(14), n represents the local unit normal out-ard from the modeled domain.

Since ion transport by diffusion is included in theharge conservation equation given by Eq. (2), boundaryonditions at all the boundaries are required. The details ofhe physical situation for the space charge at the solidoundaries such as the shields and the substrate are notnown. Feng,15 and Medlin et al.,3 used the zero gradientoundary condition on the walls. Feng et al.17 used the sameoundary condition for the shields and the substrate inorotron. Since the diffusion term in the charge transport

quation is small comparing to the drift term, no noticeable i

. Imaging Sci. Technol. 50�4�/Jul.-Aug. 2006

ifference of their results with those2,5,6,8,13,14 obtained forhe cases that the diffusion term was neglected was observed.herefore, in this study boundary condition given by Eqs.

12) and (14) are used.The boundary conditions for the charge density at the

ire and voltage at the substrate need more discussion. Tostimate the charge density on the surface of a coronatingire, the Kaptsov’s19 assumption is used. Kaptsov’s assump-

ion relates the gradient of electrical potential at the wireurface to an onset field strength. That is,

n · �V = Constant = Eonset, �15�

here n is the local unit normal vector that points into theire, �V is the gradient of potential on the wire surface, and

onset is the electric field threshold strength for the coronanset. Here Eonset can be calculated from Peek’s formula20

iven as

Eonset = �A� + B� �

Rw� . �16�

n Eq. (16) Rw is the radius of the wire, � is the gas densityonsidered as 1.225 kg/m3 in this study, and A=32.3

105 V/m, B=8.46�104 V/m1/2 are the constants ofeek’s formula.

Based on Peek’s formula given by Eq. (16), an iterativerocedure for applying the charge density boundary condi-ion on the wire was developed. A value for the charge den-ity on each node on the wire surface was first estimated.hen the value of n ·�V for each node of the wire surfaceas calculated and compared with Eonset, which was ob-

ained from Eq. (16). If the difference between the value of·�V and Eonset for any node on the wire was larger than arescribed tolerance, new corrected values for the chargeensity on each node on the wire were evaluated and theoverning equation were solved again. This iterative proce-ure was repeated until the difference between the value of·�V and Eonset for all nodes on the wire became smaller

han the prescribed tolerance.To estimate the new values for the charge density on

ach node on the wire (after a block of ten iterations) theew estimate for the value of charge density on the wire wasvaluated using

qw-New = �1 − ��qw-old + �qw* , �17�

here

qw* = qw-old�n · �V

Eonset�p

. �18�

n Eqs. (17) and (18), qw-old is the old value of the chargeensity on the wire that is being updated by the ratio ofn ·�V /Eonset�p for evaluating qw

* .To avoid sharp changes in the value of charge density

hat could drive the solution to diverge, the under-relaxationactor, �, was introduced in Eq. (17). In the beginning of

teration, a value of �=0.3 and p=1 was used. As the itera-

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Zamankhan, Ahmadi, and Fan: Variations of airflow and electric fields in a corona device

3

ion progressed, � was gradually increased to 1 and the valuef p was also subsequently increased to 4 so that a fasteronvergence can be obtained. In the present simulation, aolerance of 0.000 01 Eonset for condition (15) was used. Forhe cases studied, it was found that decreasing the tolerancerom this level to 5�10−6 Eonset had negligible effects on therofile of the wire charge density. Therefore, it was con-luded that the assumed tolerance was sufficient. To imple-ent this procedure, user defined subroutines for FIDAP™ere developed and used in the simulation.

Care should be given in applying this procedure duringhe simulation. We found that the structure of the mesh nearhe wire could significantly affect the convergence of theolution in FIDAP™. That is, the presence of skewed meshear the corona wire causes the values of Enormal on the wireodes to oscillate and do not converge to proper values. This

n turn leads to unrealistic distribution of charge density onhe wire. To avoid this problem, as shown in the magnifiedegion near the wire in Fig. 2, a larger circular region aroundhe wire was created in the computation domain. The gen-rated mesh in this region was made fine and symmetric. Asresult of using this symmetric and refined mesh near theire, satisfying the Kaptsov’s condition for the wire nodesas achieved with no problem in for the all cases studied.

The voltage boundary condition on the moving photo-eceptor follows from the conservation of surface charge onhe moving photoreceptor surface. Accordingly, in theteady-state condition the surface charge conservation maye expressed as

uph

��

�x= bq

�V

�y. �19�

n Eq. (19) uph is the photoreceptor speed and � is theurface charge density on the photoreceptor. Since the pho-

igure 3. Schematic of computational grids at the photoreceptor surface

aor evaluating the voltage boundary condition.

78

oreceptor thickness is very small, surface charge may beelated to its local voltage as

� = �0

V

td/. �20�

n Eq. (20), td is the photoreceptor thickness and is thehotoreceptor dielectric constant. Equation (20) follows

rom Guass law as described by Feng et al.17 (The derivationf Eq. (20) is given in as Supplemental Material on the ISBTebsite, www.imaging.org.)

Using Eq. (20) in Eq. (19), the voltage boundary con-ition for the photoreceptor is given as

�V

�x=

�bqtd/�

uph�0

�V

�y. �21�

Assuming that the photoreceptor voltage at point A inig. 1 is zero, Eq. (21) is integrated along the photoreceptorsing the mesh shown in Fig. 3. The voltage at differentodes at the surface of the photoreceptor is given as

V�I + 1� = bqtd/

uph�0

�V

�yx + V�I� . �22�

ith Eq. (22) for the voltage boundary condition on thehotoreceptor, the set of boundary conditions needed forolving the governing equations becomes complete. Duringhe simulation, after each block of ten iterations, in additiono the charge density profile on the wire the voltage profilen the photoreceptor surface is also updated using Eq. (22).nless stated otherwise, in the present simulations, td

25 �m and =3.3 are used. A user defined subroutine waslso developed for implementing Eq. (22) in the FIDAP™ode.

UMERICAL SCHEMEince the finite element formulation in FIDAP™ code uses thetandard Galerkin method as default, care needs to be giveno the value of nodal electrical Peclet number for the chargeransport equation. The electrical Peclet number is defined

Figure 2. Computational grid.

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Zamankhan, Ahmadi, and Fan: Variations of airflow and electric fields in a corona device

J

PeE =UEL

D. �23�

n Eq. (23), UE is the magnitude of the local ion drift veloc-ty, L is the characteristic length of the element, and D is theon diffusivity in the media. Here square root of the com-utational cell area is used for the characteristic length scale.he magnitude of ion drift velocity may also be evaluated as

UE =��ux − b�V

�x�2

+ �uy − b�V

�y�2

. �24�

n Eq. (24), b is the ion mobility and V is the electricalotential.

Several authors include Zienkiewicz and Taylor21 re-orted that high values of electrical Peclet number inher-ntly create wiggling in the solution that could lead to diver-ence. Using high order elements (for example quadratic) oresh refining can decrease the local electric Peclet number;

owever, these methods increase the computational time sig-ificantly. Increasing the diffusivity and using upwinding are

he other alternatives for stabilizing the numerical processhen the value of Peclet number is high in some part of the

omputational domain.Zienkiewicz and Taylor21 suggested that using the stan-

ard Galerkin method with a modified diffusivity given by

Da = D + 0.5�Uh �25�

or a one-dimensional advection-diffusion equation withonstant advection velocity and constant grid size is equiva-ent to a finite element formulation based on Petrov-

alerkin method with � as a parameter. In Eq. (25), Da ishe modified diffusivity, D is the true diffusivity, U is thedvection velocity, and h is the grid size. Here �=0 isquivalent to the standard Galerkin formulation which ne-lects the convection effects; while �=1 corresponds to thepwind Petrov-Galerkin method that is a pure convection

ormulation and neglects the diffusion. Since the effects ofoth diffusion and convection may be important, using �0 or 1 may not provide accurate results. Christie et al.22

Table I. Exit voltage of photoreceptor and the current per unit length17�. The photoreceptor speed is 0.5 m / s.

Wire voltage�V� Exit voltage �V�

StandardGalerkin

UpwindPetrov-Galerkin

StandardGalerkin

withmodifieddiffusivity Ex

4500 145.6 146.3 145.7

6000 660 672.7 663.8

roved that in a one dimensional problem with constant S

. Imaging Sci. Technol. 50�4�/Jul.-Aug. 2006

dvection velocity and grid size, the optimal value for � isiven by

�opt = coth�Pe� −1

Pe. �26�

lthough the cases studied in the present work are two di-ensional with variable advection velocity and variable grid

izes, still the modified diffusivity as given by Eqs. (25) and26) (with U and Pe replaced by UE and PeE, respectively)

ay be more appropriate and could be used to improve thetability of the simulations.

Using the two-dimensional upwind Petrov-Galerkinormulation that has been provided in FIDAP™ is anotherpproach that can handle the mentioned instability problem.he details of different discretization methods were given byienkiewicz and Taylor.21 Additional references may be

ound in the FIDAP™ manual.18 In the subsequent sections,he simulation results using the standard Galerkin, the stan-ard Galerkin with a modified diffusivity, and the upwindetrov-Galerkin schemes are compared with the experimen-al data of Ref. 17.

OMPARISON WITH EXPERIMENTeng et al.17 performed numerical and experimental studiesf the electrical properties in a corotron which is identical tohe one shown in Fig. 1 for different wire voltages and pho-oreceptor speeds. Since the charge transport by air flow wasssumed negligible in comparison with the charge transporty electric fields, the contribution was not included in theirimulations. The computational domain in the simulation ofeng et al.17 also covered only the corotron (section CD) andid not include the surrounding area shown in Fig. 1.

For the conditions identical to those used by Fengt al.,17 we have simulated the conditions in the corotronsing the standard Galerkin, the standard Galerkin withodified diffusivity as given by Eqs. (25) and (26) and the

pwind Petrov-Galerkin finite element approaches. Theharge conservation equation without the convective chargeransport term was used in these simulations. The compu-ational mesh for this case contained 12840 linear elements.

ire in comparison with the experimental data of Feng et al. �see Ref.

Current per unit length at the wire �mA/m�

lStandardGalerkin

UpwindPetrov-Galerkin

StandardGalerkin

withmodifieddiffusivity Experimental

0.184 0.187 0.186 0.197

1.016 1.025 1.025 1.096

at the w

perimenta

141

672

ince in this case the computational domain does not in-

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Zamankhan, Ahmadi, and Fan: Variations of airflow and electric fields in a corona device

3

lude the region outside the corotron, boundary conditions8), (9), and (13) are replaced by the zero gradients of elec-rical potential and charge density at the inlet and outlet gapetween the corotron and photoreceptor surface. Simula-ions were performed for wire voltage of 4500 and 6000 Vor a photoreceptor speed of 0.5 m/s and the results areompared with the experimental results reported by Fengt al.17

For the case that the wire voltage is 6000 V, Fig. 4 showshe charge density contours evaluated using different finitelement schemes. It is seen that the predicted charge densityontours are nearly the same; however, the standard Galerkinethod shows some wiggling due to the high values of

odal electrical Peclet number.Table I compares the exit voltage of the photoreceptor

urface and the current density from the wire as predicted byifferent finite element approaches with the experimentalata of Feng et al.17 It is seen that the simulation results for

he photoreceptor voltage and the wire current density arelmost the same and are in good agreement with the experi-ental data.

Based on the simulations performed with different finitelement methods, the Galerkin finite element method withhe modified diffusivity was selected for analyzing of thelectric and flow fields in the corotron in this study. Thetandard Galerkin method was discarded due to its inherent

igure 4. Charge density contours in the corotron for a wire voltage of000 V, photoreceptor speed as 0.5 m/s, and gap size of 5.3 mmimulated by different methods. Contours are from 0.15 to 1.2 mC/m3

ith an increment of 0.117 mC/m3. �a� Standard Galerkin. �b� Upwindetrov-Galerkin. �c� Standard Galerkin with a modified diffusivity. �d�omparison of different methods.

nability of handling high nodal electrical Peclet number c

80

onditions. While the upwind Petrov-Galerkin method canlso provide stable solution, it was not used because theurrent FIDAP™ implementation does not allow it to be gen-ralized to include both the drift and the convective trans-orts of ions.

MPLEMENTATION IN FIDAPIDAP™ is a finite element code for solving the thermofluidransport processes including species transport equations.he code has the capability of handling EHD problems. Theode default approach discretizes the governing equationssing the standard Galerkin formulation; however, differentersion of the Petrov-Galerkin formulation can also be used.he details of different discretization methods were given byienkiewicz and Taylor.21 Additional references may be

ound in the FIDAP™ manual.18

The discretized form of the governing equations can beolved by coupled or segregated solvers. In the coupled

ethod the system of governing equations are solved simul-aneously. In the segregated method, however, equations areolved consecutively. Coupled solvers are numerically moretable but they require more memory and computationalime. In contrast, the segregated solvers need less memorynd are faster but they are less stable. Both coupled andegregated solvers in FIDAP™ use the Gaussian elimination

ethod by default. There are, however, other methods avail-ble. Information concerning these additional methods maye found in the FIDAP™ manual.18

In this study, for evaluation of the charge conservationquation given by (2), the standard Galerkin formulationith a modified diffusivity based on Eqs. (25) and (26) wassed. The momentum equation was, however, discretized by

he up-wind Petrov-Galerkin formulation as available inIDAP™ to increase the stability of the numerical scheme. Toolve the discretized system of equations, the segregated

ethod using Gaussian elimination solver was used in thenalysis.

Except for the charge density condition on the wire andoltage distribution on the photoreceptor, imposing theoundary conditions was straightforward and was per-

ormed directly in FIDAP™. To impose the boundary condi-ions for the charge density on the wire and voltage on thehotoreceptor, two FORTRAN codes based on the procedureescribed in Boundary Conditions section were developednd were implemented into a user-subroutine of theoftware.

It was found that the procedure was somewhat sensitiveo the initial guess for the values of charge density on theire in that a large overestimation by a factor of 10–20 may

ause the solution to diverge. In those cases the computa-ions were repeated with a smaller value of the initial guess.

Another modification of the FIDAP™ code was in theeed for inclusion of the Coulomb force in the momentumquation through a user-defined subroutine. Here also it wasound that the Coulomb force needs to be gradually intro-uced to avoid the risk of divergence of the solution.

The grid independency of the solutions was also

hecked. Typically the grid size was increase by a factor of

J. Imaging Sci. Technol. 50�4�/Jul.-Aug. 2006

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Zamankhan, Ahmadi, and Fan: Variations of airflow and electric fields in a corona device

J

0% and the solution was repeated until the difference in theolution was insignificant.

ESULTS AND DISCUSSIONSseries of simulations were performed and the effects of

ire voltage, photoreceptor speed and the corotron-hotoreceptor gap size on the photoreceptor charging, and

he electric and flow fields in the corotron were studied.ere the fully coupled EHD governing equations including

on convection were used and the simulation results are pre-ented and discussed. To provide a more accurate simulationf the flow field, the computational domain was extended toover region beyond the corotron device. Figures 1 and 2,espectively, show the schematic of the computational do-

ain and the computational mesh used in the analysis.A corotron with the wire voltage of 6000 V, the photo-

eceptor speed of 0.5 m/s, and the gap size between theorotron and photoreceptor surface of 5.3 mm was consid-red as the reference case. A series of simulations were per-ormed and the effect of variation in wire voltage, photore-eptor speed and gap size was studied. In one case the wireoltage was reduced to 4500 V, and in the other case thehotoreceptor speed was reduced to 0.25 m/s, while allther conditions were kept fixed. For the case that the pho-oreceptor speed is 0.25 m/s, the effect of reduction of theap size from 5.3 to 2 mm was also studied.

During the operation of device, charges are accumu-ated on the photoreceptor surface during its motion underhe coronating wire due to exposure to the charge densityurrent from the wire. As charge builds up on the movinghotoreceptor surface, it will increasingly resist the ap-roaching ions and the rate of charging decreases as the

igure 5. Voltage distribution on the photoreceptor for different cases �theevice is located between x=12 and 34 mm�.

hotoreceptor moves toward the outlet section of the device. a

. Imaging Sci. Technol. 50�4�/Jul.-Aug. 2006

his process will eventually lead to the saturation of chargeuild up and the amount of surface charge on the photore-eptor surface reaches to a constant value near the corotronutlet. Since the surface charge is proportional to the voltages given by Eq. (20), the distribution of voltage on the pho-oreceptor follows a similar distribution.

Figure 5 shows the computed distribution of the pho-oreceptor surface voltage for different operating conditions.n this figure the left and right edges of the corotron are,espectively, 12 and 34 mm. For different conditions, Fig. 5hows that the trend of variation of the surface charging ishe same, while the voltage amplitude differs significantly. Its also seen that the photoreceptor surface is being chargedlightly even before it gets to the left edge of the corotron.he voltage begins to increase as the surface enters regionirectly under the corotron. The rate of charging and voltageuild up is slow at the beginning but becomes quite steepith distance form the inlet. The voltage then builds up

apidly and saturates to a constant value. The maximumoltage acquired by the photoreceptor surface varies signifi-antly depending on the corotron operating conditions. Forwire voltage of 4500 V, the photoreceptor reaches to about46 V. For the reference case with a wire voltage of 6000 V,he photoreceptor voltage reaches to about 665 V. As ex-ected, the increase of wire voltage significantly increases themplitude of the photoreceptor surface charge and the cor-esponding voltage.

For the reference conditions, when the speed is reducedo 0.25 m/s, Fig. 5 shows that photoreceptor exit voltagencreases to about 1050 V. That is, in agreement with Fengt al.,17 at lower speeds the photoreceptor is exposed to theharge flow for a longer period and the charge buildup onhe photoreceptor surface increases. The effect of reducinghe gap size between the corotron and the photoreceptor to

mm on the surface charging could also be seen from Fig.. Here the wire voltage is 6000 V and the speed is.25 m/s. It is seen that decreasing the gap size leads toecrease of the photoreceptor voltage to about 1005 V.

Figure 6 shows the simulated electrical potential con-ours in the corotron for different cases. It is seen that theotential contours are roughly concentric circles around theire. At higher wire voltage and lower photoreceptor speed,

he contours become somewhat asymmetric tending to haveigher values in the region near the outlet in comparison to

he inlet side. The asymmetric becomes more noticeable ashe wire voltage increases or the photoreceptor speed de-reases. As was noted in the discussion of Fig. 5, increasinghe wire voltage or decreasing the photoreceptor speed in-reases the nonuniformity of voltage on the photoreceptorurface leading to higher level of asymmetry in the potentialontours. Figure 6 also shows that decreasing the gap sizeoes not have a noticeable effect on the distribution of thelectrical potential in the corotron.

Figure 7 shows the computed charge density contours inhe corotron for different cases studied. This figure showshat the charge density is highest near the coronating wire

nd the contours are somewhat asymmetric in all the cases

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tudied. In particular, the asymmetry of the charge densityear the wire is more noticeable. The asymmetric distribu-

ion of charge density is also due to the nonuniform distri-ution of the voltage on the photoreceptor surface. As theire voltage increases or the photoreceptor speed decreases,

he charge density contours become more asymmetric. Sincehe voltage in the region near the outlet is higher than thatear the inlet, the ions face stronger resistance near the out-

et and the charge density values drops in this region.Figure 8 shows the charge density distribution on the

ire for different operating conditions. It is seen that theharge density distribution on the wire is markedly nonuni-orm for all cases studied. For the reference case, when theire voltage is 6000 V, the photoreceptor speed is 0.5 m/s,

nd the gap size is 5.3 mm, the amplitude of the chargeensity on the wire varies between 0.9 and 1.4 mC/m3,hich is the maximum among the cases studied. In this case,

he maximum value of the charge density on the wire occurst �=250°. When the wire voltage is reduced to 4500 V,

igure 6. Electrical potential contours for different cases. �a� Wire volt-ge of 4500 V, photoreceptor speed of 0.5 m/s, and gap size of.3 mm. �Minimum contour=450 V, increment 450 V.� �b� Wire volt-ge of 6000 V, photoreceptor speed of 0.5 m/s, and gap size of.3 mm. �c� Wire voltage of 6000 V, photoreceptor speed of.25 m/s, and gap size=5.3 mm. �d� Wire voltage of 6000 V, pho-

oreceptor speed of 0.25 m/s, and gap size=2 mm. �For �b�, �c�, andd� minimum contour=600 V, increment 600 V.�

hile the photoreceptor speed and the gap size are kept a

82

xed, respectively, at 0.5 m/s and 5.3 mm, the amplitude ofhe charge density on the wire varies between 0.12 and.28 mC/m3, which is the lowest in comparison with thether cases studied. The maximum value of the charge den-ity on the wire in this case occurs at �=262°, which showsshift toward the center compared to the reference case.

Figure 8 also shows that when the photoreceptor speedecreases from 0.5 to 0.25 m/s with same wire voltage andap size, the amplitude of charge density at the wire variesetween 0.9 and 1.2 mC/m3, which somewhat lower thanhe reference case. As noted before, reducing the photorecep-or speed leads to an increase in its voltage, and the photo-eceptor more strongly resist to the corona ion flow. Thus,he current from the wire decreases as the photoreceptorpeed decreases, which is in agreement with the observationf Feng et al.17 For this case the maximum charge density onhe wire occurs at �=230°, which shows a 20° inclinationoward the inlet side compared to the reference case.

Effects of variation in the gap size on the charge density

igure 7. Charge density contours for different cases. �a� Contours arerom 0.029 to 0.29 mC/m3 with an increment of 0.029 mc/m3 forire voltage of 4500 V, photoreceptor speed of 0.5 m/s, and gap

ize=5.3 mm. �b� Wire voltage of 6000 V, photoreceptor speed of.5 m/s, and gap size of 5.3 mm. �c� Wire voltage of 6000 V, pho-

oreceptor speed of 0.25 m/s, gap size of 5.3 mm. �d� Wire voltage of000 V, photoreceptor speed of 0.25 m/s, and gap size=2 mm. Forases �b�, �c�, and �d�, contours are from 0.15 to 1.3 mC/m3 with anncrement of 0.127 mC/m3.

t the wire surface can also be seen from Fig. 8. When the

J. Imaging Sci. Technol. 50�4�/Jul.-Aug. 2006

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ire voltage is 6000 V and the photoreceptor speed is.25 m/s, reducing the gap size to 2 mm, shows a slight

ncrease in the charge density. In this case the amplitude ofhe charge density on the wire varies between 0.9 and.3 mC/m3 with its maximum occurring at about �=236°.he slight increase of the charge density is due to the in-rease of the length of the side shields which decreases theotal resistance of the corotron toward the ion injection.

When the gap size is decreased, Fig. 5 shows that theharge density current from the wire increases slightly, andhe voltage amplitude of the photoreceptor somewhat de-reases. This is perhaps due to the fact that some of the ionsre attracted by the grounded shields instead of depositionn the highly charged regions of the photoreceptor near tohe corotron outlet.

Figure 9 show the stream traces in and around theorotron for different cases. Here the wire size was exagger-ted, and the stream traces were placed at locations to showhe important features of the flow in the corotron. (It shoulde noted here that the concentration of stream traces in aegion does not represent the velocity magnitude.) Figure(a) shows the corresponding stream traces for the case thathe wire voltage is 4500 V, photoreceptor speed is 0.5 m/s,nd the gap size is 5.3 mm. It is seen that the interaction oforona wind with the shear flow induced by the movinghotoreceptor creates rather complex flow structures. A largelockwise vortex forms around the wire, which is extendedrom the top-left to the bottom-center of the corotron. Bulkf the flow entering the corotron by the motion of the pho-oreceptor from the left inlet, revolves around the large vor-ex, and leaves from the bottom part of the outlet section.his figure also shows a smaller counter-clockwise vortex

igure 8. Charge density distribution at the wire surface for differentases.

orms near the outlet causing suction of air into the corotron v

. Imaging Sci. Technol. 50�4�/Jul.-Aug. 2006

rom the top part of outlet section. This flow rotates aroundhe small vortex and also leaves through the bottom part ofhe outlet section.

Figure 9(b) shows the stream-traces for the referencease with wire voltage of 6000 V, photoreceptor speed of.5 m/s, and the gap size of 5.3 mm. This figure shows thathe clockwise vortex around the wire is still present but be-omes smaller and shifts toward the inlet. The counter-lockwise vortex, which covers the right-lower part of theevice becomes larger and moves toward the center. It iseen that air is sucked into the corotron from a large part ofhe outlet section and rotates around the central counter-lockwise vortex. There is also a smaller vortex forms on theop-right of the corotron, Fig. 9(b) shows that at high wireoltage the corona wind effects becomes very large and gen-rates rather complex flow pattern in the corotron.

Figure 9(c) shows the stream traces for a case that theire voltage is 6000 V, the gap size is 5.3 mm, but the pho-

oreceptor speed is reduced to 0.25 m/s. It is seen that theow structure inside the corotron is quite complex with sev-ral vortices. The clockwise vortex on the left and centralart becomes somewhat larger, while the counter-clockwise

igure 9. Stream traces for different cases. �a� Wire voltage=4500 V,hotoreceptor speed=0.5 m/s, gap size=5.3 mm. �b� Wire voltage6000 V, photoreceptor speed=0.5 m/s, gap size=5.3 mm. �c�ire voltage=6000 V, photoreceptor speed=0.25 m/s, gap size

5.3 mm. �d� Wire voltage=6000 V, photoreceptor speed0.25 m/s, gap size=2 mm.

ortex on the right lower part become smaller and moves

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urther to the right. The vortex on the right side of theorotron becomes larger and a smaller vortex forms at theiddle bottom of the device. This figure also shows that air

s sucked into the corotron from nearly the entire section ofhe outlet and moves on the top of the bottom vortex andeaves the corotron from the inlet section. Interestingly, atower speed of 0.25 m/s, the viscous shear flow due to thehotoreceptor motion, is entirely overwhelmed by the co-ona wind effect and little air is entering the corotron fromhe inlet side.

Figure 9(d) shows the stream traces for a case that theire voltage is 6000 V, photoreceptor speed is 0.25 m/s,

nd the gap size is 2 mm. It is seen for a small gap size, theow in the corotron is dominated by two large counter-otating vortices on the right and left sides of the chamber.he air is drawn from the top part of the outlet section into

he device and leaves that from the top part of the inletection. The gap size appears to have an important effect onhe flow structure in the corotron, while it does not have aoticeable effect on the electrical quantities.

To check the effect of the computational domain sizend the boundary conditions used on the flow, a series ofimulations were performed where the domain size wasearly doubled. The results are described in this section.igures 10 and 11 show stream traces and the pressure dis-ribution for the extended domain for a wire voltage of000 V, substrate speed of 0.5 m/s, and the gap size of.3 mm.

Figure 10 shows that the stream traces inside theorotron predicted for the extended domain are almost iden-ical to those shown in Fig. 9(b). The stream traces on theeft hand side of the device are, however, slightly different.igure 11 shows the pressure distribution for the extendedomain. It is seen that the pressure becomes constant near

he outer boundaries which is as expected. The simulationesults for the other cases in the extended domain have simi-ar trend of behavior and therefore are not shown here.

The results were presented in this section show that thelectrical quantities and the flow field in the corotron aretrongly affected by the wire voltage and the substrate speed.he effect of gap size is important on the corotron flow butot on the electrical quantities.

ONCLUSIONSn this study the electric and the flow fields in a corotron

igure 10. Stream traces for a case with wire voltage of 6000 V, sub-trate speed=0.5 m/s, and gap size=5.3 mm for an extended domain.

nder different operating conditions were analyzed. The

84

imulations were performed using FIDAP™ commercial codeith appropriate modifications. To account for the chargeensity variation on the wire that satisfies the Kaptsov’s as-umption and for the voltage boundary condition on thehotoreceptor, two user-defined subroutines were developednd were implemented into the software. On the basis of theresented results, the following conclusions may be drawn:

• Increase of the wire voltage or decrease of the photore-ceptor speed sharply increases the saturation chargingof the photoreceptor surface.

• Increase of the wire voltage or increase of the photore-ceptor speed increases the charge density current fromthe wire.

• Corona wind generates significant secondary flows inthe corotron devices. The structure of the airflow variesdepending on the wire voltage, photoreceptor speedand gap size.

• For the range of parameters studied in this work, thecorona wind strongly affects the airflow conditions inthe corotron, but the airflow effect on the electricalproperties is relatively small.

Note that the nature of the contamination transport inhe corotron under that action of airflow and electrostaticorces which is an important topic is not discussed inhis paper due to space limitation. The subject, however, isnder study and the results will be described in a futureommunication.

CKNOWLEDGMENTShis work was supported by Xerox Corporation and by theew York State Office of Science, Technology and Academicesearch (NYSTAR) (through the Center for Advanced Ma-

erials Processing, CAMP, of Clarkson University). The au-hors would also like to thank Fluent Inc. for making theIDAP™ code available. Thanks are also given to IBM Corpo-ation for the donation of pSeries computer to Clarksonniversity.

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