A numerical simulation and validation study of the mathematical model of droplet formation in drop on demand inkjet printer and the effect of rheological properties of polymerink for automobile lighting application

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The current work attempts to provide an idea of the drop ejection behaviour based on the computation of energies required for droplet formation and splat formation.

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Nội dung Text: A numerical simulation and validation study of the mathematical model of droplet formation in drop on demand inkjet printer and the effect of rheological properties of polymerink for automobile lighting application

International Journal of Mechanical Engineering and Technology (IJMET) Volume 10, Issue 03, March 2019, pp. 1326–1338, Article ID: IJMET_10_03_134 Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=10&IType=3 ISSN Print: 0976-6340 and ISSN Online: 0976-6359 © IAEME Publication Scopus Indexed A NUMERICAL SIMULATION AND VALIDATION STUDY OF THE MATHEMATICAL MODEL OF DROPLET FORMATION IN DROP ON DEMAND INKJET PRINTER AND THE EFFECT OF RHEOLOGICAL PROPERTIES OF POLYMERINK FOR AUTOMOBILE LIGHTING APPLICATION Rajesh.P.K., and Aravindraj.S Department of Automobile Engineering, PSG College of Technology, Coimbatore, Tamilnadu. India. ABSTRACT A majority of the modern inkjet printers utilise drop on demand devices because of its precision in terms of time and easy control. The time-dependent fluid interface disruption renders the fluid dynamics process during droplet ejection complex. The current work attempts to provide an idea of the drop ejection behaviour based on the computation of energies required for droplet formation and splat formation. The simulation results for various nozzle diameters with different polymer inks are examined and it is validated with computational model. Further attempt is made to analyse the effect of rheological properties like viscosity and surface tension in the droplet formation. Key words: Drop on demand; inkjet; droplet ejection; viscosity; surface tension. Cite this Article: Rajesh.P.K. and Aravindraj.S, A Numerical Simulation and Validation Study of the Mathematical Model of Droplet Formation in Drop on Demand Inkjet Printer and the Effect of Rheological Properties of Polymerink for Automobile Lighting Application, International Journal of Mechanical Engineering and Technology 10(3), 2019, pp. 1326–1338. http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=10&IType=3 1. INTRODUCTION There is a tremendous efforts in the search for new means of further improving the quality and reducing device cost of ink jet printing due to its rapid growth over manufacturing of automotive electronics. Knowledge in fluid dynamic process of drop formation and drop ejection takes precedence in research and development of new ink jet print heads. There are http://www.iaeme.com/IJMET/index.asp 1326 editor@iaeme.com
Rajesh.P.K. and Aravindraj.S two main types of ink jet devices, namely, continuous–jet type and drop-on demand type. [3 - 4]. In a continuous-jet device, there is a disintegration into a train of drops of the liquid, emerging from the nozzle continually in the form of a jet. The amount of electric charge on each individual drop and direction of motion of each drop from the continuous jet require sophisticated electrical signals. A drop-on-demand device, on the other hand, uses electrical signal to control the actuation at the instance of the ejection of an individual drop. Due to its basic simplicity, the drop-on-demand type is common in the most modern ink jet printers. This work focuses on the basic drop ejection process in drop-on-demand devices. A drop-on-demand inkjet printer consists of a fluid chamber with a nozzle which is actuated to eject the droplet. The actuation pushes a certain amount of the liquid out of the fluid chamber through the nozzle. A drop is ejected when the liquid pushed out of the nozzle gains enough forward momentum to overcome the surface tension restoring effect, [5]. The generation and behaviour of liquid droplets [6] is effected by the Surface tension, inertia and viscosity. Surface tension is a contractive tendency of the surface of a liquid that allows it to resist an external force. Liquid atoms or molecules at a free surface have higher energy than those inside the liquid body. Therefore, the shape of liquid with the lowest surface tension energy is sphere. For the generation of a droplet, a liquid must necessarily have the tendency to form a shape with lowest energy. The attraction of water molecules to each other is greater than the molecules in the air, when the droplet is generated. As a result, an inward force at its surface makes water to behave as if its surface was covered by a stretched elastic membrane. This is also the primary cause of pinch‐off effect [7]. The surface tension of most of the liquids used in inkjet printing have the order of tens of dyn/cm (or mN/m). The importance and influence of the above parameters can characterized by three essential dimensionless numbers: 1. Reynolds number, 2.Weber number and 3.Ohnesorge number [8]. Figure 1 Stages of droplet formation process [9] The ink inside the nozzle stays at equilibrium state, before the nozzle gets actuated. Ink velocity and pressure are zero at initial stage (A). A high pressure is generated inside the nozzle when the nozzle gets actuated, and the liquid start to flow out from the nozzle orifice (B). Kinetic energy is transported from the actuator walls to outflow and it undergoes an attenuation process, in order to overcome the resistance from surface tension (C). The droplet is then connected with the liquid inside the nozzle by a skinny fluid filament (D). When the liquid column momentum is large enough, the droplet will escape from the nozzle (E). Surface tension acts as a force to pinch off the ligament. The meniscus retracts inside the nozzle (F). In the inkjet printing applications, a single droplet is invariably desired but due to surface tension additional satellite droplets which are usually smaller than intended primary droplet, are formed and they cause several problems in printing [10]. When the unexpected satellite droplets land on places other than where primary droplets do, they result in the degradation of print quality, which further leads amination or failure. This is most clearly indicated by the blurring of the trailing edge of a printed area [11]. http://www.iaeme.com/IJMET/index.asp 1327 editor@iaeme.com
A Numerical Simulation and Validation Study of the Mathematical Model of Droplet Formation in Drop on Demand Inkjet Printer and the Effect of Rheological Properties of Polymerink for Automobile Lighting Application The drop formation phenomenon is theoretically, governed by Navier–Stokes equations with appropriate boundary conditions describing fluid interface motions [12]. The conventional methods cannot be used to obtain the desired mathematical solutions because of the prevalence of the nonlinearities arising from inertia, capillarity, and coupling of the free surface kinematics to the flow field. Hence, a Computational Fluid Dynamics (CFD) package FLOW-3D V 10.0 [13] is utilised to simulate the complex fluid dynamic process during drop ejection and it is validated with energy model. Some other researches on droplet formation process in Drop-On-Demand inkjet printing need to be analysed to overcome the problem. A quantum of research work has been carried out in the mechanism of droplet formation, especially on Newtonian fluids, subsequent to the invention of the first DOD inkjet printer in the 1940s. In the recent years, as more Non‐ Newtonian fluids have been widely used in manufacturing of automobile electronics and a bulk of research on the droplet formation of Non- Newtonian fluids are carried effectively. Due to the tens of micron length and the time scale of less than a hundred micro‐second, micro scale droplet generation differs from macro scale droplet generation. Shin et al. [14] and Verkouteren et al. [15] analysed the transient process of droplet generation using a charge coupled device (CCD). Dong [16] and Carr [17] studied the dynamics of drop‐on‐demand (DOD) droplet formation using an imaging system with an inter‐frame time of 1 μs. The experiment was conducted on a viscosity range of (1.0 ‐ 5.0 cP) and surface tensions (35 – 73 mN/m). They investigated the stages of droplet formation including the ejection and stretching of liquid and the pinch‐off of liquid thread from the nozzle exit. Lopez et al. [18] studied the combination effect of ink rheological behaviour focusing on the dynamics of filament break‐up and effect of rheological properties on droplet formation. Cittadino et al. [19] developed a non‐linear model to predict the velocity of the ejected droplet, based on a balance of forces, showing that the ejection velocity is a strong function of the applied voltage. Feng and James [20] proposed an comparatively simpler approach based on a series of numerical calculations on Flow3D. This reference has given an idea about the droplet ejection behaviour for establishing nozzle head design and shows that the volume of ejected droplet is very close to the volume of fluid pushed through the nozzle by an actuation pulse. 2. NUMERICAL SIMULATION FOR DROPLET FORMATION BASED ON ENERGY APPROACH The energy required to form the droplet are equated in energy approach, to find the diameter of the droplet. Based on the law of conservation of momentum, the energies before and after impact are equated to find the splat diameter (i.e.) Diameter of the spread after fall on the substrate [21]. 2.1. Energy Required to Eject Single Droplet from the Nozzle These energies are required to eject the droplet is as follows:  Energy [E1] required to deflecting the membrane.  Frictional energy [E2] in the orifice.  Kinetic energy [E3] of droplet at the outlet of print head.  Surface tension energy [E4] of the droplet at outlet. The total energy [E] required to eject the droplet from nozzle should be greater or equal to the sum of these energies. http://www.iaeme.com/IJMET/index.asp 1328 editor@iaeme.com
Rajesh.P.K. and Aravindraj.S E=E1+ E2+ E3+ E4 2.2. Volume of the Droplet Eject from the Nozzle The volume of the droplet ejected from the nozzle is equal to the maximum volume displaced by the deflecting membrane. The driving voltage on the piezoelectric device is converted into required force [F] acting on the centre of the disc. The maximum deflection in the disc is given by the formula [22]: r2 F 2r F(D2 −4r2 ) x = 8πEI ln D + (1) 64πEI The maximum deflection is obtained by substituting Et3 r=0, ϵ = 0.3 and I= 12(1−∈2 ), we get FD2 δ= (2) 18.40 E t3 By integrating the volume displaced in small layer we get the total volume of the ink displaced (i.e.) dv = 2πrdr. x Total volume of the ink displaced is given by D/2 Fr2 2r F (D2 −4r2 ) V = ∫0 2πr[8πEI ln D + ]dr (3) 64πEI On integrating Equation 3, we get F D4 V= (4) 1024EI On simplifying the equation 4, we get D2 V= δ (5) 3 2.3. Diameter of the Droplet Formed from the Nozzle The diameter of droplet is calculated by equating the volume of the sphere and the volume of the ink displaced (i.e.) D2 4 δ= π d3 (6) 3 24 By simplifying the equation 6, we get 3 2D2 δ d= √ (7) π Equation 7 gives the diameter of the spread which depends on the ink chamber diameter and the maximum defelection of the membrane. 2.4. Energy Required for Deflecting the Membrane [E1]: The energy required for deflecting the membrane is equated to the product of force [F] and the maximum deflection (i.e.) E1 = Fxδ 18.40Et3 E1 = δ (8) D2 2.5. Frictional Energy Required at the Orifice [E2]: http://www.iaeme.com/IJMET/index.asp 1329 editor@iaeme.com
A Numerical Simulation and Validation Study of the Mathematical Model of Droplet Formation in Drop on Demand Inkjet Printer and the Effect of Rheological Properties of Polymerink for Automobile Lighting Application Friction loss (or skin friction) is the loss of pressure or “head” that occurs in nozzle flow due to the effect of the fluid's viscosity near the surface of the orifice [23]. The fictional loss is given by the Hagen-poissoulle equation (i.e.) 32μu0 l hf = (9) ρgd20 Frictional energy[E2] is given by E2 = ρ x g x hf (10) 2.6. Kinetic Energy of Droplet at the Outlet of Print Head [E3]: When the droplet moves with velocity ub, it possess kinetic energy [E3] 1 1 E3 = m u2b = ρ V u2b (11) 2 2 Substituting the value of V from Equation 5 to Equation 11, we get D2 ρu2b E3 = [ ]δ (12) 6 2.7. Surface Tension Energy Of Droplet At The Outlet [E4]: The surface tension of the liquid is given by pd σ= (13) 4 The surface tension energy is given by 4σD2 E4 = pV = [ ]δ (14) 3d 2.8. Total Energy Required for Eject the Droplet [E]: E=E1+ E2+ E3+ E4 18.40Et3 D2 ρu2b 4σD2 E= δ + ρ ∗ g ∗ hf + [ ]δ + [ ]δ (15) D2 6 3d Equation 15 refers to the total energy required to eject the droplet from the nozzle. The energy must be greater or equal to the sum of all four energies in order to actuate the nozzle to eject the droplet. 2.9. Tail and Pinch off Velocity The pinch-off time coincides with the zero crossing of the ejection velocity (slender-jet approximation) at the instance of the droplet ejection. In the slender-jet approximation with neglected radial momentum, the stretching rate tends to become infinity at the nozzle when the ejection velocity decreases through zero [24]. An instantaneous pinch off is indicated by an infinite stretching rate. This pinch-off is, therefore, imposed through the boundary condition and the approximations in the mathematical model. The imbalance in the capillary tension at the end of the tail causes the formation of the tail droplet when the tail pinches off at the meniscus. The capillary tension pulls the tail droplet toward the head droplet [25-26]. Simultaneously, the tail droplet mass increases as it sweeps up the ink in the tail, slowing down the droplet. As a consequential combined effect, the velocity of the tail droplet relative to the ink in the tail is independent of both viscosity and the size of the tail droplet. To calculate this velocity, this problem is to be considered in a frame of reference in which the tail droplet is stationary. http://www.iaeme.com/IJMET/index.asp 1330 editor@iaeme.com
Rajesh.P.K. and Aravindraj.S The forces on the control volume are advection +ρπR2 u2 , Laplace pressure +σπR, and the direct effect of surface tension−σπR, should sum up to zero if the velocity is constant. ρπR2 u2 + σπR − σ2πR = 0 (16) From this equation, we get the tail droplet velocity as σ u = √ρR 3. DIAMETER OF THE DROPLET AFTER SPREAD [D1] The diameter of the droplet after spread is calculated by equating the energy attained by the droplet before impact to the energy attained by the droplet after impact (law of conservation of energy) E3+E4+Potential energy = E7+E8 The droplet attains the surface tension energy and kinetic energy before the impact and due to the pressure applied at the membrane, it possess potential energy [4]. D2 ρu2b 4σD2 [ ]δ + [ ]δ + ρ ∗ g ∗ V ∗ h (17) 6 3d The surface tension energy attained when the droplet fall on the substrate is given by [27] π E7 = d12 σ (1 − cosθ) (18) 4 The energy needed to to spread the droplet in the substrate against the viscososity is given by [27] π 1 E8 = ρ vi2 d d12 (19) 3 √Re Equating the equation 16,17 and 18, we get D2 ρu2b 4σD2 π π 1 [ ]δ + [ ]δ + ρ ∗ g ∗ V ∗ h = d2max σ (1 − cosθ) + ρ vi2 d d12 6 3d 4 3 √Re From equation 19, we infer that the diameter of the spread (d1) and the maximum diameter of spread is related to the velocity of ejected droplet and the deflection of the membrane, which is in turn, related to F. Figure 2 Splat formation on substrate [27] 4. INK AND ITS PROPERTIES Thermal and electrochemical stability and its high transparency [28-30] make PEDOT: PSS and PEGDA a conductive material with certain versatility, such as the possibility of deposition on different substrates. The inks were purchased from Sigma Aldrich, USA. The Properties of the ink are listed in the Table 1. http://www.iaeme.com/IJMET/index.asp 1331 editor@iaeme.com
A Numerical Simulation and Validation Study of the Mathematical Model of Droplet Formation in Drop on Demand Inkjet Printer and the Effect of Rheological Properties of Polymerink for Automobile Lighting Application Table 1 Properties of the PEDOT: PSS and PEGDA inks Ink Properties PEDOT:PSS PEGDA Density 1011 Kg/m3 1120 Kg/m3 Surface Tension 33 mN/m 35.09 mN/m Viscosity 0.02 kg/ms 0.025 kg/ms 5. SIMULATION OF DROPLET FORMATION FOR INKJET PRINTING FOR BIO INK The fluid dynamic analysis of bio-ink droplet formation was done using the Computational Fluid Dynamics (CFD) package FLOW-3D software, developed by Flow Sciences Inc., Los Alamos, New Mexico and widely used for inkjet analysis [31]. Inkjet module in FLOW-3D facilitates the characterization of the droplet formation of polymer-inks for inkjet printing. Special features in FLOW-3D include,  Powerful physical modelling capabilities.  Easy meshing with multiple structured blocks.  Ability to refine a mesh, independent of the geometry and based on the required spatial accuracy.  Ability to solve the typical problems of incompressible laminar viscous flow in bio-printing.  Use of special numerical methods to locate free surfaces and applying the proper dynamic boundary conditions at those surfaces. 5.1. Inverse Ohnesorge Number Inverse Ohnesorge number (Z) is a dimensionless number that gives the relationship between the rheological properties- density, viscosity, and surface tension [32-33]. In inkjet printing, liquids with inverse Ohnesorge Number value in between 1 to 10 are jettable. √ργr Z= (20) μ Where ρ is the density of the ink, γ the surface tension of the ink, 𝑟 the nozzle radius and μ the viscosity of the ink. The inverse ohnesorge number for different nozzle diameter for polymer inks is calculated in Table [2, 3]. Table 2 Ohnesorge Number for PEDOT: PSS Diameter (𝛍𝐦) Value 20 0.913 25 1.02 30 1.29 35 1.208 40 1.118 http://www.iaeme.com/IJMET/index.asp 1332 editor@iaeme.com
Rajesh.P.K. and Aravindraj.S Table 3 Ohnesorge Number for PEGDA Diameter (𝛍𝐦) Value 20 0.7929 25 0.8865 30 0.9711 35 1.049 40 1.122 5.2. Geometrical Model for Bio Polymer Inks in Flow 3D Software A model with a cylindrical fluid chamber, movable piston and a nozzle (Figure 3) is created in FLOW 3D. The surface tension model was coupled with General Moving Objects (GMO) model for the simulation of droplet formation. The Surface Tension model is activated and wall adhesion is also activated simultaneously. In order to minimize the wet ability of bio-inks the contact angle is specified as 90°, since most of the fluids exhibit adhesion behaviour at solid surfaces. In the present study, the flow of polymer-inks is simulated using incompressible, laminar and viscous flow mode. Since the Rheological properties of polymer inks have great influence on droplet formation behaviour, size and tail length they are given as inputs, [34]. Figure 3 Nozzle Geometry 6. RESULTS AND DISCUSSION The simulation results for selected nozzle diameter for two different polymer inks based on inverse ohnesorge number are discussed and the effect of rheological properties on droplet formation is investigated. 6.1. Printability of Bio Polymer Inks Printability of bio-ink is determined by its ability to eject stable and repeatable droplets from the nozzle [35]. Drop formation can be characterized by a dimensionless quantity known as inverse ohnesorge number (Z). Generally, 10>Z>1 is the suitable range for stable drop http://www.iaeme.com/IJMET/index.asp 1333 editor@iaeme.com
A Numerical Simulation and Validation Study of the Mathematical Model of Droplet Formation in Drop on Demand Inkjet Printer and the Effect of Rheological Properties of Polymerink for Automobile Lighting Application generation. For Z10, the ink is freely ejected from the nozzle without significant viscous dissipation. The kinetic energy of the drop, however, increases leading to rupture of filament and formation of satellites [36]. A typical inkjet printer nozzle diameter ranges from 20 μm to 50 μm . For PEDOT: PSS and PEGDA, the suitable nozzle diameter is selected based on the inverse ohnerorge number (Z) obtained from the Table [5.1, 5.2] as shown in Table [4] Table 4 Suitable Diameter of Inkjet Printer for polymer inks PEDOT:PSS PEGDA Suitable Diameter 30 40 6.2. Simulation of Droplet Formation of Inkjet Printing for Polymer Inks Ink jetting was simulated by applying velocity on the piston kept over the ink chamber and caused by the piezoelectric actuation, causing ink ejection out of the nozzle. The operating conditions of the piezoelectric actuator such as driving voltage, pulse width, and waveform affect the droplet formation significantly[37-38]. t=0 𝛍𝐬 t=18𝛍𝐬 t=37𝛍𝐬 t=56𝛍𝐬 t=76𝛍𝐬 t=114𝛍𝐬 t=133𝛍𝐬 t=130𝛍𝐬 t=152𝛍𝐬 t=171𝛍𝐬 Figure 4 Droplet formation of PEDOT: PSS ink for the nozzle diameter 40μm In figure 4, at frame 1, the valve is open and pressure pulse is active but the total energy is not enough to form the droplet. At 15μs, in frame 2 the valve is closed, the negative pressure is created on top of liquid inside reservoir which ejects the droplet from the nozzle [39]. At this stage, the ink neck is sufficiently thin to be broken while the rest is sucked into reservoir. At 30μs, the detached volume of liquid outside the nozzle forms a spherical shape. At 30μs, the tail formation takes place and pinch off occurs at 115μs. The diameter of the PEDOT: PSS ink observed from the simulated results is 1.255 cm. t=0 𝛍𝐬 t=19𝛍𝐬 t=38𝛍𝐬 t=57𝛍𝐬 t=76𝛍𝐬 t=95𝛍𝐬 t=114𝛍𝐬 t=133𝛍𝐬 t=152𝛍𝐬 t=190𝛍𝐬 http://www.iaeme.com/IJMET/index.asp 1334 editor@iaeme.com
Rajesh.P.K. and Aravindraj.S Figure 5 Droplet formation of PEGDA ink for the nozzle diameter 40μm In figure 5, at frame 1, the valve is open and pressure pulse was active but total energy is not enough to form the droplet. At 19μs, in frame 2 the valve is closed,a negative pressure is created on top of the liquid inside the reservoir which ejects the droplet from the nozzle [40]. At this stage, the ink neck is sufficiently thin to be broken while the rest is sucked into the reservoir. At 57μs, the detached volume of liquid outside the nozzle forms a spherical shape and pinch off occurs at 152μs and when compared to PEDOT:PSS ink, the pinch off time in PEGDA ink is more due to high viscosity. 6.3. Comparison of Numerical Approach With Simulated Results: From the simulated results, the diameter from droplet is observed to be 1.255 cm and in numerical approach, by substituting the values [Table 5] in the equation 7, the diameter of the droplet is observed to be 1.23 cm. Table 5 Parameters for Force profile used in printing PEDOT: PSS [41] Pulse Profile Parameters Setting Force Required to Deflect the Membrane 55 N Rise Time (R) 30 μs Fall Time 20 μs Thickness of the Membrane 0.01 m 7. CONCLUSIONS In the present work, using polymer inks and simulating different nozzle diameters with FLOW- 3D, provided considerable fundamental insights into the factors that control the performance of a drop-on-demand inkjet printer. Energy equations were developed to simulate the droplet formation in DOD inkjet printer. These were used to find the droplet diameter and diameter of the spread as well as the pinch off velocity of the droplet. From the results given here, properties of the flow that may be useful in the development and design of suitable print head in the laboratory for experimental purpose, can be suggested. From the simulated results, it is evident that the efficiency of droplet generation from drop on demand print‐head depends on the viscosity, surface tension, nozzle size, density, and the driving waveform like wave shape, frequency, and amplitude. The comparison of the results obtained from the numerical approach and the simulated results shows that the numerical approach values are slightly deviated from the simulated value. http://www.iaeme.com/IJMET/index.asp 1335 editor@iaeme.com
A Numerical Simulation and Validation Study of the Mathematical Model of Droplet Formation in Drop on Demand Inkjet Printer and the Effect of Rheological Properties of Polymerink for Automobile Lighting Application NOMENCLATURE S No Symbols Description 1 E1 Energy required for deflecting diaphragm 2 E2 Frictional energy in orifice 3 E3 Kinetic energy of the droplet at the outlet of the print head 4 E4 Surface tension energy of the droplet at the outlet 5 E Total Energy to eject the droplet 6 r Local radius of the membrane from its centre 7 D Diameter of the chamber 8 E Young's modulus of the membrane 9 I Flexural rigidity of the membrane 10 ∈ Poisson's ratio of the membrane (assumed as 0.3) 11 t Thickness of the membrane 12 δ Maximum deflection of the membrane 13 d Diameter of the droplet 14 μ Apparent viscosity 15 uo Average velocity of the fluid inside orifice 16 do Diameter of the orifice 17 ρ Density of the ink 18 hf Frictional head 19 V Volume of the droplet 20 ub Velocity of the droplet at the beginning of its ejection 21 p Pressure inside the droplet 22 θ Contact angle 23 d1 Diameter of the spread 24 Re Reynold’s number 25 Vi Droplet impact velocity REFERENCES [1] Mills, R. N., Ink jet printing–past, present, and future, 10th International Congress on Advances in Non-Impact Printing Technologies, 1994, pp. 410–414. [2] Fromm, J.E., Numerical calculation of the fluid dynamics of drop-on-demand jets, IBM Journal of Research and Development, 28, 1984, pp. 322-33. [3] Heinzl, J. and Hertz, C.H. Ink-jet printing, Advances in electronics and electron physics, 65, 1985, pp. 91–171. [4] Htchings, I.M. and Martin, G.D. Inkjet technology for digital fabrication, John Wiley & Sons Ltd., 2013, pp. 14-28. [5] Kyser, E. L., Collins, L.F. and Herbert, N. Design of an impulse ink Jet, Journal of applied photographic engineering, 7, 1981, pp. 73–79. [6] Brindha, J., Privita Edwina. R.A., Rani.J. and Rajesh, P.K. Influence of rheological properties of protein bio-inks on printability: a simulation and validation study, Materials Today: Proceedings, 3, 2016, pp. 3285–3295. [7] Jang, Kim, D. and Moon, J. Influence of fluid physical properties on ink jet printability, Langmuir, 25, 2009, pp. 2629‐2635. [8] Dijksman, J.F. and Duineveld, P.C. Precision ink jet printing of polymer light emitting displays, Journal of Materials Chemistry, 17, 2007, pp. 511‐522. http://www.iaeme.com/IJMET/index.asp 1336 editor@iaeme.com
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