Modeling on Microdroplet Formation for Cell Printing Based on Alternating Viscous-Inertial Force Jetting

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Long Zhao ◽  
Karen Chang Yan ◽  
Rui Yao ◽  
Feng Lin ◽  
Wei Sun
Keyword(s):  
Inertial Force ◽  
Droplet Formation ◽  
Experimental Results ◽  
Viscous Force ◽  
Drop Diameter ◽  
Maximum Difference ◽  
Engineering Model ◽  
Cell Printing ◽  
Cylindrical Nozzle ◽  
Drop On Demand

Drop-on-demand (DOD) microdroplet jetting technology has diverse applications ranging from additive manufacturing (AM) and the integrated circuit (IC) industry to cell printing. An engineering model of droplet formation can provide insights for optimizing the process and ensuring its controllability and reproducibility. This paper reports a development of an engineering model on the fluid outflow and microdroplet formation based on alternating viscous-inertial force jetting (AVIFJ). The model provides a fundamental understanding on the mechanism of droplet formation driven by the alternating viscous force and inetial force. Furthermore, the model studies the fluid acceleration, velocity, and displacement under the conditions of a uniform cylindrical nozzle and a nonuniform cylindrical nozzle. In conjunction with an energy-based criterion for droplet formation, the model is applied to predict the formability of single microdroplets and the volume and velocity of formed microdroplets. A series of experiments was conducted to validate the developed model. The results show that the model predictions agree well with the experimental results. Specifically, comparing the model prediction and experimental results, the maximum difference of drop diameter is 4 μm, and the maximum difference of drop velocity is 0.3 m/s. These results suggest that the developed theoretical model will provide guidance to the subsequent cell printing applications.

Alternating Force Based Drop-on-Demand Microdroplet Formation and Three-Dimensional Deposition

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
Long Zhao ◽  
Karen Chang Yan ◽  
Rui Yao ◽  
Feng Lin ◽  
Wei Sun
Keyword(s):  
Process Parameters ◽  
Droplet Diameter ◽  
Three Dimensional ◽  
Inertial Force ◽  
Deposition Process ◽  
Droplet Formation ◽  
Solution Viscosity ◽  
Cell Printing ◽  
On Demand ◽  
Drop On Demand

Drop-on-demand (DOD) microdroplet formation and deposition play an important role in additive manufacturing, particularly in printing of three-dimensional (3D) in vitro biological models for pharmacological and pathological studies, for tissue engineering and regenerative medicine applications, and for building of cell-integrated microfluidic devices. In development of a DOD based microdroplet deposition process for 3D cell printing, the droplet formation, controlled on-demand deposition and at the single-cell level, and most importantly, maintaining the viability and functionality of the cells during and after the printing are all remaining to be challenged. This report presents our recent study on developing a novel DOD based microdroplet deposition process for 3D printing by utilization of an alternating viscous and inertial force jetting (AVIFJ) mechanism. The results include an analysis of droplet formation mechanism, the system configuration, and experimental study of the effects of process parameters on microdroplet formation. Sodium alginate solutions are used for microdroplet formation and deposition. Key process parameters include actuation signal waveforms, nozzle dimensional features, and solution viscosity. Sizes of formed microdroplets are examined by measuring the droplet diameter and velocity. Results show that by utilizing a nozzle at a 45 μm diameter, the size of the formed microdroplets is in the range of 52–72 μm in diameter and 0.4–2.0 m/s in jetting speed, respectively. Reproducibility of the system is also examined and the results show that the deviation of the formed microdroplet diameter and the droplet deposition accuracy is within 6% and 6.2 μm range, respectively. Experimental results demonstrate a high controllability and precision for the developed DOD microdroplet deposition system with a potential for precise cell printing.

Droplet Formation Under the Effect of a Flexible Nozzle Plate

2007 ◽  
Author(s):  
S. Sangplung ◽  
J. A. Liburdy
Keyword(s):  
Surface Tension ◽  
Droplet Formation ◽  
Step Function ◽  
Droplet Velocity ◽  
Viscous Force ◽  
Flexible Plate ◽  
Computational Domain ◽  
Cfd Model ◽  
Drop On Demand ◽  
Nozzle Plate

Droplet formation from a flexible nozzle plate driven by a prescribed-waveform excitation of a piezoelectric is numerically investigated using a computational fluid dynamics (CFD) model with the VOF method. The droplet generator with a flexible nozzle plate, which is free to vibrate due to the pressure acting on the plate, is modeled in a CFD computational domain. The CFD analysis includes the fluid-structure interaction between fluid and a flexible plate using large deflection theory. The problem is characterized by the nondimensional variables based on the capillary parameters of time, velocity, and pressure. The CFD model is validated with the experiment results. This study examines the characteristics of the applied waveforms and nozzle plate material properties to change the vibrational characteristics of the nozzle plate. The effect of fluid properties on the droplet formation process is also investigated focusing on surface tension and viscous forces. The mechanism of the droplet formation excited by a drop-on-demand piezoelectric waveform is investigated using a step-function and a pulse waveform. The piezoelectric displacement plays an important role in generating either forward-driven momentum or a suction pressure inside the chamber. For the step-function waveform, the nondimensional applied impulse is defined and used to characterize the post-breakoff droplet volume. Increasing the impulse of the piezoelectric can be used to cause a faster droplet velocity and it is shown that the vibration of the nozzle plate has a strong effect on the droplet velocity, shape, and volume. Surface tension has strong influence to the droplet formation characteristics which is contrast to a viscous force that makes no difference on the droplet formation for different viscosities. For the combination of a fluid with high surface tension and the most flexible nozzle plate, this system can not cause the droplet ejected out of the nozzle.

scholarly journals The role of concentration on drop formation and breakup of collagen, fibrinogen, and thrombin solutions during inkjet bioprinting

2020 ◽  
Author(s):  
Hemanth Gudapati ◽  
Ibrahim T. Ozbolat
Keyword(s):  
Inertial Force ◽  
Viscous Force ◽  
Protein Solutions ◽  
Drop Formation ◽  
Minimum Diameter ◽  
Subvisible Particles ◽  
Potential Flows ◽  
Drop On Demand ◽  
Initial Onset

AbstractThe influence of protein concentration on drop formation and breakup of aqueous solutions of fibrous proteins collagen, fibrinogen, and globular protein thrombin in different concentration regimes is investigated during drop-on-demand (DOD) inkjet bioprinting. The capillary-driven thinning and breakup of dilute (c/c* < 1, where c is the concentration and c* is the overlap concentration) collagen, fibrinogen, and thrombin solutions is predominantly resisted by inertial force on the initial onset of necking. The minimum diameter (Dfmin(t)) of the necked fluid up to the critical pinch-off time (tc) scales with time as Dfmin(t) ∼ (tc − t)2/3, a characteristic of potential flows. Although the capillary-driven thinning and breakup of semidilute unentangled collagen (1 ≤ c/c* ≤ 4) and fibrinogen (1 ≤ c/c* ≤ 1.3) solutions is predominantly resisted by inertial force on the initial onset of necking, the breakup of droplets is delayed beyond tc, where the minimum diameter of the necked fluid decreases exponentially with time because of the resistance of elastic force. The resistance of viscous force to the necking of both the dilute and semidilute untangled protein solutions is negligible. Aggregates or subvisible particles (between 1 and 100 μm) constantly disrupt the formation of droplets for the semidilute unentangled protein solutions, even when their inverse Ohnesorge number (Z) is within the printability range of 4 ≤ Z ≤ 14. Although aggregates are present in the dilute protein solutions, they do not disrupt the formation of droplets.

Investigation of the Hydrodynamics of Suspended Cells for Reliable Inkjet Cell Printing

2014 ◽  
Author(s):  
Eric Cheng ◽  
Ali Ahmadi ◽  
Karen C. Cheung
Keyword(s):  
High Speed ◽  
Cell Tracking ◽  
Droplet Formation ◽  
Vertical Position ◽  
Cell Behaviour ◽  
Nozzle Orifice ◽  
Cell Printing ◽  
Drop On Demand ◽  
Droplet Ejection ◽  
A Cell

Reliable inkjet drop-on-demand dispensing of cells has numerous applications including cell assays and tissue engineering. Previous work on inkjet cell printing has demonstrated that the cell count per droplet is inhomogeneous and does not follow the expected Poisson distribution. In the present work, the flow-induced cell behaviour is characterised to better understand the hydrodynamic mechanisms behind unreliable cell printing. A glass piezoelectric inkjet nozzle with an 80 μm diameter orifice is mounted on a PDMS cast which acts as a refractive index matching material for cell tracking through an inverted microscope. Droplet formation is achieved by a bipolar waveform. A high-speed camera focused on the centre plane of the nozzle captures images which are then analysed by a cell tracking algorithm to obtain the horizontal and vertical position of the cells over time. High-speed tracking of cells within a transparent inkjet nozzle revealed three possible cell behaviours caused by the formation and break-off of droplets. These behaviours are cell travel, cell ejection and cell reflection, determined as a function of the position of the cell at the onset of droplet formation. The first behaviour, cell travel, is characterised as the displacement of the cell towards the orifice during droplet formation followed by a small backwards motion due to the retracting meniscus after droplet pinch-off. Cell travel results in a net forward displacement of the cell towards the nozzle orifice. The second observed cell behaviour is cell ejection, where a cell is ejected with a droplet and can no longer be observed within the nozzle after the droplet break-off. The third observed cell behaviour is cell reflection. In this case, hydrodynamic forces produced during droplet ejection acts on the cell to move it further away from the nozzle orifice resulting in a net displacement of the cell away from the orifice after droplet ejection. Through the cell tracking information, it is hypothesized that cell reflection is caused by fluid flow reversal during the droplet ejection process. As a result of cell reflection, certain cells within a region close to the orifice will not be printed; instead they are pushed to a location further away from the orifice. Therefore, mapping of cell positions before droplet formation is performed to identify regions within the nozzle that exhibit a high probability of cell ejection and reflection. Overall, the results from this study will greatly contribute to our understanding of the cell printing process, which will allow us to optimize current inkjet systems for cell printing applications.

scholarly journals Taylor state dynamos found by optimal control: axisymmetric examples

2018 ◽  
Vol 853 ◽  
pp. 647-697 ◽  
Author(s):  
Kuan Li ◽  
Andrew Jackson ◽  
Philip W. Livermore
Keyword(s):  
Magnetic Field ◽  
Optimal Control ◽  
Vector Fields ◽  
Inertial Force ◽  
Basis Set ◽  
Viscous Force ◽  
Time Step ◽  
Geostrophic Flow ◽  
Spectral Expansions ◽  
The Magnetic Field

Earth’s magnetic field is generated in its fluid metallic core through motional induction in a process termed the geodynamo. Fluid flow is heavily influenced by a combination of rapid rotation (Coriolis forces), Lorentz forces (from the interaction of electrical currents and magnetic fields) and buoyancy; it is believed that the inertial force and the viscous force are negligible. Direct approaches to this regime are far beyond the reach of modern high-performance computing power, hence an alternative ‘reduced’ approach may be beneficial. Taylor (Proc. R. Soc. Lond. A, vol. 274 (1357), 1963, pp. 274–283) studied an inertia-free and viscosity-free model as an asymptotic limit of such a rapidly rotating system. In this theoretical limit, the velocity and the magnetic field organize themselves in a special manner, such that the Lorentz torque acting on every geostrophic cylinder is zero, a property referred to as Taylor’s constraint. Moreover, the flow is instantaneously and uniquely determined by the buoyancy and the magnetic field. In order to find solutions to this mathematical system of equations in a full sphere, we use methods of optimal control to ensure that the required conditions on the geostrophic cylinders are satisfied at all times, through a conventional time-stepping procedure that implements the constraints at the end of each time step. A derivative-based approach is used to discover the correct geostrophic flow required so that the constraints are always satisfied. We report a new quantity, termed the Taylicity, that measures the adherence to Taylor’s constraint by analysing squared Lorentz torques, normalized by the squared energy in the magnetic field, over the entire core. Neglecting buoyancy, we solve the equations in a full sphere and seek axisymmetric solutions to the equations; we invoke $\unicode[STIX]{x1D6FC}$- and $\unicode[STIX]{x1D714}$-effects in order to sidestep Cowling’s anti-dynamo theorem so that the dynamo system possesses non-trivial solutions. Our methodology draws heavily on the use of fully spectral expansions for all divergenceless vector fields. We employ five special Galerkin polynomial bases in radius such that the boundary conditions are honoured by each member of the basis set, whilst satisfying an orthogonality relation defined in terms of energies. We demonstrate via numerous examples that there are stable solutions to the equations that possess a rapidly decreasing spectrum and are thus well-converged. Classic distributions for the $\unicode[STIX]{x1D6FC}$- and $\unicode[STIX]{x1D714}$-effects are invoked, as well as new distributions. One such new $\unicode[STIX]{x1D6FC}$-effect model possesses oscillatory solutions for the magnetic field, rarely before seen. By comparing our Taylor state model with one that allows torsional oscillations to develop and decay, we show the equilibrium state of both configurations to be coincident. In all our models, the geostrophic flow dominates the ageostrophic flow. Our work corroborates some results previously reported by Wu & Roberts (Geophys. Astrophys. Fluid Dyn., vol. 109 (1), 2015, pp. 84–110), as well as presenting new results; it sets the stage for a three-dimensional implementation where the system is driven by, for example, thermal convection.

Large Eddy Simulation of Two-Phase Flow Pattern and Transformation Characteristics of Flow Mixing Nozzle

2019 ◽  
Vol 35 (5) ◽  
pp. 693-704
Author(s):  
Jin Zhao ◽  
Zhi Ning ◽  
Ming Lü
Keyword(s):  
Flow Pattern ◽  
Two Phase Flow ◽  
Velocity Ratio ◽  
Inertial Force ◽  
Surface Tension Force ◽  
Viscous Force ◽  
Phase Flow ◽  
Two Phase ◽  
Jet Breakup ◽  
Flow Mixing

ABSTRACTThe two-phase flow pattern of a flow mixing nozzle plays an important role in jet breakup and atomization. However, the flow pattern of this nozzle and its transformation characteristics are still unclear. A diesel-air injection simulation model of a flow mixing nozzle is established. Then the two-phase flow pattern and transformation characteristics of the flow mixing nozzle is studied using a numerical simulation method. The effect of the air-diesel velocity ratio, ratio of the distance between the tube orifice and nozzle hole and the tube diameter (H/D), and the diesel inlet velocity was studied in terms of the jet breakup diameter (jet diameter at the breakup position) and jet breakup length (length of the diesel jet from the breakup position to the nozzle outlet). The results show that the jet breakup diameter decreases with the decrease in H/D or the increase in the air-diesel velocity ratio and diesel inlet velocity. The jet breakup length increases first and then decreases with the increase in H/D and air-diesel velocity ratio; the trend of the diesel inlet velocity is complicated. In addition, a change in the working conditions also causes some morphological changes that cannot be quantitatively analyzed in the diesel-air flow pattern. The transition characteristics of the flow pattern are analyzed, and it is found that the main reason for the change in the flow pattern is the change in the inertial force of the air, surface tension force, and viscous force of diesel (non-dimensional Reynolds number and Weber number describe the transition characteristics in this paper). The surface tension force of diesel decreases and the viscous force of diesel and inertial force of air increase when the air-diesel velocity ratio increases or H/D decreases. However, the effects of the diesel surface tension force and viscous force effect are much smaller than that of the air inertial force, which changes the diesel-air flow pattern from a drop pattern to a vibration jet pattern, broken jet pattern, and then a chaotic jet pattern.

Analytical Model for the Deformation of Viscoelastic Non-Newtonian Drops Undergoing Secondary Atomization

2016 ◽  
Author(s):  
Sharon E. Snyder ◽  
Varun Kulkarni ◽  
Paul E. Sojka
Keyword(s):  
Analytical Model ◽  
Xanthan Gum ◽  
Experimental Results ◽  
Analytical Models ◽  
Drop Diameter ◽  
Droplet Deformation ◽  
Secondary Atomization ◽  
Starting Point ◽  
Breakup Model ◽  
Xanthan Gum Solution

While there is no single analytical model that accurately predicts all stages and modes of secondary atomization, many groups have developed models that predict deformation and oscillation of a single, isolated drop. The TAB (Taylor Analogy Breakup) model was chosen for this investigation, mainly due to its widespread use by Liu and Reitz [1], Hwang et al. [2], Tanner [3], and Lee and Reitz [4], among others. Since the TAB model is also the foundation for many other analytical models, it will also be used here as a starting point for the development of a viscoelastic non-Newtonian model to predict droplet deformed radii, droplet deformation time, and velocity at deformation time for viscoelastic xanthan gum - DI water solutions. Three additional improvements are made to this viscoelastic TAB model: the first is a change to a TAB coefficient; the second to the equation for the drag coefficient, and the third modification is to the breakup criterion. This model uses Carreau rheology and Zimm relaxation time. Non-dimensional drop diameter and initiation times are plotted against We; model results are compared to experimental results for a range of xanthan gum solution concentrations. Results show fair agreement between experimental results and model results for non-dimensional drop diameter, with the best match at low XG concentration and low-to-medium We (10–30). It was also noted that increased viscoelasticity seems to increase this drop diameter. Good agreement between experimental data and model results has been seen for initiation time, with increased viscoelasticity increasing this parameter as well.

Learning-Based Cell Injection Control for Precise Drop-on-Demand Cell Printing

2018 ◽  
Vol 46 (9) ◽  
pp. 1267-1279 ◽  
Author(s):  
Jia Shi ◽  
Bin Wu ◽  
Bin Song ◽  
Jinchun Song ◽  
Shihao Li ◽  
...  
Keyword(s):  
Cell Injection ◽  
Cell Printing ◽  
On Demand ◽  
Drop On Demand ◽  
Injection Control

Vibration Study of the Piezo-Driven Pipettes Immersed in Viscous Liquids

2005 ◽  
Author(s):  
Mingxuan Fan ◽  
Yuksel Agca ◽  
John Critser ◽  
Z. C. Feng
Keyword(s):  
Integration Method ◽  
Inertial Force ◽  
Dynamic Responses ◽  
Viscous Force ◽  
The Finite Element Method ◽  
Viscous Liquids ◽  
State Response ◽  
Glass Needle ◽  
Precise Movement ◽  
Surrounding Liquid

Intracytoplasmic Sperm Injection (ICSI) is regarded as one of the most useful assisted reproductive technology (ART). During ICSI, a single spermatozoon is mechanically injected into cytoplasm of an oocyte using a glass needle, called a micro-injection pipette. The micro-injection pipette is usually controlled by a micromanipulator for the precise movement. In the case of rodent ICSI the Piezo-driven pipette is needed. However, one undesirable aspect of the Piezo-driven pipette is that the technicians have to use mercury in the micro-injection pipette in order to achieve consistent results. It is commonly held that the large density of mercury strongly affects the pipette vibration. In this work, we analyze the effect of mercury on the vibration characteristics of the Piezo-driven pipette. The pipette is modeled as a cantilever beam immersed in a viscous liquid. The forces on the pipette by the surrounding liquid include both inertial force and viscous force. The steady state response of the pipette is obtained by the finite element method together with the numerical integration method. We investigate the pipette dynamic responses when different fluids are used as the plug inside the pipette and as the fluid surrounding the pipette. Based on the analysis, we conclude that the effect mercury has on the vibration is not the main reason that it facilitates the ICSI.

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