A Dynamical Model of Drop Spreading in Electrohydrodynamic Jet Printing

Abstract

Electrohydrodynamic jet (e-jet) printing is a microscale additive manufacturing technique used to print microscale constructs, including next-generation biological and optical sensors. Despite the many advantages to e-jet over competing microscale additive manufacturing techniques, there do not exist validated models of build material drop formation in e-jet, relegating process design and control to be heuristic and ad hoc. This work provides a model to map deposited drop volume to final spread topography and validates this model over the drop volume range of 0.68–13.4 pL. The model couples a spherical cap volume conservation law to a molecular kinetic relationship for contact line velocity and assumes an initial contact angle of 180 deg to predict the drop shape dynamics of dynamic contact angle and dynamic base radius. For validation, the spreading of e-jet-printed drops of a viscous adhesive is captured by high-speed microscopy. Our model is validated to have a relative error less than 3% in dynamic contact angle and 1% in dynamic base radius.

Subtractive Patterning of Nanoscale Thin Films Using Acid‐Based Electrohydrodynamic‐Jet Printing

“…This nonideal patterning behavior is attributed to the extremely small volume of the ejected ink that is characteristic of high‐resolution e‐jet printing (in the range of fL), along with the relatively high vapor pressure of the aqueous HCl solution, which results in nearly instantaneous evaporation when the ink contacts with the substrate surface (in situ visualization of the aqueous HCl ink printing process is provided in Video S1, Supporting Information). [ 44 ] If the ink evaporation takes place faster than the etching reaction, only the very top layer of ZnO is removed. To characterize the resulting changes to the film surface, atomic force microscopy (AFM) analysis was performed after printing with a 1 m HCl ink, and minimal changes in topology were observed.…”

Layer-to-Layer Stability of Linear Layerwise Spatially Varying Systems: Applications in Fused Deposition Modeling

“…In [10] a spatial modeling framework for electrohydrodynamic-jet printing (e-jet), a micro-AM process, is introduced and an efficient spatial iterative learning control algorithm is introduced. Drop spreading dynamics for the e-jet spatial deposition process are presented in [9], and various heightmap models for L2L dynamics at varying fidelities are presented in [20]. A task-basis controller model to ensure uniform deposition width in a microrobotic deposition is given in [3].…”

“…1) For a Gaussian bell-curve shape, θ encodes the mean and covariance [9], [10], [12]. 2) For an ellipsoidal shape, θ encodes the minor and major radii [14], [18], [30].…”

“…IV. L2L STABILITY In this section, the L2L stability of the system in (9) [equivalently (4)] is investigated. In addition, robustness margins for L2L stability are given for the uncertainty reformulation of the system in (10).…”

“…Temporal dynamics constitute the transient response of the deposition process and include material preprocess (e.g., heating), volumetric flow of material through a deposition nozzle [3]- [5], and the motion of the deposition system [6]- [8]. Spatial dynamics constitute the spatial characteristics of the process and include the change of material volume and location as a function of space, deposited material interactions with the build plate, and the geometry of the deposited material and the printed part [9]- [14]. Although most of the temporal dynamics can be modeled using existing tools in robotics, physics, and kinematics, the spatial dynamics of AM processes pose research challenges that require novel modeling and control tools.…”