Jan Lienemann

Modeling, Simulation, and Optimization of Electrowetting

Electrowetting is an elegant method to realize the motion, dispensing, splitting, and mixing of single droplets in a microfluidic system without the need for any mechanical—and fault-prone—components. By only applying an electric voltage, the interfacial energy of the fluid–solid interface is altered and the contact line of the droplet is changed. However, since the droplet shape is usually heavily distorted, it is difficult to estimate the droplet shape during the process. Further, it is often necessary to know if a process, e.g., droplet splitting on a given geometry, is possible at all, and what can be done to increase the systems reliability. It is thus important to use computer simulations to gain an understanding about the behavior of a droplet for a given electrode geometry and voltage curve. Special care must be exercised when considering surface-tension effects. We present computer simulations done with the Surface Evolver program and a template library combined with a graphical user interface (GUI) that facilitates standard tasks in the simulation of electrowetting arrays.

Parameter preserving model order reduction for MEMS applications

Model order reduction techniques are known to work reliably for finite element-type simulations of micro-electro-mechanical systems devices. These techniques can tremendously shorten computational times for transient and harmonic analyses. However, standard model reduction techniques cannot be applied if the equation system incorporates time-varying matrices or parameters that are to be preserved for the reduced model. However, design cycles often involve parameter modification, which should remain possible also in the reduced model. In this article we demonstrate a novel parameterization method to numerically construct highly accurate parametric ordinary differential equation systems based on a small number of systems with different parameter settings. This method is demonstrated to parameterize the geometry of a model of a micro-gyroscope, where the relative error introduced by the parameterization lies in the region of . We also present recent developments on semi-automatic order reduction methods that can preserve scalar parameters or functions during the reduction process. The first approach is based on a multivariate Padé-type expansion. The second approach is a coupling of the balanced truncation method for model order reduction of (deterministic) linear, time-invariant systems with interpolation. The approach is quite flexible in allowing the use of numerous interpolation techniques like polynomial, Hermite, rational, sinc and spline interpolation. As technical examples we investigate a micro anemometer as well as the gyroscope. Speed-up factors of 20–80 could be achieved, while retaining up to six parameters and keeping typical relative errors below 1%.

Modeling, Design, and Verification for the Analog Front-End of a MEMS-Based Parallel Scanning-Probe Storage Device

We present an integrated analog front-end (AFE) for the read-channel of a parallel scanning-probe storage device. The read/write element is based on an array of microfabricated silicon cantilevers equipped with heating elements to form nanometer-sized indentations in a polymer surface using integral atomic-force microscope (AFM) tips. An accurate cantilever model based on the combination of a thermal/electrical lumped-element model and a behavioral model of the electrostatic/mechanical part are introduced. The behavioral model of the electrostatic/mechanical part is automatically generated from a full finite-element model (FEM). The model is completely implemented in Verilog-A and was used to co-develop the integrated analog front-end circuitry together with the read/write cantilever. The cantilever model and the analog front-end were simulated together and the results were experimentally verified. The approach chosen is well suited for system-level simulation and verification/extraction in a design environment based on standard EDA tools.

Surface tension defects in microfluidic self-alignment

Self-alignment in the fluidic phase is an alternative technique to conventional pick-and-place assembly, providing cost-effective, precise assembly of millions of microparts. For accurate alignment, the control of unwanted surface defects lowering alignment precision. Local minima are investigated and the modulation of the energy curve is simulated. Furthermore, hytsteresis effects are studied. The simulation results allow predictions for the modeling of the fluidic surface tension driven self alignment and thus provide conditions for the robustness of the fabrication process.

Smoothed particle hydrodynamics-based numerical investigation on sessile, oscillating droplets

Forced oscillations in sessile droplets can be exploited in electrowetting mixing of fluid fractions. The necessary complex flows and large shape deformations require a numerical investigation of fluid dynamics in the transient regime. We provide a means to characterize oscillations qualitatively and quantitatively with the goal to examine and to classify flow patterns occurring inside. A superposition of different harmonic excitation patterns gives the possibility to control the convective flow. In this investigation, we apply a generic and accurate multi-phase smoothed particle hydrodynamics model to a two-dimensional three-phase flow and consider an oscillating droplet sitting on a substrate and immersed in a fluidic phase. These vibrations are investigated in two ways: the analysis of a step response due to an abrupt change of the contact angle is applied to identify the resonance frequencies. Secondly, the time evolution of the shape of the droplet in terms of harmonic functions is determined. Their amplitudes are examined in the time and frequency domain. This gives the possibility to relate resonance frequencies to mode shapes and to detect a coupling between them. Our approach is successfully applied to different numerical case studies.

A Simulation free Reduction Scheme and Nonlinear Modelling of an Electrostatic Beam

Abstract In this paper, a new approach to the model order reduction of a type of singular nonlinear systems is presented. This approach does not need simulation or linearization of the original system and therefore, it is suitable for large systems. By separating the linear and nonlinear parts of the original nonlinear model, the idea is considering the nonlinearities of the resulting system as additional inputs and applying a Krylov subspace method. We apply the method for reduced order modelling of an electrostatic actuated beam model which is a typical structure whose generic layout corresponds to an RF switch as well as an RF electromechanical filter.

Nonlinear Heat Transfer Modeling

The simulation of heat transport for a single device is easily tackled by current computational resources, even for a complex, finely structured geometry; however, the calculation of a multi-scale system consisting of a large number of those devices, e.g., assembled printed circuit boards, is still a challenge. A further problem is the large change in heat conductivity of many semiconductor materials with temperature. We model the heat transfer along a 1D beam that has a nonlinear heat capacity which is represented by a polynomial of arbitrary degree as a function of the temperature state. For accurate modeling of the temperature distribution, the resulting model requires many state variables to be described adequately. The resulting complexity, i.e., number of first order differential equations and nonlinear parts, is such that a simplification or model reduction is needed in order to perform a simulation in an acceptable amount of time for the applications at hand.

SPH BASED OPTIMIZATION OF ELECTROWETTING-DRIVEN DIGITAL MICROFLUIDICS WITH ADVANCED ACTUATION PATTERNS

Fast and thorough mixing is a crucial operation of digital microfluidic devices, where discrete and small fluid portions are moved and processed. In this paper, we want to analyze and to optimize the mixing process by substituting conventional motion and superposing oscillatory and translational modes. An accurate multiphase smoothed particle hydrodynamics (SPH) discretization for incompressible flow is instantiated. Different harmonic excitation patterns for the solid–liquid surface energy are applied and their influence on droplet mode shapes, formation of eddies and the Shannon entropy of droplet fluid components are measured. We tailor enhanced actuation patterns which improve mixing grade and reduce mixing time.

Modeling, Design, and Verification for the Analog Front-end of a MEMS-based Parallel Scanning-probe Storage Device

The paper presents an integrated analog front-end (AFE) for the read-channel of a parallel scanning-probe storage device. The read/write element is based on an array of microfabricated silicon cantilevers equipped with heating elements to form nanometer-sized indentations in a polymer surface using integral atomic-force microscopy (AFM) tips. A detailed model based on a combination of a thermal/electrical lumped-element model and behavioral model of the electrostatic/mechanical part was developed. The behavioral model of the electrostatic/mechanical part is automatically generated from a full finite-element model (FEM). The model is completely implemented in Verilog-A and was used to co-develop the integrated analog front-end circuitry together with the read/write cantilever. The model and the analog front-end were simulated together and the results were experimentally verified. The approach chosen is well suited for system-level simulation and verification/extraction in a design environment based on standard EDA tools

AUTOMATIC ORDER REDUCTION FOR FINITE ELEMENT MODELS

In the process of physical modelling of microsystems operating on various energy domains, the engineer is used to apply Finite Element techniques for the discrete representation of the functionality of the device under investigation in a simulation environment. There are many commercial products that help the engineer in performing this task. The common feature of all these simulation tools is that the discrete representation consists of a system of ordinary differential equations. The dimension of this system is directly connected to the number of degrees of freedom for the respective problem. For a spatial displacement field, e.g., the degrees of freedom are three times the number of discretization nodes. The higher the requirements for precision of the simulation results, the more discretization nodes are usually introduced. Nevertheless, the results the engineer will use are in most cases of low dimensional order. In other words, the characteristic features of the required functionality of the device under developement are well represented in low dimensional subspace of the entire solution space of a very fine Finite Element model. Moreover, the requirement for system behaviour simulation makes it impossible to couple large-scale