Membrane Deflection Research Articles

Miniature Deformable MEMS Mirrors for Ultrafast Optical Focusing.

Here, we introduce ultrafast tunable MEMS mirrors consisting of a miniature circular mirrored membrane, which can be electrostatically actuated to change the mirror curvature at unprecedented speeds. The central deflection zone is a close approximation to a parabolic mirror. The device is fabricated with a minimal membrane diameter, but at least double the size of a focused optical spot. The theory and simulations are used to predict maximum relative focal shifts as a function of membrane size and deflection, beam waist, and incident focal position. These devices are demonstrated to enable fast tuning of the focal wavefront of laser beams at ≈MHz tuning rates, two to three orders of magnitude faster than current optical focusing technologies. The fabricated devices have a silicon membrane with a 30-100 μm radius and a 350 nm gap spacing between the top and bottom electrodes. These devices can change the focal position of a tightly focused beam by ≈1 mm at rates up to 4.9 MHz and with response times smaller than 5 μs.

Mechanics of diffusion-mediated budding and implications for virus replication and infection.

Budding allows virus replication and macromolecular secretion in cells through the formation of a membrane protrusion (bud) that evolves into an envelope. The largest energetic barrier to bud formation is membrane deflection and is trespassed primarily thanks to nucleocapsid-membrane adhesion. Transmembrane proteins (TPs), which later form the virus ligands, are the main promotors of adhesion and can accommodate membrane bending thanks to an induced spontaneous curvature. Adhesive TPs must diffuse across the membrane from remote regions to gather on the bud surface, thus, diffusivity controls the kinetics. This paper proposes a simple model to describe diffusion-mediated budding unravelling important size limitations and size-dependent kinetics. The predicted optimal virion radius, giving the fastest budding, is validated against experiments for coronavirus, HIV, flu and hepatitis. Assuming exponential replication of virions and hereditary size, the model can predict the size distribution of a virus population. This is verified against experiments for SARS-CoV-2. All the above comparisons rely on the premise that budding poses the tightest size constraint. This is true in most cases, as demonstrated in this paper, where the proposed model is extended to describe virus infection via receptor- and clathrin-mediated endocytosis, and via membrane fusion.

Identification of partial differential equations in structural mechanics theory through k-space analysis and design

This paper presents a method to identify wave equations’ parameters using wave dispersion characteristics (k-space) on two-dimensional domains. The proposed approach uses the minimization of the difference of an analytic formulation of the dispersion relation to wavenumbers calculated from solution fields. The implementation of partial differential equations (PDE) resolution on finite element software is explained and tested with analytic solutions in order to generate the test solution fields for the identification process. The coefficient identification is tested on solution fields generated by finite element solver for some 2nd- and 4th-order equations. In particular the test cases are the equations at different frequencies of deflection of isotropic and orthotropic membrane, flexion of isotropic and orthotropic plate and an original model of orthotropic plate equivalent to a bi-directional ribbed plate. In the limits of the spatial sampling rate and the domain size, the process allows an accurate retrieval of the wave equation parameters.

A Novel Experimental Static Deflection Equation for Specific Cantilever beam Made of Ionic Polymer–Metal Composite

Background: Nowadays, ionic polymer–metal composites are widely used in various industries. They are in the group of electroactive polymers and smart materials with electromechanical properties. By applying a small amount of voltage, the nonlinear stress inside them will happen and their deformation can be seen. The energy transformation from electrical to mechanical is observable during the process of giving voltage to a specimen. The aim of this study is to investigate a novel experimental static deflection equation for specific cantilever beam made of ionic polymer–metal composite. Methods: In this paper, an ionic-polymer-metal composite is provided; the main core is based on an electroactive Fluoropolymer named Nafion, and the coated electrodes are made of Platinum. The length of the specimen is 27.131 mm and its width is 5.728mm. Voltage from 1.5 to 4.3V was applied to the specimen used in this study; the y-directional displacement of the IPMC at each step is measured and recorded; then, a finite element analysis was performed. Curve fitting of the data for the experimental analysis was also done. Moreover, the governing relations of IPMC according to the Nernst–Planck equation were investigated in this study. Results: The results have been validated in two forms of finite element method and experimental analysis. The results of finite element analysis showed that the ion flux in the polymer is calculated by the equation: [INSIDE:1]. In other words, this equation, which is called Nernst–Planck, is the basic equation of this type of material. This equation is the main governing equation to describe the transfer phenomena of IPMC materials. Furthermore, in order to calculate the deflection of IPMC membrane, 19 equations designed in this study were used. In the next step, the results of the experimental analysis showed that, based on the field emission scanning electron microscope images, the Nafion surface is completely sandblasted and its area is completely uniform. The right image taken by Dino-Lite shows the thesis effect on the electrode. Furthermore, the results showed that IPMC has high-quality coated electrodes. Conclusions: It is shown that a nonlinear equation governs the behavior of IPMCs' deflection versus voltage.

Design and Optimization of a Pressure Sensor Based on Serpentine-Shaped Graphene Piezoresistors for Measuring Low Pressure.

This thesis describes a novel microelectromechanical system (MEMS) piezoresistive pressure sensor based on serpentine-shaped graphene piezoresistors paired with trapezoidal prisms under the diaphragm for measuring low pressure. The finite element method (FEM) is utilized to analyze the mechanical stress and membrane deflection to enhance the degree of stress concentration in this unique sensor. The functional relationship between mechanical performance and dimension variables is established after using the curve fitting approach to handle the stress and deflection. Additionally, the Taguchi optimization method is employed to identify the best dimensions for the proposed structure. Then, the suggested design is compared to the other three designs in terms of operating performance. It is revealed that the recommended sensor can significantly improve sensitivity while maintaining extremely low nonlinearity. In this study, three different types of serpentine-shaped graphene piezoresistors are also designed, and their sensing capability is compared to silicon. The simulation results indicate that the pressure sensor with Type 2 graphene piezoresistors has a maximum sensitivity of 24.50 mV/psi and ultra-low nonlinearity of 0.06% FSS in the pressure range of 0–3 psi.

A Refined Closed-Form Solution for the Large Deflections of Alekseev-Type Annular Membranes Subjected to Uniformly Distributed Transverse Loads: Simultaneous Improvement of Out-of-Plane Equilibrium Equation and Geometric Equation

The Alekseev-type annular membranes here refer to annular membranes fixed at outer edges and connected with a movable, weightless, stiff, con-centric, circular thin plate at inner edges, which were proposed originally by Alekseev for bearing centrally concentrated loads. They are used to bear the pressure acting on both membranes and plates, which was proposed originally in our previous work for developing pressure sensors. The pressure is applied onto an Alekseev-type annular membrane, resulting in the parallel movement of the circular thin plate. Such a movement can be used to develop a capacitive pressure sensor using the circular thin plate as a movable electrode plate of a parallel plate capacitor. The pressure applied can be determined by measuring the change in capacitance of the parallel plate capacitor, based on the closed-form solution for the elastic behavior of Alekseev-type annular membranes. However, the previous closed-form solution is unsuitable for annular membranes with too large deflection, which limits the range of pressure operation of the developed sensors. A new and more refined closed-form solution is presented here by improving simultaneously the out-of-plane equilibrium equation and geometric equation, making it possible to develop capacitive pressure sensors with a wide range of pressure operations. The new closed-form solution is numerically discussed in its convergence and effectiveness and compared with the previous one. Additionally, its beneficial effect on developing the proposed capacitive pressure sensors is illustrated.

Bio-Functionalized Ultra-Thin, Large-Area and Waterproof Silicone Membranes for Biomechanical Cellular Loading and Compliance Experiments.

Biocompatibility, flexibility and durability make polydimethylsiloxane (PDMS) membranes top candidates in biomedical applications. CellDrum technology uses large area, <10 µm thin membranes as mechanical stress sensors of thin cell layers. For this to be successful, the properties (thickness, temperature, dust, wrinkles, etc.) must be precisely controlled. The following parameters of membrane fabrication by means of the Floating-on-Water (FoW) method were investigated: (1) PDMS volume, (2) ambient temperature, (3) membrane deflection and (4) membrane mechanical compliance. Significant differences were found between all PDMS volumes and thicknesses tested (p < 0.01). They also differed from the calculated values. At room temperatures between 22 and 26 °C, significant differences in average thickness values were found, as well as a continuous decrease in thicknesses within a 4 °C temperature elevation. No correlation was found between the membrane thickness groups (between 3–4 µm) in terms of deflection and compliance. We successfully present a fabrication method for thin bio-functionalized membranes in conjunction with a four-step quality management system. The results highlight the importance of tight regulation of production parameters through quality control. The use of membranes described here could also become the basis for material testing on thin, viscous layers such as polymers, dyes and adhesives, which goes far beyond biological applications.

Fluid–structure interactions of energy-harvesting membrane hydrofoils

We study the kinematics, dynamics and flow fields generated by an oscillating, compliant membrane hydrofoil extracting energy from a uniform water stream at a chord-based Reynolds number $Re \approx 3 \times 10^4$ . Hydrodynamic forces during the foil's motion cause the membrane to dynamically morph its shape, effectively increasing the camber during the oscillation cycle. The membrane's deflection is modelled using the Young–Laplace equation, with pressure term approximated from thin-airfoil theory. Simultaneous tracking of the membrane deformation and the surrounding flow field using laser profiling and particle image velocimetry, respectively, reveals the role of dynamic cambering in stabilizing the leading-edge vortices on the membrane. In this regime of operation, we obtain up to 160 % higher power extraction when compared to a rigid, symmetric hydrofoil. The present work provides a demonstration of how passive compliance of soft materials interacting with fluids may be exploited in tidal and fluvial energy extraction.

Flow separation sensing on airfoil using a 3D printed biomimetic artificial hair sensor

Small-scale unmanned air vehicles require lightweight, compact, and low-power sensors that encompass a variety of sensing modalities to enable flight control and navigation in challenging environments. Flow sensing is one such modality that has attracted much interest in recent years. In this paper, a micro-scale artificial hair sensor is developed to resolve both the direction and magnitude of airflow. The sensor structure employs a high-aspect ratio hair structure and a thin flexible membrane to facilitate the transduction of directional airflow to membrane deflection. The sensor readout is based on capacitive sensing and two pairs of electrodes orthogonal to each other are used to obtain airflow directional information. The sensor structure was fabricated using two-photon polymerization and integration onto a miniature printed circuit board to enable simple measurement. The sensor’s responses to static displacement loading from different directions were characterized. The experimental results are in good agreement with the simulation results. Furthermore, the sensor’s capability to measure the direction and magnitude of flow was demonstrated. Finally, the sensor was mounted on an airfoil and its ability to detect flow separation was verified.

Modular Kirigami Arrays for Distributed Actuation Systems in Adaptive Optics

The demands on adaptive optics are increasing to achieve high performance and meet the requirements for accuracy and reliability with these systems. At present, common technologies for actuator arrays are highly developed and designed in complex arrangements leading to bulky devices. In this work, we propose an approach for designing modular actuation arrays by means of kirigami metasheets realigned in parallel and leveled in plane. The study focuses on the numerical analysis of different cut patterns to couple lift-off motions within a thin, scalable sheet. A design of a modular actuation array is explained and illustrated in the context of a deformable mirror. The optimal lift-off positions within the array are calculated for this example by a proposed positioning algorithm, which makes use of common methods in adaptive optics such as Zernike polynomial fitting. The algorithm is validated by several simulations calculating the membrane deflection, and the overall concept is discussed.

An Integrated OpenFOAM Membrane Fluid-Structure Interaction Solver

The scope of this paper is to present the design and verification of an integrated OpenFOAM membrane fluid-structure interaction (FSI) solver for small deflections, which employs the finite volume method (FVM) for solving the flow field and the finite area method (FAM) for solution of the membrane deflection. A key feature is that both the fluid and the solid solver operate on a common mesh geometry and are included into a single executable. Although the scope of applicability is narrow due to limitations of the membrane solver at its current state, positive verification results prove the practicability of the design, which allows for lightweight implementation as well as simple data transfers and post-processing.

Bio-Interface on Freestanding Nanosheet of Microelectromechanical System Optical Interferometric Immunosensor for Label-Free Attomolar Prostate Cancer Marker Detection.

Various biosensors that are based on microfabrication technology have been developed as point-of-care testing devices for disease screening. The Fabry–Pérot interferometric (FPI) surface-stress sensor was developed to improve detection sensitivity by performing label-free biomarker detection as a nanomechanical deflection of a freestanding membrane to adsorb the molecules. However, chemically functionalizing the freestanding nanosheet with excellent stress sensitivity for selective molecular detection may cause the surface chemical reaction to deteriorate the nanosheet quality. In this study, we developed a minimally invasive chemical functionalization technique to create a biosolid interface on the freestanding nanosheet of a microelectromechanical system optical interferometric surface-stress immunosensor. For receptor immobilization, glutaraldehyde cross-linking on the surface of the amino-functionalized parylene membrane reduced the shape variation of the freestanding nanosheet to 1/5–1/10 of the previous study and achieved a yield of 95%. In addition, the FPI surface-stress sensor demonstrated molecular selectivity and concentration dependence for prostate-specific antigen with a dynamic range of concentrations from 100 ag/mL to 1 µg/mL. In addition, the minimum limit of detection of the proposed sensor was 2,000,000 times lower than that of the conventional nanomechanical cantilevers.

Peculiarities of deformation of round thin-film membranes and experimental determination of their effective characteristics

The features of thin-film membranes, which are formed above round holes in silicon substrates using the Bosch-process are considered. The membrane has a complex shape due to the presence of the stress state of the initial films. The analysis of the dependence of the membrane deflection w on the supplied overpressure P is used to calculate the mechanical characteristics of the membranes. In this case, it is necessary to determine directly on the membrane its diameter, the thickness of the constituent layers, the change in the topography of the membrane surface over its entire area as the overpressure increases. Determination of the membrane diameter and the thicknesses of the constituent layers is shown by the example of p-Si*/SiNx/SiO2 and SiNx/SiO2/SiNx/SiO2 membranes. We used spectral ellipsometry, energy-dispersive X-ray spectroscopy, optical profilometry, optical microscopy. The influence of the peculiarities of the fixing conditions on the stress-strain state of membranes is shown, and the assessment is carried out by means of numerical modeling. A technique has been developed for measuring and calculating the mechanical characteristics of membranes that have an initial deflection. The calculation result is shown on the example of a membrane with an initial deflection of 2 μm --- SiNx/SiO2/SiNx/SiO2 and a membrane with an initial deflection of 30 μm --- Al/SiO2/Al. Keywords: stress, bulging method, films, thin-layer coating, film thickness, membrane, pressure blister test, residual stress, microelectromechanical systems, MEMS, silicon substrate, large deformations, strain, deflections, circular membrane, bulge testing.

An alN-based piezoelectric micromachined ultrasonic transducer with a double-beam suspended structure

ABSTRACT This paper presents an AlN-based piezoelectric micromachined ultrasonic transducer (PMUT) with a double-beam suspended structure. In order to obtain greater deflection displacement and output sound pressure compared to standard systems, a suspended structure is proposed, achieved by utilizing double-sided deep reactive ion etching of the silicon substrate. This structure is capable of greatly reducing the tensile stress caused by deflection on the membrane edge, thereby improving the piezoelectric micromachined ultrasound transducer performance. Simulations are performed using the finite element method and COMSOL software, with results demonstrating that the suspension structure exhibits a lower resonant frequency and a larger membrane deflection displacement than other methods, implying higher penetration and acoustic energy levels. Thus, the sound pressure is improved by changing the PMUT structure. Moreover, a PMUT with a double-beam is fabricated, and the impedance diagram is determined with an impedance analyzer. The resonant frequency of the transducer was 31.88 kHz, while the sound wave received by the standard lead zirconate titanate (PZT) ultrasonic transducer was converted to a voltage of 277.5 mV. In comparison, the proposed PMUT demonstrates an improved acoustic emission performance. In addition, the electromechanical coupling coefficient of the suspended PMUT is observed to be approximately 3.08%, which is significantly better than that of a fully clamped PMUT. This demonstrates the strong electromechanical conversion performance of the proposed PMUT. Results from the transmission and reception air experiments prove that the proposed double-beam PMUT can potentially be used for ranging and wireless energy transmission applications.

Science, Medicine, and the Anesthesiologist

Science, Medicine, and the Anesthesiologist

Design, fabrication, and calibration of a micro-load cell for micro-resistojet development.

In this paper, a micro-load cell utilized for the thrust measurement of a micro-resistojet is described. To improve the degree of completion of the micro-resistojet during the development process, a concept of a micro-load cell, which enables sufficient performance evaluation under space environmental conditions, was proposed through minimization and simplification of a thrust measurement stand. The piezoresistive sensing method was applied to this load cell, which was composed of a membrane, strain gauges, and a built-in Wheatstone bridge. The membrane size was designed using large-deflection theory so that the load cell could exhibit linear characteristics within the measurement range. A polysilicon strain gauge with a high gauge factor was used for the piezoresistor. The strain gauge also had very low sensitivity to temperature, allowing accurate measurement of the membrane deflection caused by thrust without requiring an additional compensation circuit. Four strain gauges were placed to form a full-bridge circuit at the edge of the membrane. The load cell was then realized by a microelectromechanical system fabrication process. The fabricated load cell was calibrated using a three-axis precision moving stage and a commercial load cell. As a result, the load cell output signal was linear in the measurement range of 1-7 mN and the measured sensitivity of the sensor was 1.566 31 × 10-4 V/mN. The calculated nonlinearity was within 1% in the measurement range.

Microelectromechanical Transducer to Monitor High-Doses of Nuclear Irradiation.

This paper reports the design, fabrication and measured performance of a passive microelectromechanical transducer for the wireless monitoring of high irradiation doses in nuclear environments. The sensing device is composed of a polymer material (high-density polyethylene) sealed inside a cavity. Subjected to ionizing radiation, this material releases various gases, which increases the pressure inside the cavity and deflects a dielectric membrane. From the measurement of the deflection, the variation of the applied pressure can be estimated, and, in turn, the dose may be determined. The microelectromechanical structure can also be used to study and validate the radiolysis properties of the polymer through its gas emission yield factor. Measurement of the dielectric membrane deflection is performed here to validate on the one hand the required airtightness of the cavity exposed to doses about 4 MGy and on the other hand, the functionality of the fabricated dosimeter for doses up to 80 kGy. The selection of appropriate materials for the microelectromechanical device is discussed, and the outgassing properties of the selected high-density polyethylene are analysed. Moreover, the technological fabrication process of the transducer is detailed.

Liquid vibrations in cylindrical tanks with flexible membranes

The objectives of this paper are in studying the liquid vibrations in rigid circular cylindrical shells with internal flexible membranes or covered by membranes. The liquid in the container is supposed to be an ideal and incompressible one, and the fluid motion is irrotational. In above formulated suppositions the velocity potential is introduced; it satisfies the Laplace equation. The boundary value problem is formulated for the velocity potential. To obtain boundary conditions on the liquid free surface, the membrane deflection is considered, and the equality of normal components of liquid and membrane velocities is satisfied. The incompressible and inviscid liquid is supposed to perform irrotational motion in the fluid domain divided into two sub-domains by internal flexible membrane that is installed at the given height. For solutions of the problems both numerical and analytical methods are in use. The analytical solutions of two boundary value problems are obtained for unknown velocity potential and membrane deflection as the Fourier–Bessel series with coefficients depending on unknown frequency. Satisfying boundary conditions, we obtain the system of homogeneous algebraic equations. The condition of a non-trivial solution of this system gives the non-linear equation for evaluating the frequencies. The coupled membrane and liquid vibrations in cylindrical tanks are studied also by FEM and BEM methods. The comparison of results obtained using analytical approach with ones received with boundary and finite element method is provided. The main results are as follows. As follows from numerical simulations, if the membrane is installed inside the cylinder, then the most important parameter affecting the result, is the height of the membrane installation. If the membrane is installed at a considerable distance from the free surface, then the sloshing frequency practically does not change, and more precisely, it slightly increases. The dependencies of frequencies via the filling level are identified. The novelty of proposed approach consists in possibility to study the influence of elastic baffles and roofs in the liquid-filled tanks.

Battery-free, wireless soft sensors for continuous multi-site measurements of pressure and temperature from patients at risk for pressure injuries

Capabilities for continuous monitoring of pressures and temperatures at critical skin interfaces can help to guide care strategies that minimize the potential for pressure injuries in hospitalized patients or in individuals confined to the bed. This paper introduces a soft, skin-mountable class of sensor system for this purpose. The design includes a pressure-responsive element based on membrane deflection and a battery-free, wireless mode of operation capable of multi-site measurements at strategic locations across the body. Such devices yield continuous, simultaneous readings of pressure and temperature in a sequential readout scheme from a pair of primary antennas mounted under the bedding and connected to a wireless reader and a multiplexer located at the bedside. Experimental evaluation of the sensor and the complete system includes benchtop measurements and numerical simulations of the key features. Clinical trials involving two hemiplegic patients and a tetraplegic patient demonstrate the feasibility, functionality and long-term stability of this technology in operating hospital settings.

A Review on Analytical Modeling for Collapse Mode Capacitive Micromachined Ultrasonic Transducer of the Collapse Voltage and the Static Membrane Deflections

Analytical modeling of capacitive micromachined ultrasonic transducer (CMUT) is one of the commonly used modeling methods and has the advantages of intuitive understanding of the physics of CMUTs and convergent when modeling of collapse mode CMUT. This review article summarizes analytical modeling of the collapse voltage and shows that the collapse voltage of a CMUT correlates with the effective gap height and the electrode area. There are analytical expressions for the collapse voltage. Modeling of the membrane deflections are characterized by governing equations from Timoshenko, von Kármán equations and the 2D plate equation, and solved by various methods such as Galerkin’s method and perturbation method. Analytical expressions from Timoshenko’s equation can be used for small deflections, while analytical expression from von Kármán equations can be used for both small and large deflections.