Membrane Deflection Research Articles

Analysis on the deflection of thin membrane with a droplet according to the surface tension and elasticity

Thin membranes that may be exposed to water droplet deposition have been used in various industrial and research fields. Deflection of these membranes by water droplets may greatly affect their characteristics. Therefore, it is important to predict deflection of these thin membranes by water droplets. Here, the contact angle effect of a sessile drop was analyzed by a combination of deformation and surface energy; the deflection of elastomer thin membranes was investigated by experiment and simulation. Circular thin membranes were fabricated comprising various materials (i.e., expanded polytetrafluoroethylene, polytetrafluoroethylene, and polyethylene). Modal characteristics for thin membranes mounted on a ring fixture were measured when all edge points were clamped. Based on the measured fundamental frequency, initial tension was determined in accordance with circular thin membrane vibration theory. A numerical model was derived to describe the water droplet profile and membrane deflection by thermodynamics and mechanical energy. Contact angles and profiles were measured for three types of thin membrane and for various water droplet sizes, using a high-speed camera. Deflections were measured using a laser sensor with water droplets of various sizes and various contact angles, along with various ethanol concentrations on the thin membrane. Experimental results were consistent with simulation results. The degree of nonlinearity could be ignored for thin membranes with water droplet volume of ≤ 200 $$\mu L$$ . Maximum deflection of various thin membranes and various contact angles could be predicted using compensation factors. Maximum deflection of the thin membrane could be sufficiently predicted when considering the contact angle effect.

Fast Nondestructive Technique for Analyzing Deflection of Membranes Located on the Substrate

We describe a nondestructive technique for automated analysis of deflection of substrate-mounted membrane structures, which are a key element of devices based on microelectromechanical systems (MEMS devices). The technique includes analysis of substrates with an optical profiler operating in a specialized mode and mathematical processing of measurement results. The technique allows determining the magnitude and sign of deflection of membrane structures for each measurement area. The procedure results in grading the value of deflection and detecting the following types of the state of membrane structures, which are important for assessing the yield and reliability of MEMS devices based on these structures: separation or rupture of the structure, its significant deflection, its slight deflection, and lack of a deflection. All results are displayed in map format on the surface of a substrate with membrane structures with the ability to access more detailed data. The developed technique makes it possible to localize regions with a maximum, predetermined, and low yield of suitable crystals of MEMS devices, as well as flawed regions over the entire substrate surface. The use of the technique significantly increases the accuracy and reduces the measurement time for estimating the yield of suitable membrane structures, and also makes it possible to adjust the process route so as to increase the yield of suitable crystals of MEMS devices.

MEMS piezoresistive pressure sensor with patterned thinning of diaphragm

PurposeThe purpose of this study is to find a new design that can increase the sensitivity of the sensor without sacrificing the linearity. A novel and very efficient method for increasing the sensitivity of MEMS pressure sensor has been proposed for the first time. Rather than perforation, we propose patterned thinning of the diaphragm so that specific regions on it are thinner. This method allows the diaphragm to deflect more in response with regard to the pressure. The best excavation depth has been calculated and a pressure sensor with an optimal pattern for thinned regions has been designed. Compared to the perforated diaphragm with the same pattern, larger output voltage is achieved for the proposed sensor. Unlike the perforations that have to be near the edges of the diaphragm, it is possible for the thin regions to be placed around the center of the diaphragm. This significantly increases the sensitivity of the sensor. In our designation, we have reached a 60 per cent thinning (of the diaphragm area) while perforations larger than 40 per cent degrade the operation of the sensor. The proposed method is applicable to other MEMS sensors and actuators and improves their ultimate performance.Design/methodology/approachInstead of perforating the diaphragm, we propose a patterned thinning scheme which improves the sensor performance.FindingsBy using thinned regions on the diaphragm rather than perforations, the sensitivity of the sensor was improved. The simulation results show that the proposed design provides larger membrane deflections and higher output voltages compared to the pressure sensors with a normal or perforated diaphragm.Originality/valueThe proposed MEMS piezoelectric pressure sensor for the first time takes advantage of thinned diaphragm with optimum pattern of thinned regions, larger outputs and larger sensitivity compared with the simple or perforated diaphragm pressure sensors.

Metallic glass thin film integrated with flexible membrane for electromagnetic micropump application

In this work, metallic glass (MG) thin film integrated with flexible membrane for use in an electromagnetic micropump was proposed and developed. Fe-based MG thin film deposited on a flexible membrane was employed as the actuation membrane. The electromagnetic force generated between the electromagnetic coil and the magnetized thin film was used to excite the actuation membrane. The actuation membrane was integrated with a microchannel for the micropump application. The fluid in the microchannel was driven by the pressure change resulting from the membrane deflection. Membrane deflection of 45 μm was achieved when a current of 0.12 A was applied to the electromagnetic coil. In addition, a maximum flow rate of 0.17 μl min−1 was achieved and driven by the electromagnetic micropump. The Fe-based MG integrated with the flexible membrane actuated by electromagnetic force could be applied to the actuation membrane for the electromagnetic micropump.

Non‐invasive Neuromodulation Using Ultrasound

The discovery of light sensitive proteins led to the development of optogenetics and allowed the precise manipulation of neuronal and non‐neuronal cells. This technique uses particular wavelengths of light to manipulate both neuronal and non‐neuronal cells [2, 5]. It has enabled the study of information processing in the brain and recent studies are looking into clinical translational applications of the technique [1]. Despite the advantages offered by optegenetics, it has the drawback of being invasive as light does not penetrate skin past a few millimeters. It is not possible to target deep tissue within the body using this technique and this limits the application in the context of diseases such as Parkinson’s [3] or heart malfunction [4].We are developing devices that can non‐invasively manipulate cells using a technique termed “sonogenetics”. This technique uses a combination of engineering cells to be more sensitive to mechanical stimuli as well as developing ultrasound transducers capable of stimulating cells in freely moving, awake mice. We demonstrate the development of miniature transducers made from non‐hysteretic single crystal lithium niobate to be used for the development of sonogenetics. In addition, we o er mathematical insights to the mechanism of action of ultrasound on neurons. Our analysis of membrane deflection enables us to predict cellular activity based on the applied ultrasound stimulus. By extension, we use this analytical framework to inform the development of transducers and stimulation parameters for achieving non‐invasive stimulation of cells.Support or Funding InformationWM Keck FoundationNational Institute of HealthMembrane Deflection and Capacitance Change due to Ultrasounda–d) Membrane deflection due to an ultrasound stimulus, with parameters 7 MHz and 1 MPa pressure. The stimulus is provided for 10 ms, the resulting area change(e) and the capacitance (f) are then calculated from the input parameters. The value of capacitance generated in this model is then used in a Hodgkin‐Huxley neuron model to determine action potential generation.Figure 1a) LN transducer housed in a MMCX coaxial connector designed for long term behavioral studies in awake, freely‐moving mice. b) Device mounted on a mouse skull to be used for characterization using an automated hydrophone setup (c). d)Pressure profile over the transducer face with a 450 mV input results in up to 2 MPa pressures. e) Transducer attached to mouse skull for long term behavioral studies.Figure 2

Design and Characterization of 3-Stack MEMS-Based Passive Flow Regulators for Implantable and Ambulatory Infusion Pumps

Passive implantable or portable infusion pumps comprise an energy source to pressurize a drug and a fluidic restriction to determine the delivery rate. MEMS technology enables the design of microfluidic chips that can passively regulate the flow rate and therefore limit the impact of pressure variations on flow accuracy. The device is a triple-stack structure made of silicon and borosilicate with valves associated in parallel. Flow regulation is obtained from the deflection of a silicon membrane that progressively obstructs the valves as the reservoir pressure increases. Samples dedicated to the infusion at 1 ml/h and 1 ml/day have been designed, manufactured and tested. Flow regulation in the pressure range 200–1000mbar was obtained, with an overall flow rate variability of +/−10% with respect to nominal targets. By comparison to commercial devices, these data showed a reduction of the flow variability up to a factor 2.4 and the lowering of the reservoir pressure by a factor 5. A passive flow regulator coupled with an active valve would match the flow control capabilities of the state-of-the-art programmable implantable pumps. Furthermore, these microfluidic chips could be adapted to disposable pumps to improve the flow accuracy during the infusion of potent drugs having short half-lives. [2019-0161]

Using of fast expansions in the construction of two-dimensional exact solutions of the Poisson equation

Using the fast expansion method, we obtained several exact solutions of the boundary value problem for the Poisson equation in a rectangular domain. We have given graphs of exact solutions corresponding to different boundary conditions and different types of the Poisson equation free term. We showed the influence of the type of boundary conditions and the right-hand side on the type of exact solution. We obtained a solution to the problem of membrane deflections under the action of variable load. We have given graphs of the stress components, from the analysis of which it follows that the greatest stress is in the middle of the rectangular membrane long sides.

Analysis of water wave interaction with a submerged fluid-filled semi-circular membrane breakwater

This study investigates the hydroelastic interaction between water waves and a submerged fluid-filled semi-circular membrane breakwater based on potential theory. An analytical solution for wave interaction with the membrane breakwater is developed. The series solutions for velocity potentials in the external and internal fluid domains of the breakwater are obtained using the multipole expansions and the separation of variables, respectively. The unknowns in the series solutions are determined by the boundary conditions on the surface and at the two ends of the semi-circular membrane. In addition, a numerical solution for wave interaction with a submerged fluid-filled circular-arc membrane breakwater is developed using the multi-domain boundary element method (BEM). In the numerical solution, the boundary condition on the membrane's surface is directly discretized by expressing the membrane deflection as an integral representation involving the unknown dynamic pressure jump across the membrane. The calculation results from the present analytical solution and the numerical solution are in good agreement. The present numerical results also show reasonable agreement with the numerical and experimental results in literature. Calculation examples are presented to examine the basic features of the hydrodynamic quantities (reflection and transmission coefficients, wave surface elevation and membrane deflection) for the fluid-filled membrane breakwater. Valuable results are given for the engineering design.

Modeling of a square-shape ZnO, ZnS and AlN membrane for mems capacitive pressure-sensor applications

In this paper, mathematical modeling and simulation of a MEMS-based clamped square-shape membrane for capacitive pressure sensors have been performed. Three types of membrane materials were investigated (i.e. Zinc Oxide (ZnO), Zinc Sulfide (ZnS) and Aluminum Nitride (AlN)). Various performance parameters such as capacitance changes, deflection, nonlinearity, the sensitivity of the membrane structure for different materials and film-thicknesses have been considered using the Finite Element Method (FEM) and analytically determined using the FORTRAN environment. The simulation model outperforms in terms of the effective capacitance value. The results show that the membrane deflection is linearly related to the applied pressure. The ZnS membrane provides a capacitance of 0.023 pico-Farad at 25 kPa with a 42.5% relative capacitance changes to reference capacitance. Additionally, the results show that for ZnO and AlN membranes the deflection with no thermal stress is higher than that with thermal stress. However, an opposite behavior for the ZnS membrane structure has been observed. The mechanical and capacitance sensitivities are affected by the membrane thickness as the capacitance changes are inversely proportional to the membrane thickness. Such results open possibilities to utilize various materials for pressure sensor applications by means of the capacitance-based detection technique.

Comparison of Point and Snow Load Deflections in Design and Analysis of Tensile Membrane Structures

Tensile membrane structures are often used as protective structures in order to provide cover from snow, rain, and direct sunlight. They are widely popular because of their advanced structural and architectural properties. Currently, their application is common at sport stadia and public spaces. There are several types of loads acting on tensile membrane structures, most importantly prestress, snow load, and wind load. However, concentrated loads also act on these structures, but they are frequently neglected during the structural analysis. There is yet no European standard on designing tensile membrane structures that would give guidance on structural analysis and incorporation of point load actions in the analysis. In addition, there is little scientific knowledge on how point loads affect tensile membrane structures. This research aims at revealing whether point loads can produce significant membrane deflections and in such way cause damage to the structure or to the objects underneath the membrane. In order to evaluate their importance, point load deflections are compared to deflections induced by snow load. This was done on a large number of numerical models differing in several parameters. Models represent typical geometries of hypar membrane structures on a square base. Obtained results show that, in many cases, point loads can produce larger membrane deflections compared to the snow load. This finding will have an impact on including the point load actions into standardization of design and analysis procedures of tensile membrane structures in Europe.

A Theoretical Study of Circular Orthotropic Membrane Under Concentrated Load: The Relation of Load and Deflection

In this study, the deformation of circular orthotropic membranes subjected to a central concentrated force is investigated. An orthotropic membrane equation indicating load-deflection behavior based on Foppl-von Karman membrane theory is obtained and the numerical solutions are gotten by using MATLAB. A variable k, which is the most influential parameter on the load-deflection behavior, is proposed. In isotropic membrane, the change of material parameters mainly influences the deflection of membranes subjected to a concentrated force; however, when studying for orthotropic membrane, the shape of membrane after deformation can be controlled by changing the value of xk. Only change in elastic modulus and Poisson's ratio, with k constant, mainly influence the deflection of curves, instead of the shape of curves. Then, four numerical simulations by ABAQUS are conducted and the membrane element M3D4R is used to set up a finite-element model. By comparing these simulation results with the solutions from orthotropic membrane equation, it is shown that the orthotropic membrane equation gives a good estimation of load-deflection behavior.

Determination of the viscous resistance of a plane damper with a newtonian fluid using the equation similarity with the shaft torsion problem

This paper describes the similarity between the Reynolds equation for a thin viscous layer of liquid in a plane damper and the commonly known equations of membrane deflections and equations of free torsion of a shaft. Based on the similarity of equations, a viscous resistance coefficient of a plane damper in the normal direction was determined. An approximate formula of the viscous friction coefficient in tangential direction was derived using the Couette flow assumption. The paper shows that acquiring the same viscous friction coefficients in the normal and tangential direction for a plane damper with a thin lubricating layer is not possible.

Transversal Otolithic Membrane Deflections Evoked by the Linear Accelerations

Considered is the model of the transversal utricle membrane deflections evoked by the linear accelerations. The basic idea underlying this consideration is that the linear accelerations can cause both longitudinal and transversal deformations when acting along the membrane in the buckling way. The real 3D utricle membrane structure was simplified by considering its middle section and evaluating its elastic properties in 2D space. The steady state transversal deflections along the membrane are analytically evaluated and numerically simulated using the 2D elasticity theory. The transversal deflections are found to be more expressive and stronger as compared to the conventional longitudinal deformations. The maxima of longitudinal deformations and transversal deflections are observable in different regions of the utricle membrane. The revealed properties could be used for explanation of the transduction processes in the otolith organ. Based on the implemented modeling approach the new otolithic membrane mechanical properties are discussed and new explanations for the available experimental data are given.

Wave energy dissipation of a submerged horizontal flexible porous membrane under oblique wave interaction

An analytical model associated with oblique wave interaction with a submerged horizontal flexible porous membrane is presented under the assumption of linearized small amplitude and structural response in finite water depth. The expansion formula associated with Green's functions using fundamental source potentials based on reduced wave equation is derived. Further, a physical problem of oblique wave interaction with a moored finite horizontal submerged flexible porous membrane on wave energy dissipation is illustrated to analyse the different design parameter based on matched eigenfunction expansion method. The roots of the complex dispersion relation are obtained by applying a perturbation scheme and the accuracy of the numerical computation is demonstrated by analysing the convergence of reflection, transmission, and dissipation coefficients for different spring stiffness and porous-effect parameters. Further, the correctness of the present solution is checked by validating against analytical, numerical boundary element method, and experimental data available in the literature. The effects of spring stiffness, porous-effect parameter, submergence depth, structural length, angle of incidence, and flow pattern on reflection, transmission, dissipation coefficients, membrane deflection, vertical force, and contour plots are analysed. The present analysis on different design parameters will be helpful for better understanding for engineers to design as an effective breakwater/wave absorber.

Accuracy of Föppl–von Karman membrane theory for determining elastic constants of monolayer graphene

For interpreting results of an indentation test on a single-layer graphene sheet (SLGS), it is frequently modeled as an elastic, isotropic, and homogeneous membrane. With a small thickness (∼10−10 m) as compared to a characteristic length (∼10−6 m) of specimens used in experiments, the non-dimensional von-Karman factor (vKf ∼ 108) for a SLGS predicts negligible flexural rigidity (D ∼ 10−19 Nm). Since the membrane undergoes large deformations under a small force, a direct relationship between the resulting force-displacement curves and elasticities of the graphene sheet is still elusive. Here we compare predicted load-displacement curves for nanoindentation of a SLGS by using a full non-linear theory with St. Venant–Kirchhoff material, and the Föppl–von Karman nonlinear equations with a Hookean material. The nonlinear governing equations in each formulation are numerically integrated by the shooting method. Even though the radial variations of the membrane deflections computed with the two theories differ by at most 1.5%, the stresses, the declination angles, the curvatures and the strain energy densities may reach differences as high as 6.4%, 7.4%, 70% and 25%, respectively. These differences are significant enough to reexamine using the FvK derived solutions to find elastic constants from the test data.

A fast electrochemical actuator in the non-explosive regime

Microfluidic systems require a compact, energy-efficient and microtechnology-compatible actuator that pushes the liquid through the channels. Electrochemical devices are promising candidates, but they suffer from a long response time due to slow gas recombination. An actuator with a millisecond response time was demonstrated recently. A micron-sized chamber of the device with two titanium electrodes is sealed by a polydimethylsiloxane membrane. A series of microsecond voltage pulses of alternating polarity is applied to the electrodes. Nanobubbles generated in the chamber push the membrane up, but disappear quickly due to spontaneous combustion of hydrogen and oxygen. In this work, operation of the device is investigated in detail. The pulses with a frequency from 100 to 500 kHz are used for actuation. It is demonstrated that higher frequency and higher amplitude of the pulses provide larger deflection of the membrane, but finally the deflection is saturated. The stroke of 8–9 µm can be achieved. In a cyclic operation regime the actuator is driven by series of pulses. If the time interval between the series is too short, the gas accumulates in the chamber. The membrane lifts during several cycles and then oscillates in the lifted position. In this regime the operating frequency as high as several hundred hertz can be achieved. The higher the frequency, the higher is the lift. The stroke also increases with the frequency, making a higher value more beneficial. Destruction of the electrodes is not observed, but the oxidation of titanium with time suppresses the gas production and decreases the membrane deflection. At a high frequency of the pulses the oxidation goes slower, but still significantly affects the performance. The oxidation of the electrodes is recognized as the main problem of the device. Methods to solve the problem are proposed.

Optimized Design of CMUT with Hexagonal Membranes

A Capacitive Micro-machined Ultrasonic Transducer (CMUT) with hexagonal membrane is constructed to work as a transmitter and compared to a CMUT with circular membrane. In this paper, three desirable combination of circular and hexagon are analyzed to select the dimensions for hexagonal shaped CMUT. Capacitive Micro-machined Ultrasonic Transducer (CMUT) is a micro constructed transducer used both as transmitter for generating ultrasonic waves and as receiver to modulate the electrical capacitance of the capacitive transducer. It can be fabricated with many geometries especially circular, square, rectangular, and hexagon. Circular CMUTs offers optimum performance in terms of deflection with DC, deflection of biased membrane with AC bias, resonant frequency, capacitance and deflection along frequency but for array formation the wafer area is wasted. A CMUT with hexagonal membrane gives an ultrasonic signal of constant amplitude with less deflection of membrane within the cavity and the outside environment. Stationary analysis is carried out with electro-mechanics for discussing the capacitance change of CMUT. The collapse or pull in voltage of hexagon CMUT is found to be high and increases the bandwidth of CMUT. The absolute percent difference of resonant frequency is observed to be 2.3 % with dimensions selected from the COH configuration of the CMUT.

A Flexible Membrane Breakwater with a Piezoelectric Layer for Providing Harborage and Wave-Energy Conversion

Liu, C. and Huang, Z., 2020. A flexible membrane breakwater with a piezoelectric layer for providing harborage and wave-energy conversion. Journal of Coastal Research, 36(1), 148–156. Coconut Creek (Florida), ISSN 0749-0208.Integration of wave-energy converters with coastal structures provides a way to make wave-energy utilization economically viable. This theoretical study examines a piezoelectric membrane system that serves as a breakwater and a wave-energy harvester. The system is in the form of a piezoelectric layer built into a flexible membrane wave barrier. Series resistor-inductor-capacitor electric circuits are used to obtain electrical output power from ocean waves through the piezoelectric layer. This type of piezoelectric membrane system is proposed for providing harborage and wave-energy extraction at marinas and small boat harbors. Use of an eigenfunction expansion method, solutions to the wave-scattering problem, the calculation of the deflection of the piezoelectric membrane, and an analytical expression for the electric-power output per unit surface area of the piezoelectric layer (output power density) are described. The output power density can reach its maximum value at an optimum resistance, which increases with the thickness and surface area of the piezoelectric layer and decreases with wave frequency. At the optimum resistance, the maximum power output density and the minimum transmission coefficient occur at the same critical frequency, which is controlled by the dimensions and initial tension of the piezoelectric membrane. The surface area and the inductance of the piezoelectric layer have little effect on the output power density, which increases with the thickness of piezoelectric layer nearly linearly.

An electromagnetic micro-actuator with PDMS-Fe3O4 nanocomposite magnetic membrane

Polydimethylsiloxane-Fe3O4 nanocomposite is introduced as a competent magnetic material to utilize in the magnetic membrane micro-actuators, for first time in this paper. Using this magnetic composite, two types of electromagnetic micro-actuators are presented in this paper: unidirectional micro-actuator and bidirectional micro-actuator. In all the other similar micro-actuators already proposed in the literature, a unidirectional actuating mechanism has been used where there is no control on the return time of the membrane and where the return time is very long. To solve this problem, a bidirectional micro-actuator is proposed in the present article, where the return time of the magnetic membrane can be controlled as well as the forward time. Using this micro-actuator, we achieved a favorable membrane deflection of 8 μm in merely 2 s (compared to the deflections of 9.16 and 12.87 μm in 60s, reported by the recent papers) as well as a considerable displacement of 66 μm in 20 s. In our proposed micro-actuator, the stress and strain developed in the magnetic membrane (at identical displacements) are far less than those developed in a unidirectional micro-actuator, an advantage that would increase the life of the magnetic membrane. The effective parameters on the performance of the magnetic nanocomposite micro-actuator including the number of coil turns, electric current, concentration of Fe3O4 nanoparticles, and the spacer thickness were also investigated.

Design and Analysis of Capacitive Micromachined Ultrasonic Transducer

Background:Objective:To simulate a Micromechanical systems (MEMS) based CMUT working as a transmitter with the existing design and provide comparison within the possible architectural geometries.Methods:FEM simulation software COMSOL is used to simulate the 3D model of the transducer radiating in the air. The classical thin-plate theory is employed to solve for CMUT with a circular shape which is sufficient when the ratio of the diameter to thickness of the plate is very large, an aspect common in CMUTs. The Galerkin-weighted residual technique is used to get a solution for thin plate equation with the presumption that the deflections are small in comparison to the thickness of the plate.Results:The resonant frequency of CMUT with different geometries have been calculated. The deflection of membrane with applied DC bias is shown along with collapse voltage calculation. The generated ultrasound is shown with the AC bias superimposed on the DC bias. The capacitance change with the increasing DC voltage is discussed. The deflection of membrane is maximum as the resonance frequency is proved.Conclusion:The review of Capacitive Micromachined Ultrasonic Transducer architectures with different shapes is highlighted. The working behavior of CMUT with suitable dimension is simulated in 3D providing researcher data to wisely choose the CMUT prior to the fabrication. The CMUT is prioritized on various characteristics like wafer area utilization, deflection percentage within the cavity and durability of the transducer.