We propose a planar hydrogel-based micro-valve design which is modeled as a library element for Matlab Simulink. For this test case, a pressure pump (voltage source) in series with a micro-valve model (variable fluidic resistance) is built up. The micro-valve subsystem is separated in four main parts. Based on the applied temperature stimulus, the equilibrium length is determined according to an experimentally verified fit function. Furthermore, the equilibrium length considers a static hysteresis effect which is modeled in analogy to the saturation of magnetization in electric transformers. In a second step, the transient behavior follows a first order differential equation, but the cooperate diffusion coefficient is size dependent affecting the rise time of the system. This causes a faster swelling than deswelling of the hydrogel. In the third section, the stiffness property is implemented to calculate the maximum sealing pressure and the resulting gap between the hydrogel and the wall. The fluidic resistance of the micro-valve considers a three-dimensional geometry and is calculated based on a look-up table, extracted from a fluid-structure-interaction (FSI) model generated from a finite element structure. The proposed model allows a full description of the fluidic hydrogel-based micro-valve and is part of an upcoming microfluidic toolbox for Matlab Simulink containing passive elements and optional chemical reactions like mixing fluids and enzyme reactions for future applications.

We present a mathematical model to guide and interpret ongoing Cell-in-Gel experiments, where isolated cardiac myocytes are embedded in a constraining viscoelastic hydrogel, to study mechano-chemo-transduction mechanisms at the single cell level. A recently developed mathematical model, based on the elastic Eshelby inclusion problem, is here extended to account for viscoelasticity of the inclusion (cell) and the matrix (gel). This provides a tool to calculate time-dependent 3D stress and strain fields of a single myocyte contracting periodically inside a viscoelastic matrix, which is used to explore the sensitivity of the cell’s mechanical response to constitutive properties and geometry. A parametric study indicates that increased gel crosslink concentration significantly alters the strain and stress fields inside the cell and creates an increased time-lag in the mechanical response of the cell during contraction. It is also found that autoregulation at the cellular level in response to afterload, potentially in the form of increased cell stiffness, has a strong influence on cell contraction.

This paper presents the design, fabrication, and operation of a chemo-mechatronic system that changes its geometry and electrical functionality in the presence of specific chemical signals. To accomplish this, we integrated a protein hydrogel with an aluminum substrate and flexible circuit in a low-profile laminate. To demonstrate the concept, we have built and tested a sensor that lights an LED when actuated in the presence of polyethylene glycol (PEG).

We propose an improved micro reactor design for a scalable microfluidic device, in which enzymes are immobilized in a hydrogel matrix. Furthermore, fluid flow is controlled by means of hydrogel-based micro-valves. In this work, computational flow simulations will be compared to experimental results to highlight new design ideas and to improve wetting and concentration distribution through the entire chamber volume, even for high aspect ratios. Additionally, modelling concepts will be introduced to efficiently describe multi-domain problems like enzyme reactions. With the help of a computer-aided design process which is capable to simulate hydrogel-based microfluidic systems it is possible to better understand, predict and visualize the behavior of micro-reactors and support the development of highly integrated hydrogel-based microfluidic circuits.

Photochemical actuation systems, those that employ coupled photo-stimuli and chemical reactions to power and control mechanical motion, have the potential to combine the benefits of precise light driven control with chemical energy storage. Furthermore, these systems are inherently soft, making them ideal for use in the emerging field of soft robotics. However, such systems have received comparatively little attention, perhaps due to the poor cycle life and limited activation time of past systems. Here we address these two challenges by switching from the technique of past systems, that of aqueous photoacid solutions and pH-responsive hydrogel actuators, to one employing organic solvents instead. While this switch of solvents successfully eliminates cycle life constraints and allows for tuning of the activation recovery time it also shifts the relative activation point of the hydrogel actuator in such a way that actuation is no longer observed. Several options for addressing this are discussed, with the prospect of using the lessons learned within to make a more informed selection of a different photoacid compound considered the most feasible. While the exploration of photochemical actuation systems is still in a nascent stage, we have great hope for such systems to form the basis of future smart machines with unique functionality.

We propose a finite element model which describes the dynamic behavior of hydrogels for step-responses and quasi-static regimes. The material properties are implemented in a fluid structure interaction (FSI) model which simulates the swelling behavior of hydrogels within a micro-valve. The resulting volume change effects the fluid domain describing the mass-flow behavior of the micro-valve. Furthermore, the concept is implemented in a high-level circuit and flow chart model to efficiently predict the response behavior of hydrogel-based micro-valves. With these tools a foundation is set to efficiently simulate microfluidic systems with the aim to develop a fully computer-aided design process. The presented method will help to better understand, predict and visualize the behavior of hydrogels and support the development of highly integrated hydrogel-based microfluidic circuits.

Micro-valves play an important role in controlling and operating microfluidic systems. Utilizing stimuli-sensitive hydrogels facilitates the construction of smart micro-valves controlled by temperature, concentration (salt, organic solvent) or pH level. We propose a finite element model which uses the thermal domain as an auxiliary domain for the volume change response of hydrogels. Behaviors like local displacements within the hydrogel are difficult to measure, but can be reproduced with finite elements. For the application of the micro-valve, the hydrogel model is connected to the fluid domain. The hydrogel is placed directly into the fluid flow and opens or closes the flow path. For this, a full iterative cycle with material properties and remeshing in each simulation step is implemented in ANSYS ® . This model concept and the results will help to better understand, predict and visualize the behavior of hydrogels and support the development of highly integrated hydrogel-based microfluidic circuits.

Embedded piezoelectric energy harvesting (PEH) systems in medical pacemakers have been an attractive and well visited research area. These systems typically utilize different configurations of beam structures with forcing originating from heart beat oscillations. The goal of these systems is to remove the pacemaker battery, which makes up 60–80% of the device volume, and replace it with a self-reliant power option. With emerging technologies encouraging a push towards leadless pacemakers typical energy harvesting beam structures are becoming inherently coupled with the heart system. The introduction of the nonlinearity resulting from the bistable magnetic interaction of two magnets is known to enhance energy harvesting performance due to its double-well potential behavior. Introducing the elastic magnifier enables large tip oscillations and high energy orbits for the bistable system. A continuous nonlinear model is derived for the bistable system (BPEH) and a one-degree-of-freedom linear mass-spring-damper model is derived for the elastic magnifier. The elastic magnifier (EM) will not consider the damping negligible due to the viscous nature of the heart, unlike most models. For experimental testing a physical model was created for the bistable structure and fashioned to an elastic magnifier. A hydrogel was chosen as the physical model for the EM. Experimental results have shown that the bistable piezoelectric energy harvester coupled with a linear elastic magnifier (BPEH+LEM) produces more power at certain input frequencies and operates a larger bandwidth than a PEH, BPEH, and a standard piezoelectric energy harvester with the elastic magnifier (PEH+LEM). Numerical simulations were validated by these results showing that this system enters high-energy and high orbit oscillations. It has been shown that BPEH systems implemented in medical pacemakers can have enhanced performance if positioned over the myocardial heart wall.

A new equivalent circuit is presented, which describes the transport of a chemical solution with a certain concentration in a fluidic channel. Channels are basic parts of a microfluidic systems and the concentration of the chemical solution can control the opening and closing of valves based on smart hydrogels. This type of microfluidic systems facilitates the autonomous control of fluid flow, e.g. in chemo-fluidic oscillators. Through this channel, the solution is transported at a velocity determined by the flow rate through the channel and its cross section. While the volumetric flow is not delayed in an ideal channel, the channel acts as delay line for the particles and thus for a certain concentration transport through the channel. In this setting, the transport of the dissolved chemical by water traveling along the delay channel can be described by the one-dimensional transport equation. In order to derive the equivalent circuit, the transport equation is numerically approximated based on the well-known Method of Lines. This method consists in approximating the original PDE via a large system of ODEs. The ODEs are obtained by discretizing the PDE in space, in such a way that each component of the resulting system of ODEs approximates the solution of the PDE at some grid point along the spatial interval. Once the system of ODEs has been constructed, a flow and a difference quantity can be defined and the ODEs interpreted as finite network elements. Since the equations are isomorphic to electrical ODEs of electrical network elements, the fluidic channel can be expressed by an equivalent circuit. Thus the transient behavior of the transport mechanism can be calculated using a circuit simulator as part of a design automation. Simulation results are presented.

Smart hydrogel micro-valves are essential components of micro-chemo-mechanical fluid systems. These valves show a transistor-like behavior and are based on phase-changeable polymers. They can open and close micro-fluidic channels depending on chemical concentrations in the fluid. These highly complex systems are challenging to engineer and their development will advance faster if proper simulations take place beforehand. A concept of how to simulate concentration-triggered, phase-changeable hydrogels is proposed. A simplified flow simulations will be presented to demonstrate the feasibility of this approach and to highlight geometrical problems. Based on the results, structurally more advanced models will be introduced with implemented multi-field solver interactions including thermal, mechanical and fluidic domains. The results of these models show the closing behavior of a micro-valve. The computed parameters of such valves are implemented into a circuit representation, which is capable of efficiently computing large scale micro-fluidic systems using an electric circuit simulator. These methods will help to predict, visualize and understand polymeric swelling behavior and demonstrate the performance of large-scale chip applications before any complex experiment is performed.

Hydrogels consist of a network of cross-linked polymers that swell when put into water. For temperature-sensitive smart hydrogels the equilibrium hydrogel size depends on the temperature of the liquid. These hydrogels are used to build temperature-controlled fluidic valves. Here we present an equivalent circuit model of such a hydrogel valve. The transient behavior is based on the model by Tanaka with three additional assumptions: 1. Only the fundamental mode of the deformation field, i.e. the slowest-decaying exponential temporal behavior, is relevant. 2. There are distinct equilibrium sizes for the swollen and the de-swollen state. 3. As observed in experiment, the swollen gel and the de-swollen gel have different elastic moduli, which affect the time constants of swelling vs. de-swelling. The resulting network model includes three physical subsystems: the thermal subsystem, the polymeric subsystem and the fluidic subsystem. The thermal subsystem considers the temperature of the heater, of the adhesive and of the hydrogel. It is assumed that adhesive, housing and hydrogel act as heat capacities in combination with heat resistors. The modeled polymeric subsystem causes in addition time delays for swelling and de-swelling of first order with different delay constants. The fluidic subsystem basically includes the fluidic channel between hydrogel and housing with time varying cross section, which is modeled as controlled source. All subsystems are described and coupled within one single circuit. Thus the transient behavior of the hydrogel can be calculated using a circuit simulator. Simulation results for an assumed hydrogel setup are presented.

The hair cell is a biological sensor that uses microscopic hair-like structures to detect delicate motions of surrounding fluid. Inspired by this principle, we have created an artificial hair cell (AHC) sensory method based on biomolecular transduction for sensing spatial variations in air flow. The key feature of this method is the use of one-dimensional arrays built from modular AHC units which measure local velocity at different points in a flow profile. Each of the AHC units uses thinly extruded glass fibers as mechanical receptors of air velocity. Hair vibrations are converted to current via hydrogel-supported lipid bilayer membranes through their mechanocapacitive properties. Preliminary tests with linear arrays of three AHC units attempt to measure the air source profile with varying position and intensity. Each unit was fabricated with a hair of different length, giving it a unique vibrational response. This technique was inspired by how organisms use hair cells with tuned responses to mechanically process flow stimuli. A significant challenge in processing the sensors’ output was the limitation of one input channel on the current measurement unit, thus each sensor output had to be sent over the same channel. When several AHC units are excited simultaneously by an airflow, the resulting signal is a superposition of each sensor’s individual response. To separate the signals back into their individual measurements, the Hair Frequency Response Decomposition method is developed, which maps the spectral content of a combined output to the location of excitation in the array. This method takes advantage of the AHC’s high signal-to-noise ratio (compared to other membrane-based AHCs) and linear output response to flow velocity. Results show that the bilayers’ consistent spectral responses allow for an accurate localization of sensor excitation within the array. However, temporal variations in bilayer size affect sensitivity properties and make accurate flow velocity estimation difficult. Nevertheless, under stable bilayer conditions the measured velocity profiles matched closely with theoretical predictions. The implementation of the array sensing method demonstrates the sensory capability of bilayer-based AHC arrays, but highlights the difficulties of achieving consistent performance with bio-molecular materials.

In this work, we present a process for the fabrication of meso-scale hydrogel-based lipid bilayer arrays. The hydrogels support lipid monolayers at an oil-water interface, and when brought together, form stable bilayers. The substrates are formed using 3D printed molds and include built-in, customizable circuits patterned with silver paint. The system can be adapted to varying network sizes and circuit designs, and new arrays are fabricated quickly and inexpensively using common laboratory techniques. An enclosed 3×3 array with 3 mm spacing between neighboring hydrogels and electrodes to individually examine each bilayer has been created using this method. An alternative test setup was also developed to better observe the formation of bilayers in a small array. Using this setup, two bilayers were formed simultaneously, demonstrating the feasibility of this type of system and providing valuable information for expanding and improving the enclosed network. Many of the design concepts presented here can be adapted for use at smaller scales using microfabrication techniques.

A fully hydrogel-supported, artificial hair cell (AHC) sensor based on bilayer membrane mechanotransduction is designed with sensitivity and versatility in mind. Thanks to fabrication improvements from previous generations, the sensor demonstrates peak current outputs in the nanoamp range and can clearly measure inputs as high as 2k Hz. Characterization of the AHC response to base excitation and air pulses show that membrane current oscillates with the first three bending modes of the hair. Output magnitudes reflect of vibrations near the base of the hair. A 2 DOF Rayleigh-Ritz approximation of the system dynamics yields estimates of 19 N/m and 0.0011 Nm/rad for the equivalent linear and torsional stiffness of the hair’s hydrogel base, although double modes suggest non-symmetry in the gel’s linear stiffness. The sensor output scales linearly with applied voltage (1.79 pA/V), avoiding a higher-order dependence on electrowetting effects. The free vibration amplitude of the sensor also increases in a linear fashion with applied airflow pressure (18.4 pA/psi). Based on these sensitivity characteristics, an array sensing strategy for these sensors is proposed.

This paper presents the results of our fully coupled, two-dimensional (2D) simulation of the swelling behavior of glucose-sensitive hydrogels at a constant glucose level with change in the surrounding pH. The model consists of a system of glucose-sensitive hydrogel and ionic fluid as a solvent. The hydrogel consists of two enzymes: glucose-oxidase and catalase, which are immobilized on the polymeric network. The surrounding solvent has certain level of glucose. The diffusion of glucose from a solvent and its reaction within the hydrogel are simulated using the Nernst-Planck equation. The local electrical charge is calculated by the Poisson’s equation, and deformation of the hydrogel is determined by the mechanical field equation. These equations are fully coupled and simulations are performed for varying pH and glucose concentrations. The glucose concentration was taken at 7.7mM (140mg/mL) and the pH is varied from 6.8 to 7.4. As glucose reacts with oxygen, gluconic acid is produced in the presence of glucose-oxidase. The formation of gluconic acid within the gel results in protonation and thereby causes the hydrogel expansion. The glucose level in the surrounding solution limits diffusion in the hydrogel. As the surrounding solution pH increases the available fixed charged for ionization increases, which results in an increase in maximum equilibrium swelling and gluconic acid as a product of the reaction. The gluconic acid production was found to be proportional to the change in pH. The gluconic acid decreases the internal pH of the hydrogel, which ultimately reduced the deformation of the gel.

An artificial hair cell sensor imitates the function of cilia in natural hair cells in order to detect surrounding fluid displacement. Here, a novel structure for creating artificial hair cell sensors uses established methods of creating lipid bilayers at the interfaces of millimeter scale hydrogel shapes. This paper describes the fabrication of the sensor components and the manner in which they are assembled and tested. The hair’s vibration can be detected by monitoring changes in the current produced by mechanical fluctuations in the bilayer. The cross-sectional geometry of the hair can be changed to enable directional sensitivity. Spectral analysis of the sensor current response indicates that frequencies and magnitudes change when a flattened hair is excited in different directions. Finally, the sensor is shown to become more sensitive with applied potential across the bilayer. Results agree with similar studies on this phenomenon.

We present our simulation results of swelling responses of the pH-sensitive, 3D-arbitarary-geometry hydrogel in steady state conditions. The swelling responses of the hydrogels to the changes in environmental stimuli such as solution pH are discussed. The finite element simulation uses three nonlinear partial-differential equations for responsible physical phenomena namely- chemical for ionic transport across the hydrogel, electrical for local electric charge balance within hydrogel, and mechanical for expansion of the hydrogel by the Nernst-Planck, the Poisson’s, and the mechanical field equations respectively. In the case of pH-sensitive hydrogel, material properties such as modulus of elasticity and Poisson’s ratio changes with a change in surrounding environments. Finite element analysis used for present study was carried out by full coupling of above three partial-differential equations with variable material properties. Employing a moving mesh method for 3D geometry, the FEM simulation was performed to account for large-swelling of the pH-sensitive hydrogel. This highly nonlinear and computationally intensive simulation was performed using multicore parallel-processing computer. The simulation results using above mentioned strategy has been validated for 2D geometry and results are in agreement with other published experimental results.

One of the most common sensory structures in nature is the hair cell. Examples of hair cells include the inner and outer hair cells in the inner ears of vertebrates, external sensory hairs on the legs of spiders, and neuromasts found along the lateral lines of fish. Recent work by Sarles and Leo demonstrated that self-assembly methods could be used to construct a membrane-based hair cell that responds to a physical disturbance of the hair. An artificial cell membrane (or lipid bilayer) formed at the interface of two lipid-encased hydrogel volumes, serves as the transduction element in the device. In this study, a revised sensor embodiment is presented in which the hair is fixed at its base by the encapsulating polymeric substrate. In addition, a highly elastic, photo-polymerizable aqueous gel (PEGDA, 6000g/mole) is used to further increase the resiliency of the hair and to provide a compliant cushion for the bilayer. These changes yield a considerably more durable hair cell sensor. We perform a series of experimental tests to characterize the transduction element (i.e. the bilayer) and the sensing current produced by free vibration of the hair, and we study the directional sensitivity of this hair cell embodiment by perturbing the hair in three directions. These tests demonstrate that the magnitude of the sensing current (30–300pA) is significantly affected by direction of perturbation, where the largest signals result from motion of the hair in a direction perpendicular to the plane of the bilayer.

Recent research in our group has shown that artificial cell membranes formed at the base of a hair-like structure can be used to sense air flow in a manner similar to the mechanotransduction processes found in mammalian hair cells. Our previous work demonstrated that a single artificial hair cell can be formed in an open substrate. However, that study also motivated the need to develop fully-encapsulated devices that feature arrays of hair-cells. Since the transduction element in this concept is an artificial cell membrane, or lipid bilayer, this work investigates two parallel substrate designs for providing encapsulation and a method for forming arrays of bilayers. In one effort, a flexible substrate with internal compartments for hosting the biomolecules and mating cap are constructed and experimentally characterized. The regulated attachment method (RAM) is used to form interface bilayers within the sealed device. Capacitance measurements of the sealed interface bilayer show that the sealing cap slightly compresses the bottom insert and reduces the size of the enclosed bilayer. Single channel measurements of alamethicin peptides further verify that the sealed device, which is also leak-proof under water, can be used to detect the insertion and gating activity of transmembrane proteins in the membrane. The second effort pursued herein is the fabrication and initial testing of a method to form arrays of interface bilayers by using anchored hydrogel pads that support curved aqueous lenses in oil. In this fashion, the configuration of the array does not require manipulating droplets, but instead depends on the arrangement of the built-in gels used to support the aqueous lenses. As with RAM, mechanical force is used to promote contact of adjacent aqueous lenses held in the flexible substrate. Initial tests show that gel-supported lenses can be used for forming multiple lipid bilayers within the device and that these interfaces can be interrogated individually or collectively using an electrode switching circuit.

This study involved the development and characterization of novel porous, non-permeable, and conductive hydrogels. The hydrogels were fabricated with HEMA and crosslinked with PEGDA through a complete parametric study of the synthesis parameters which included water content and crosslinking content. The hydrogels were fabricated using UV photopolymerization and in situ polymerization of PPy, and characterization was conducted with respect to their physical, thermal, mechanical, and electrical properties. The physical properties were analyzed with respect to their swelling ratio and equilibrium water content. The thermal properties were analyzed based on the decomposition temperature and residue weight. The mechanical properties examined the elastic modulus of the hydrogels, and the electrical properties investigated the conductivity of the hydrogels. The relationships observed between the processing, structure, and resulting properties provide the basis for further development and application of these porous, non-permeable, and conductive hydrogels.