Fick's second law transformed: one path to cloaking in mass diffusion

Mass Diffusion Metamaterials with "Plug and Switch" Modules for Ion Cloaking, Concentrating, and Selection: Design and Experiments

The outstanding abilities of metamaterials to manipulate physical fields are extensively studied in both wave-based and diffusion-based fields. However, mass diffusion metamaterials, with the ability to manipulate diffusion with practical applications associated with chemical and biochemical engineering, have not yet been experimentally demonstrated. In this work, ion cloaking, concentrating, and selection in liquid solvents are verified by both simulations and experiments, and the concept of a "plug and switch" metamaterial is proposed based on scattering cancellation (SC) to achieve switchable functions by plugging modularized functional units into a functional motherboard. Plugging in any module barely affects the environmental diffusion field, but the module choice impacts different diffusion behaviors in the central region. Cloaking strictly hinds ion diffusion, and concentrating increase diffusion flux, while cytomembrane-like ion selection permits the entrance of some ions but blocks others. In addition, these functions are demonstrated in special applications like the catalytic enhancement by the concentrator and the protein protection by the ion selector. This work not only experimentally demonstrates the effective manipulation of mass diffusion by metamaterials, but also shows that the "plug and switch" design is extensible and reconfigurable. It facilitates novel applications including sustained drug release, catalytic enhancement, bioinspired cytomembranes, etc.

Fast active thermal cloaking through PDE-constrained optimization and reduced-order modelling

In this paper, we show how to efficiently achieve thermal cloaking from a computational standpoint in several virtual scenarios by controlling a distribution of active heat sources. We frame this problem in the setting of PDE-constrained optimization, where the reference field is the solution of the time-dependent heat equation in the absence of the object to cloak. The optimal control problem then aims at actuating the space–time control field so that the thermal field outside the obstacle is indistinguishable from the reference field. In particular, we consider multiple scenarios where material’s thermal diffusivity, source intensity and obstacle’s temperature are allowed to vary within a user-defined range. To tackle the thermal cloaking problem in a rapid and reliable way, we rely on a parametrized reduced order model built through the reduced basis method, thus entailing huge computational speedups compared with a high-fidelity, full-order model exploiting the finite-element method while dealing both with complex target shapes and disconnected control domains.

Thermal Cloak: Theory, Experiment and Application

In the past two decades, owing to the development of metamaterials and the theoretical tools of transformation optics and the scattering cancellation method, a plethora of unprecedented functional devices, especially invisibility cloaks, have been experimentally demonstrated in various fields, e.g., electromagnetics, acoustics, and thermodynamics. Since the first thermal cloak was theoretically reported in 2008 and experimentally demonstrated in 2012, great progress has been made in both theory and experiment. In this review, we report the recent advances in thermal cloaks, including the theoretical designs, experimental realizations, and potential applications. The three areas are classified according to the different mechanisms of heat transfer, namely, thermal conduction, thermal convection, and thermal radiation. We also provide an outlook toward the challenges and future directions in this fascinating area.

Optimized lattice-based metamaterials for elastostatic cloaking

An optimization-based approach is proposed to design elastostatic cloaking devices in two-dimensional (2D) lattices. Given an elastic lattice with a defect, i.e. a circular or elliptical hole, a small region (cloak) around the hole is designed to hide the effect of the hole on the elastostatic response of the lattice. Inspired by the direct lattice transformation approach to elastostatic cloaking in 2D lattices, the lattice nodal positions in the design region are obtained using a coordinate transformation of the reference (undisturbed) lattice nodes. Subsequently, additional connectivity (i.e. a ground structure) is defined in the design region and the stiffness properties of these elements are optimized to mimic the global stiffness characteristics of the reference lattice. A weighted least-squares objective function is proposed, where the weights have a physical interpretation—they are the design-dependent coefficients of the design lattice stiffness matrix. The formulation leads to a convex objective function that does not require a solution to an additional adjoint system. Optimization-based cloaks are designed considering uniaxial tension in multiple directions and are shown to exhibit approximate elastostatic cloaking, not only when subjected to the boundary conditions they were designed for but also for uniaxial tension in directions not used in design and for shear loading.

Active thermal cloaking and mimicking

We present an active cloaking method for the parabolic heat (and mass or light diffusion) equation that can hide both objects and sources. By active, we mean that it relies on designing monopole and dipole heat source distributions on the boundary of the region to be cloaked. The same technique can be used to make a source or an object look like a different one to an observer outside the cloaked region, from the perspective of thermal measurements. Our results assume a homogeneous isotropic bulk medium and require knowledge of the source to cloak or mimic, but are in most cases independent of the object to cloak.

Geometric phase and bilayer cloak in macroscopic particle-diffusion systems

Particle diffusion is a fundamental process in various systems, so its effective manipulation is crucially important. For this purpose, here we design a basic structure composed of two moving rings with equal-but-opposite velocities and a stationary intermediate layer, which can realize multiple functions to control particle diffusion. On the one hand, the intermediate layer allows particle exchange between the two moving rings, which gives birth to an exceptional point of velocity. As a result, a geometric phase appears for a loop evolution of velocity containing the exceptional point. On the other hand, the two moving rings also enhance the effective diffusivity of the intermediate layer, which helps design a bilayer particle-diffusion cloak. The present cloak only requires homogeneous parameters and simple structures, and meanwhile, its on and off can be flexibly controlled by velocity. These results broaden the scope of geometric phase and provide hints for designing particle-diffusion metamaterials.

Chemical cloaking

Hiding an object in a chemical gradient requires one to suppress the distortions it would naturally cause on it. To do so, we propose a strategy based on coating the object with a chemical reaction-diffusion network which can act as an active cloaking device. By controlling the concentration of some species in its immediate surrounding, the chemical reactions redirect the gradient as if the object was not there. We also show that a substantial fraction of the energy required to cloak can be extracted from the chemical gradient itself.

Optimization and Analysis of Acid Treated Trimethylamine using Surface Response and Gas Chromatography Analytical Methods

Background:

Trimethylamine (TMA) is a nitrogenous base aliphatic organic compound accounting for the odor of rotten fish and it is used as an indicator for analyzing the quality of fish products.

Introduction:

Extraction procedures and analytical methods including colorimetric and Gas- Chromatography (GC) can quantify the TMA contents of fish products after pre-treatment with basic solutions. However, the extraction procedure and analytical methods for acid-treated samples are not known, despite the majority of fish products being preserved using acid preservatives.

Methods:

The methodologies used included solid-phase micro-extraction of TMA followed by its quantification by a GC-based analytical method. An analysis of response surface methodology was also conducted to verify the optimum conditions for TMA detection in acid-treated liquid samples affected by factors including trapping time, temperature, and stirring speed.

Results:

The results obtained from this study showed that the optimum conditions for the best yield of TMA extraction are 20 min of trapping, emission at 55°C, and stirring at 400 rpm. The validation of the developed method was carried out using rotten fish after acid treatment. Acid treatment decreased TMA by up to 73.01%, however, when adding NaOH solution of the same volume to the samples, TMA increased similar to the control group.

Conclusion:

Here, we report a simple, sensitive, and rapid extraction procedure. A GC-based analytical method was developed for the analysis of TMA from the acid-treated sample. The developed extraction procedure and analytical methods were optimized and validated, which could be helpful for the extraction of TMA without damaging the sample.

Tailoring drug release rates in hydrogel-based therapeutic delivery applications using graphene oxide

Graphene oxide (GO) is increasingly used for controlling mass diffusion in hydrogel-based drug delivery applications. On the macro-scale, the density of GO in the hydrogel is a critical parameter for modulating drug release. Here, we investigate the diffusion of a peptide drug through a network of GO membranes and GO-embedded hydrogels, modelled as porous matrices resembling both laminated and ‘house of cards’ structures. Our experiments use a therapeutic peptide and show a tunable nonlinear dependence of the peptide concentration upon time. We establish models using numerical simulations with a diffusion equation accounting for the photo-thermal degradation of fluorophores and an effective percolation model to simulate the experimental data. The modelling yields an interpretation of the control of drug diffusion through GO membranes, which is extended to the diffusion of the peptide in GO-embedded agarose hydrogels. Varying the density of micron-sized GO flakes allows for fine control of the drug diffusion. We further show that both GO density and size influence the drug release rate. The ability to tune the density of hydrogel-like GO membranes to control drug release rates has exciting implications to offer guidelines for tailoring drug release rates in hydrogel-based therapeutic delivery applications.

Frequency domain transformation optics for diffusive photon density waves' cloaking

We make use of transformation optics technique to realize cloaking operation in the light diffusive regime, for spherical objects. The cloak requires spatially heterogeneous anisotropic diffusivity, as well as spatially varying speed of light and absorption. Analytic calculations of Photon's fluence confirm minor role of absorption in reduction of far-field scattering, and a monopole fluence field converging to a constant in the static regime in the invisibility region. The latter is in contrast to acoustic and electromagnetic cloaks, for which the field vanishes inside the core. These results are finally discussed in the context of mass diffusion, where cloaking can be achieved with a heterogeneous anisotropic diffusivity.

Optimization of Flavonoid Extraction from Red and Brown Rice Bran and Evaluation of the Antioxidant Properties

Recently, the quality-by-design concept has been widely implemented in the optimization of pharmaceutical processes to improve batch-to-batch consistency. As flavonoid compounds in pigmented rice bran may provide natural antioxidants, extraction of flavonoid components from red and brown rice bran was optimized using central composite design (CCD) and response surface methodology (RSM). Among the solvents tested, ethanol was most efficient for extracting flavonoids from rice bran. The examined parameters were temperature, solvent percentage, extraction time, and solvent-to-solid ratio. The highest total flavonoid content (TFC) in red rice bran was predicted as 958.14 mg quercetin equivalents (QE)/100 g dry matter (DM) at 58.5 °C, 71.5% (v/v), 36.2 min, and 7.94 mL/g, respectively, whereas the highest TFC in brown rice bran was predicted as 782.52 mg QE/100 g DM at 56.7 °C, 74.4% (v/v), 36.9 min, and 7.18 mL/g, respectively. Verification experiment results under these optimized conditions showed that the TFC values for red and brown rice bran were 962.38 and 788.21 mg QE/100 g DM, respectively. No significant differences were observed between the predicted and experimental TFC values, indicating that the developed models are accurate. Analysis of the extracts showed that apigenin and p-coumaric acid are abundant in red and brown rice bran. Further, red rice bran with its higher flavonoid content exhibited higher nitric oxide and 2,2-diphenyl-1-picrylhydrazyl scavenging activities (EC₅₀ values of 41.3 and 33.6 μg/mL, respectively) than brown rice bran. In this study, an extraction process for flavonoid compounds from red and brown rice bran was successfully optimized. The accuracy of the developed models indicated that the approach is applicable to larger-scale extraction processes.

Optimization-based design of an elastostatic cloaking device

We present a new method for the design of devices to manipulate the displacement field in Elastic materials. It consists of solving a nonlinear optimization problem where the objective function defines the error in matching a desired displacement field, and the design variables determine the required material distribution within the device. In order to facilitate fabrication, the material at a given point of the device is chosen from a set of predefined materials, giving raise to a discrete optimization problem that is converted into a continuous one using the Discrete Material Optimization technique. The candidate materials maybe simple, isotropic materials, but the device made of them behaves as a whole as a metamaterial, enabling the manipulation of the displacement field in ways that are inconceivable in nature. As an example of application, a device for elastostatic cloaking or unfeelability is designed.

A Unified Approach to Nonlinear Transformation Materials

The advances in geometric approaches to optical devices due to transformation optics has led to the development of cloaks, concentrators, and other devices. It has also been shown that transformation optics can be used to gravitational fields from general relativity. However, the technique is currently constrained to linear devices, as a consistent approach to nonlinearity (including both the case of a nonlinear background medium and a nonlinear transformation) remains an open question. Here we show that nonlinearity can be incorporated into transformation optics in a consistent way. We use this to illustrate a number of novel effects, including cloaking an optical soliton, modeling nonlinear solutions to Einstein’s field equations, controlling transport in a Debye solid, and developing a set of constitutive to relations for relativistic cloaks in arbitrary nonlinear backgrounds.

Theory of transformation thermal convection for creeping flow in porous media: Cloaking, concentrating, and camouflage

Heat can transfer via thermal conduction, thermal radiation, and thermal convection. All the existing theories of transformation thermotics and optics can treat thermal conduction and thermal radiation, respectively. Unfortunately, thermal convection has seldom been touched in transformation theories due to the lack of a suitable theory, thus limiting applications associated with heat transfer through fluids (liquid or gas). Here, we develop a theory of transformation thermal convection by considering the convection-diffusion equation, the equation of continuity, and the Darcy law. By introducing porous media, we get a set of equations keeping their forms under coordinate transformation. As model applications, the theory helps to show the effects of cloaking, concentrating, and camouflage. Our finite-element simulations confirm the theoretical findings. This work offers a transformation theory for thermal convection, thus revealing novel behaviors associated with potential applications; it not only provides different hints on how to control heat transfer by combining thermal conduction, thermal convection, and thermal radiation, but also benefits mass diffusion and other related fields that contain a set of equations and need to transform velocities at the same time.

Spanning the scales of mechanical metamaterials using time domain simulations in transformed crystals, graphene flakes and structured soils

We begin with a brief historical survey of discoveries of quasi-crystals and graphene, and then introduce the concept of transformation crystallography, which consists of the application of geometric transforms to periodic structures. We consider motifs with three-fold, four-fold and six-fold symmetries according to the crystallographic restriction theorem. Furthermore, we define motifs with five-fold symmetry such as quasi-crystals generated by a cut-and-projection method from periodic structures in higher-dimensional space. We analyze elastic wave propagation in the transformed crystals and (Penrose-type) quasi-crystals with the finite difference time domain freeware SimSonic. We consider geometric transforms underpinning the design of seismic cloaks with square, circular, elliptical and peanut shapes in the context of honeycomb crystals that can be viewed as scaled-up versions of graphene. Interestingly, the use of morphing techniques leads to the design of cloaks with interpolated geometries reminiscent of Victor Vasarely's artwork. Employing the case of transformed graphene-like (honeycomb) structures allows one to draw useful analogies between large-scale seismic metamaterials such as soils structured with columns of concrete or grout with soil and nanoscale biochemical metamaterials. We further identify similarities in designs of cloaks for elastodynamic and hydrodynamic waves and cloaks for diffusion (heat or mass) processes, as these are underpinned by geometric transforms. Experimental data extracted from field test analysis of soil structured with boreholes demonstrates the application of crystallography to large scale phononic crystals, coined as seismic metamaterials, as they might exhibit low frequency stop bands. This brings us to the outlook of mechanical metamaterials, with control of phonon emission in graphene through extreme anisotropy, attenuation of vibrations of suspension bridges via low frequency stop bands and the concept of transformed meta-cities. We conclude that these novel materials hold strong applications spanning different disciplines or across different scales from biophysics to geophysics.

Bifunctional metamaterials with simultaneous and independent manipulation of thermal and electric fields

Metamaterials offer a powerful way to manipulate a variety of physical fields ranging from wave fields (electromagnetic field, acoustic field, elastic wave, etc.), static fields (static magnetic field, static electric field) to diffusive fields (thermal field, diffusive mass). However, the relevant reports and studies are usually limited to a single physical field or functionality. In this study, we proposed and experimentally demonstrated a bifunctional metamaterial which could manipulate thermal and electric fields simultaneously and independently. Specifically, a composite with independently controllable thermal and electric conductivity was introduced, on the basis of which a bifunctional device capable of shielding thermal flux and concentrating electric current simultaneously was designed, fabricated and characterized. This work provides an encouraging example of metamaterials transcending their natural limitations, which offers a promising future in building a broad platform for the manipulation of multi-physics fields.

Detecting Thermal Cloaks via Transient Effects

Recent research on the development of a thermal cloak has concentrated on engineering an inhomogeneous thermal conductivity and an approximate, homogeneous volumetric heat capacity. While the perfect cloak of inhomogeneous κ and inhomogeneous ρc_p is known to be exact (no signals scattering and only mean values penetrating to the cloak’s interior), the sensitivity of diffusive cloaks to defects and approximations has not been analyzed. We analytically demonstrate that these approximate cloaks are detectable. Although they work as perfect cloaks in the steady-state, their transient (time-dependent) response is imperfect and a small amount of heat is scattered. This is sufficient to determine the presence of a cloak and any heat source it contains, but the material composition hidden within the cloak is not detectable in practice. To demonstrate the feasibility of this technique, we constructed a cloak with similar approximation and directly detected its presence using these transient temperature deviations outside the cloak. Due to limitations in the range of experimentally accessible volumetric specific heats, our detection scheme should allow us to find any realizable cloak, assuming a sufficiently large temperature difference.

Mass Separation by Metamaterials

Being able to manipulate mass flow is critically important in a variety of physical processes in chemical and biomolecular science. For example, separation and catalytic systems, which requires precise control of mass diffusion, are crucial in the manufacturing of chemicals, crystal growth of semiconductors, waste recovery of biological solutes or chemicals, and production of artificial kidneys. Coordinate transformations and metamaterials are powerful methods to achieve precise manipulation of molecular diffusion. Here, we introduce a novel approach to obtain mass separation based on metamaterials that can sort chemical and biomolecular species by cloaking one compound while concentrating the other. A design strategy to realize such metamaterial using homogeneous isotropic materials is proposed. We present a practical case where a mixture of oxygen and nitrogen is manipulated using a metamaterial that cloaks nitrogen and concentrates oxygen. This work lays the foundation for molecular mass separation in biophysical and chemical systems through metamaterial devices.

Nanoscale thermal cloaking in graphene via chemical functionalization

We achieved thermal cloaking at the nanoscale for the first time.

Electrostatic Field Invisibility Cloak

The invisibility cloak has been drawing much attention due to its new concept for manipulating many physical fields, from oscillating wave fields (electromagnetic, acoustic and elastic) to static magnetic fields, dc electric fields, and diffusive fields. Here, an electrostatic field invisibility cloak has been theoretically investigated and experimentally demonstrated to perfectly hide two dimensional objects without disturbing their external electrostatic fields. The desired cloaking effect has been achieved via both cancelling technology and transformation optics (TO). This study demonstrates a novel way for manipulating electrostatic fields, which shows promise for a wide range of potential applications.

Analogies between optical propagation and heat diffusion: applications to microcavities, gratings and cloaks

A new analogy between optical propagation and heat diffusion in heterogeneous anisotropic media has been proposed recently by three of the present authors. A detailed derivation of this unconventional correspondence is presented and developed. In time harmonic regime, all thermal parameters are related to optical ones in artificial metallic media, thus making possible to use numerical codes developed for optics. Then, the optical admittance formalism is extended to heat conduction in multilayered structures. The concepts of planar microcavities, diffraction gratings and planar transformation optics for heat conduction are addressed. Results and limitations of the analogy are emphasized.

Simultaneously concentrated electric and thermal fields using fan-shaped structure

In recent years, considerable attention has been focused on transformation optics and metamaterial due to their fascinating properties and wide range of promising applications. Concentrator, one of the most well-known applications of transformation optics and metamaterial, is now limited only to a single physical domain. Here we propose and give the experimental demonstration of a bifunctional concentrator that can concentrate both electric and thermal fields to a given region simultaneously while keeping the external fields undistorted. Fan-shaped structure composed of alternating wedges made of two kinds of natural materials is proposed to achieve this goal. Numerical simulation and experimental results show good agreement, indicating the soundness and feasibility of our scheme.

Manipulating Steady Heat Conduction by Sensu-shaped Thermal Metamaterials

The ability to design the control of heat flow has innumerable benefits in the design of electronic systems such as thermoelectric energy harvesters, solid-state lighting, and thermal imagers, where the thermal design plays a key role in performance and device reliability. In this work, we employ one identical sensu-unit with facile natural composition to experimentally realize a new class of thermal metamaterials for controlling thermal conduction (e.g., thermal concentrator, focusing/resolving, uniform heating), only resorting to positioning and locating the same unit element of sensu-shape structure. The thermal metamaterial unit and the proper arrangement of multiple identical units are capable of transferring, redistributing and managing thermal energy in a versatile fashion. It is also shown that our sensu-shape unit elements can be used in manipulating dc currents without any change in the layout for the thermal counterpart. These could markedly enhance the capabilities in thermal sensing, thermal imaging, thermal-energy storage, thermal packaging, thermal therapy, and more domains beyond.

Mechanical cloak design by direct lattice transformation

Spatial coordinate transformations have helped simplifying mathematical issues and solving complex boundary-value problems in physics for decades already. More recently, material-parameter transformations have also become an intuitive and powerful engineering tool for designing inhomogeneous and anisotropic material distributions that perform wanted functions, e.g., invisibility cloaking. A necessary mathematical prerequisite for this approach to work is that the underlying equations are form invariant with respect to general coordinate transformations. Unfortunately, this condition is not fulfilled in elastic-solid mechanics for materials that can be described by ordinary elasticity tensors. Here, we introduce a different and simpler approach. We directly transform the lattice points of a 2D discrete lattice composed of a single constituent material, while keeping the properties of the elements connecting the lattice points the same. After showing that the approach works in various areas, we focus on elastic-solid mechanics. As a demanding example, we cloak a void in an effective elastic material with respect to static uniaxial compression. Corresponding numerical calculations and experiments on polymer structures made by 3D printing are presented. The cloaking quality is quantified by comparing the average relative SD of the strain vectors outside of the cloaked void with respect to the homogeneous reference lattice. Theory and experiment agree and exhibit very good cloaking performance.

Spectral effectiveness of engineered thermal cloaks in the frequency regime

We analyse basic thermal cloaks designed via different geometric transforms applied to thermal cloaking. We evaluate quantitatively the effectiveness of these heterogeneous anisotropic thermal cloaks through the calculation of the standard deviation of the isotherms. The study addresses the frequency regime and we point out the cloak's spectral effectiveness. We find that all these cloaks have comparable effectiveness irrespective of whether or not they have singular conductivity at their inner boundary. However, approximate cloaking with multi-layered cloak critically depends upon the homogenization algorithm and it is shown that the standard deviation varies linearly with the inverse of the number of layers.

Metamaterials beyond electromagnetism

Metamaterials are rationally designed man-made structures composed of functional building blocks that are densely packed into an effective (crystalline) material. While metamaterials are mostly associated with negative refractive indices and invisibility cloaking in electromagnetism or optics, the deceptively simple metamaterial concept also applies to rather different areas such as thermodynamics, classical mechanics (including elastostatics, acoustics, fluid dynamics and elastodynamics), and, in principle, also to quantum mechanics. We review the basic concepts, analogies and differences to electromagnetism, and give an overview on the current state of the art regarding theory and experiment-all from the viewpoint of an experimentalist. This review includes homogeneous metamaterials as well as intentionally inhomogeneous metamaterial architectures designed by coordinate-transformation-based approaches analogous to transformation optics. Examples are laminates, transient thermal cloaks, thermal concentrators and inverters, 'space-coiling' metamaterials, anisotropic acoustic metamaterials, acoustic free-space and carpet cloaks, cloaks for gravitational surface waves, auxetic mechanical metamaterials, pentamode metamaterials ('meta-liquids'), mechanical metamaterials with negative dynamic mass density, negative dynamic bulk modulus, or negative phase velocity, seismic metamaterials, cloaks for flexural waves in thin plates and three-dimensional elastostatic cloaks.

Controlling chloride ions diffusion in concrete

The corrosion of steel in concrete is mainly due to the chemical reaction between the chloride ions and iron ions. Indeed, this is a serious threaten for reinforced concrete structure, especially for the reinforced concrete structure in the sea. So it is urgent and important to protect concrete against chloride ions corrosion. In this work, we report multilayer concrete can cloak chloride ions. We formulated five kinds of concrete A, B, C, D and E, which are made of different proportion of cement, sand and glue, and fabricated six-layer (ABACAD) cylinder diffusion cloak and background media E. The simulation results show that the six-layer mass diffusion cloak can protect concrete against chloride ions penetration, while the experiment results show that the concentration gradients are parallel and equal outside the outer circle in the diffusion flux lines, the iso-concentration lines are parallel outside the outer circle, and the concentration gradients in the inner circle are smaller than those outside the outer circle.