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Inspired by nature, the research of functionalized nanoparticles and nanodevices has been in-depth developed in recent years. In this paper, we theoretically studied the interaction between functional polyelectrolyte brush layer-modified nanoparticles and a silica flat substrate. Based on the Poisson-Nernst-Planck equations, the mathematical model is established. The changes of the volume charge density and electric field energy density when the nanoparticle interacts with the silica flat substrate under multi-ions regulation were investigated. The results show that when there is a strong interaction between the silica flat substrate and nanoparticles, such as the distances between the nanoparticle and silica flat substrate, which are 2 or 5 nm, the isoelectric point shift under the influence of silica flat substrate and the total charge density in the brush layer is jointly controlled by the cations in the solution and the volume charge density of the brush layer. With the increase of the distances between the nanoparticle and silica flat substrate, the regulation of the volume charge density of the brush layer dominates. These results will provide guidance for the movement mechanism of functionalized nanoparticles in silica nanochannels.

Due to its characteristics of noncontact, non-damage, high flux, and easy-to-achieve flexible manipulation, optically induced dielectrophoresis (ODEP) technology has been employed to manipulate microspherical biological particles, including separation, enrichment, capture, arrangement, and fusion. However, in nature, biomolecules are morphologically diverse, and some of them are rodlike. In order to illustrate the electrodynamics of rodlike particles under the action of ODEP, a transient multi-physical field coupling model of ODEP chip under the hypothesis of electrical double layer thin layer was established in this paper. The arbitrary Lagrangian-Eulerian method is used to track single-rod particle in the strong coupled flow field and electric field simultaneously. The influence of several key factors, including the applied alternating current (AC) electric voltage, the width of optical bright area, and the initial position of particle, on the trajectory of particle center was analyzed in positive dielectrophoresis (DEP) action and negative DEP action, respectively. Especially, the planar motion process of rodlike particles was discussed together. The research results reveal the electrodynamics behavior of rodlike particles based on the action of ODEP, which may provide theoretical support for the further design of rodlike biological cells manipulation chip based on AC ODEP technology in the future.

Metalenses can achieve diffraction-limited focusing via localized phase modification of the incoming light beam. However, the current metalenses face to the restrictions on simultaneously achieving large diameter, large numerical aperture, broad working bandwidth and the structure manufacturability. Herein, we present a kind of metalenses composed of concentric nanorings that can address these restrictions using topology optimization approach. Compared to existing inverse design approaches, the computational cost of our optimization method is greatly reduced for large-size metalenses. With its design flexibility, the achieved metalens can work in the whole visible range with millimeter size and a numerical aperture of 0.8 without involving high-aspect ratio structures and large refractive index materials. Electron-beam resist PMMA with a low refractive index is directly used as the material of the metalens, enabling a much more simplified manufacturing process. Experimental results show that the imaging performance of the fabricated metalens has a resolution better than 600 nm corresponding to the measured FWHM of 745 nm.

The nanopore-based biosensing technology is built up on the fluctuation of the ionic current induced by the electrokinetic translation of a particle penetrating the nanopore. It is expected that the current change of a deformable bioparticle is dissimilar from that of a rigid one. This study theoretically investigated the transient translocation process of a deformable particle through a nanopore for the first time. The mathematical model considers the Poisson equation for the electric potential, the Nernst-Planck equations for the ionic transport, the Navier-Stokes equations for the flow field, and the stress-strain equation for the dynamics of the deformable bioparticle. The arbitrary Lagrangian-Eulerian method is used for the fully coupled particle-fluid dynamic interaction. Results show that the deformation degree of the particle, the velocity deviation, and the current is different from the rigid particle. The deformation degree of the particle will reach the maximum when the particle passes a nanopore. Because of the deformation of particles, the total force applied on deformable particles is larger than that of rigid particles, resulting in larger velocity deviation and current deviation. The influences of the ratio of the nanoparticle radius to the Debye length and surface charge density of the nanopore are also studied. The research results illustrate the translocation mechanism of a deformable nanoparticle in the nanopore, which can provide theoretical guidance for the biosensing technology based on the nanopore.

A simple 1D blazed metagrating is proposed. The metagrating consists of SiO2 film sandwiched by Ag substrate and Ag nanostrips, which can achieve high-efficiency −1st-order diffraction in the range of 550 nm to 700 nm, and the peak efficiency is nearly 98%. The SiO2 dielectric layer in previous designs is used chiefly as a waveguide layer to support a guided mode. In comparison, it is introduced here to suppress the unwanted diffraction order (zero-order), which helps achieve high-efficiency diffraction at a high diffraction order. For analysis, the metagrating is disassembled into two parts, including a flat plate and a grating. By analysing the far-field radiation pattern of scattered waves and the reflection phase of a specific mode for these two parts, we conclude that the cause of high-efficiency blazing draws support from suppressing zero-order based on destructive interference. This work provides an intuitive physical image for this type of metagrating and an idea to design high-efficiency diffraction and beam deflection devices from the perspective of interference.

The metal–insulator–metal (MIM) waveguide, which can directly couple free space photons, acts as an important interface between conventional optics and subwavelength photoelectrons. The reason for the difficulty of this optical coupling is the mismatch between the large wave vector of the MIM plasmon mode and photons. With the increase in the wave vector, there is an increase in the field and Ohmic losses of the metal layer, and the strength of the MIM mode decreases accordingly. To solve those problems, this paper reports on inversely designed nanoantennas that can couple the free space and MIM waveguide and efficiently excite the MIM plasmon modes at multiple wavelengths and under oblique angles. This was achieved by implementing an inverse design procedure using a topology optimization approach. Simulation analysis shows that the coupling efficiency is enhanced 9.47-fold by the nanoantenna at the incident wavelength of 1338 nm. The topology optimization problem of the nanoantennas was analyzed by using a continuous adjoint method. The nanoantennas can be inversely designed with decreased dependence on the wavelength and oblique angle of the incident waves. A nanostructured interface on the subwavelength scale can be configured in order to control the refraction of a photonic wave, where the periodic unit of the interface is composed of two inversely designed nanoantennas that are decoupled and connected by an MIM waveguide.

Robust Cassie–Baxter wettability of a rough solid surface with micro-textures is a key factor for stable hydrophobicity. Overlayed micro-textures are potentially more effective in ensuring the robustness of the surface properties, because of the layer-by-layer increase of the duty ratio and their effective approximation of the full hierarchy. However, a design methodology that includes considering manufacturability is lacking. In this article, we address this deficiency and present a monolithic inverse design approach, composed of a series of topology optimizations, to derive micro-textures with hierarchy approximated by overlayed geometries. The optimization are implemented in a dimensionless manner using a periodic regular-polygon tiling of the plane, in which the corresponding dimensionless Young-Laplace equation is used to describe the physics at the liquid/vapor interface. Two sequential and neighboring optimization tasks are linked through the design domain of the downward layer, determined by a conformal extension of the physical density representing the pattern of the upward layer. This ensures the manufacturability e.g. for an overlayed lithography process. Layer-by-layer robustness enhancement is thereby achieved, and the capability to anchor the three-phase contact line after the collapse of the liquid/vapor interface supported by the upward layer. In generating the overlayed micro-textures, a rigorous scaling factor for the patterns was determined, leading to a recursion inequality based on the depth of the liquid/vapor interfaces at the critical static pressures that determines the extrusion distance of the patterns. The trace height and minimal aspect ratio of the micro-textures are specified by the scaling factor and extrusion distance for a layer. This allows a compromise between performance and manufacturability, and thereby avoid instabilities caused by elasto-capillary collapse of the micro-/nano-structures. We computationally confirm the optimality by comparing the derived micro-textures with previously reported designs.

Improvements to the signal-to-noise ratio of magnetic resonance detection leads to a strong reduction in measurement time, yet as a sole optimization goal for resonator design it would be an oversimplification of the problem at hand. Multiple constraints, for example for field homogeneity, and sample shape, suggests the use of numerical optimization to obtain resonator designs that delivers the intended improvement. Here we consider the 2D Lenz lens as a sufficiently broad-band flux transforming interposer between the sample and an RF circuit, as a flexible and an easily manufacturable device family with which to mediate different design requirements. We report on a method to apply topology optimization to determine the optimal layout of a Lenz lens, and demonstrate realisations for both low (45 MHz), and high frequency (500 MHz) NMR.

In confined microfluidic spaces such as microchannels, electroosmosis is a convenient Coulomb-force mechanism used to electrically actuate charged particles and ions presented in the fluid and pump the electrolytic fluid itself through drag forces. The shape and position of electrode pairs, whose induced charges are in contact with the fluid, determine the electric field and hence the resulting fluid-dynamic velocity distribution. In this paper, we address the inverse design of the electrode-pair patterns in such actuation mechanisms. Our approach is to use topology optimization to inversely determine the patterns of an electrode pair. The optimization procedure requires a mathematical description of the desired fluid behaviour, and then drives the patterns of the electrode pairs to achieve the goal performance. We demonstrate the behaviour of the procedure, which couples the Navier-Stokes equations with charge transportation, to implement an efficient electroosmotic micromixer for laminar microflow. We show that the procedure allows to investigate such microflows under the influence of selected parameter variations, thereby exploring the design space towards optimal device performance. This developed method is novel on the topology optimization of a surface structure to control bulk performance and its implementation over a lower-dimensional surface of an otherwise volumetric domain, where the material interpolation is implemented between Dirichlet and Newmann types of boundary conditions.

The robust Cassie–Baxter mode of the wetting behaviour on a micro-textured solid surface, is a key topography element yielding stable super-hydrophobicity. To meet this purpose, we propose an inverse computational design procedure for the discovery of suitable periodic micro-textures, based on three different tilings of the plane. The symmetric tiles of the lattice are regular triangles, quadrangles, and hexagons. The goal of the inverse design procedure is to achieve the robust Cassie–Baxter state, in which the liquid/vapour interface is mathematically described using the Young–Laplace equation on the lattice, and a topology optimisation approach is utilised to construct a variational problem for the inverse design procedure. Based on numerical calculations of the constructed variational problem, underlying effects are revealed for several factors, including the Bond number, duty ratio, feature size, and lattice constant. The effects of feature size and lattice constant provide approaches for compromisingly considering the robustness of the Cassie–Baxter mode and manufacturability of the inversely designed micro-textures; the effect of the lattice constant permits the scaling properties of the derived patterns, and this in turn provides an approach to avoid the elasto-capillary instability driven collapse of the micro/nanostructures in the derived micro-textures. Further, a monolithic inverse design procedure for the periodic micro-textures is proposed in the conclusions, with synthetically considering the manufacturability as well as contact angle and surface-volume ratio of the liquid bulge held by the supported liquid/vapour interface.

In topology optimization of electromagnetic waves, the Gâteaux differentiability of the conjugate operator to the complex field variable results in the complexity of the adjoint sensitivity, which evolves the original real-valued design variable to be complex during the iterative solution procedure. Therefore, the self-inconsistency of the adjoint sensitivity is presented. To enforce the self-consistency, the real part operator has been used to extract the real part of the sensitivity to keep the real-value property of the design variable. However, this enforced self-consistency can cause the problem that the derived structural topology has unreasonable dependence on the phase of the incident wave. To solve this problem, this article focuses on the self-consistent adjoint analysis of the topology optimization problems for electromagnetic waves. This self-consistent adjoint analysis is implemented by splitting the complex variables of the wave equations into the corresponding real parts and imaginary parts, sequentially substituting the split complex variables into the wave equations with deriving the coupled equations equivalent to the original wave equations, where the infinite free space is truncated by the perfectly matched layers. Then, the topology optimization problems of electromagnetic waves are transformed into the forms defined on real functional spaces instead of complex functional spaces; the adjoint analysis of the topology optimization problems is implemented on real functional spaces with removing the variational of the conjugate operator; the self-consistent adjoint sensitivity is derived, and the phase-dependence problem is avoided for the derived structural topology. Several numerical examples are implemented to demonstrate the robustness of the derived self-consistent adjoint analysis.

This paper presents the inverse design of resonant nanostructures for extraordinary optical transmission of periodic metallic slits, where the topology optimization approach is utilized to implement the inverse design procedure and find the geometrical configurations of the nanostructures. By using the inverse design method, the subwavelength-sized resonant nanostructures, localized at the inlet and outlet sides of the periodic metallic slits, are derived with transmission peaks at the prescribed incident wavelengths. The transmissivity is enhanced by effective excitation and guidance of surface plasmon polariton at the inlet side of the slits, the coherent resonance of surface plasmon polariton inside the slits, and radiation of the photonic energy at the outlet side of the slits. The transmission peaks of the periodic metallic slits, with inversely designed resonant nanostructures, are raised along with the red shift of the incident wavelength. The position of the transmission peak of periodic metallic slits can be controlled and localized at the desired frequency, by specifying the incident wave with the wavelength corresponding to the desired frequency preset in the inverse design procedure. By maximizing the minimum transmissivity of the periodic metallic slits with incident wavelengths in a prescribed wavelength range, the extraordinary optical transmission bandwidth can be enlarged, and the sensitivity of transmissivity to wavelength can be decreased equivalently.

This paper presents topology optimization of capillary, the typical two-phase flow with immiscible fluids, where the level set method and diffuse-interface model are combined to implement the proposed method. The two-phase flow is described by the diffuse-interface model with essential no slip condition imposed on the wall, where the singularity at the contact line is regularized by the molecular diffusion at the interface between two immiscible fluids. The level set method is utilized to express the fluid and solid phases in the flows and the wall energy at the implicit fluid-solid interface. Based on the variational procedure for the total free energy of two-phase flow, the Cahn-Hilliard equations for the diffuse-interface model are modified for the two-phase flow with implicit boundary expressed by the level set method. Then the topology optimization problem for the two-phase flow is constructed for the cost functional with general formulation. The sensitivity analysis is implemented by using the continuous adjoint method. The level set function is evolved by solving the Hamilton-Jacobian equation, and numerical test is carried out for capillary to demonstrate the robustness of the proposed topology optimization method. It is straightforward to extend this proposed method into the other two-phase flows with two immiscible fluids.

A completely new droplet breakup phenomenon is reported for droplets passing through a constriction in an electrokinetic flow. The breakup occurs during the droplet shape recovery process past the constriction throat by the interplay of the dielectrophoretic stress release and the interface energy for droplets with smaller permittivity than that of the ambient fluid. There are conditions for constriction ratios and droplet size that the droplet breakup occurs. The numerical predictions provided here require experimental verification, and then can give rise to a novel microfluidic device design with novel droplet manipulations.

In many applications, a cloaked resonator is highly desired, which can harvest and maximize the energy within the resonator without being detected. This paper presents the resonator cloaking achieved by topology optimization-based inverse design methodology. The resonator cloaking is inversely designed by solving the topology optimization problem with minimizing the ratio of the scattering field energy outside the cloak and the cloaked resonating field energy. By inversely designing the resonator cloaking with relative permittivity 2 for both the resonator and cloak, the topology optimization-based inverse design methodology is demonstrated, where the incident angle sensitivity is considered to derive incident angle insensitive design. Then, the proposed methodology is applied for the cases with resonator and cloak materials chosen from dielectrics with low, moderate and high permittivity, respectively. The derived results demonstrate that the resonator cloaking can be categorized into three types, which are the Fabry-Perot resonance cloaking, Mie resonance cloaking and hybrid resonance cloaking.

This note presents an inverse design methodology of metal nanostructures for localized surface plasmon resonances, based on the topology optimization approach. Using the proposed method, determination of the metal distribution in nanostructures is implemented for surface enhanced Raman spectroscopy to maximize the enhancement factor. The obtained results demonstrate that the outlined approach can be used to design metal nanostructure with resonant peak and significant enhancement factor at specified incident wavelength, and to control the shift of the resonant peak by topologically optimizing the nanostructure.

The dielectrophoretic (DEP) choking phenomenon is revisited for Janus particles that are transported electrokinetically through a microchannel constriction by a direct-current (DC) electric field. The negative DEP force that would block a particle with a diameter significantly smaller than that of the constriction at its inlet is seen to be relaxed by the rotation of the Janus particle in a direction that minimizes the magnitude of the DEP force. This allows the particle to pass through the constriction completely. An arbitrary Lagrangian-Eulerian (ALE) numerical method is used to solve the nonlinearly coupled electric field, flow field, and moving particle, and the DEP force is calculated by the Maxwell stress tensor (MST) method. The results show how Janus particles with non-uniform surface potentials overcome the DEP force and present new conditions for the DEP choking by a parametric study. Particle transportation through microchannel constrictions is ubiquitous, and particle surface properties are more likely to be non-uniform than not in practical applications. This study provides new insights of importance for non-uniform particles transported electrokinetically in a microdevice.

Viscoelastic solution is encountered extensively in microfluidics. In this work, the particle movement of the viscoelastic flow in the contraction–expansion channel is demonstrated. The fluid is described by the Oldroyd-B model, and the particle is driven by dielectrophoretic (DEP) forces induced by the applied electric field. A time-dependent multiphysics numerical model with the thin electric double layer (EDL) assumption was developed, in which the Oldroyd-B viscoelastic fluid flow field, the electric field, and the movement of finite-size particles are solved simultaneously by an arbitrary Lagrangian–Eulerian (ALE) numerical method. By the numerically validated ALE method, the trajectories of particle with different sizes were obtained for the fluid with the Weissenberg number (Wi) of 1 and 0, which can be regarded as the Newtonian fluid. The trajectory in the Oldroyd-B flow with Wi = 1 is compared with that in the Newtonian fluid. Also, trajectories for different particles with different particle sizes moving in the flow with Wi = 1 are compared, which proves that the contraction–expansion channel can also be used for particle separation in the viscoelastic flow. The above results for this work provide the physical insight into the particle movement in the flow of viscous and elastic features.

This paper presents an optimization-based design method of passive micromixers for immiscible fluids, which means that the Peclet number infinitely large. Based on topology optimization method, an optimization model is constructed to find the optimal layout of the passive micromixers. Being different from the topology optimization methods with Eulerian description of the convection-diffusion dynamics, this proposed method considers the extreme case, where the mixing is dominated completely by the convection with negligible diffusion. In this method, the mixing dynamics is modeled by the mapping method, a Lagrangian description that can deal with the case with convection-dominance. Several numerical examples have been presented to demonstrate the validity of the proposed method.

In this chapter, several typical microfluidic components are inversely designed, to demonstrate the power of the topology optimization for microfluidics. And the typical microfluidic components include the passive micromixer, electroosmotic micromixer, no-moving-part microvalve, and valveless micropump.

This chapter presents topology optimization of two-phase flow with immiscible fluids, where the level set method and diffuse-interface model are combined to implement the proposed method.

This chapter presents the topology optimization of unsteady incompressible Navier-Stokes flows, where the density method and level set method are respectively used to implement the implicitly expression of the unsteady flows.

This chapter presents the topology optimization method for the steady and unsteady incompressible Navier-Stokes flows driven by body forces that influence the optimal shape and topology of fluid flows.