Narrow Confinement Research Articles

The peak viscosity of decaying foam with natural drainage and coarsening.

Studying the change in foam viscosity during foam decay, a spontaneous and inevitable process, is of fundamental and practical interest across many applications, ranging from the froth in a cup of coffee to the carbon sequestration in deep geological reservoirs. However, standard rheological measurements impose several experimental constraints, such as the narrow sample confinement and the long initial setup time, interfering with the natural conditions for foam decay. Here, we perform fast and in situ measurements on decaying foam immediately after its generation in a wide column, measuring the viscosity by vibrational probes and measuring the foam structure by optical imaging. We successfully capture the changes during the transition from the drainage-dominated stage to the coarsening-dominated stage. The viscosity reaches its maximum at the crossover point, elucidating the competing effects of drainage and coarsening. The viscosity peaks magnitude and position are influenced by the gas solubility and diffusion coefficient. The phenomena are quantitatively explained by the film-shearing model. Our findings provide the foundation for enhancing foam stability and performance, improving the efficiency of foam-based applications.

Features of biology and coenopopulation characteristics of Silene cretacea Fisch. ex Spreng. on the Ilovli river valley, Volgograd region

One of the modern environmental problems is the reduction in the number of rare plant species due to an increase in anthropogenic pressure on natural phytocenoses. Cenopopulation studies of Silene cretacea Fisch. ex Spreng. will make it possible to study the real state of natural coenopopulations, which is the result of the intrapopulation distribution of individuals. We studied 7 cenopopulations of Silene cretacea in the natural conditions of the Volgograd region on the Cretaceous outcrops of the valley of the river Ilovlya, which differ in species composition and degree of anthropogenic impact. An ontogenetic strategy has been defined that corresponds to the S (patient) type, which allows the species, in the struggle for existence, due to its endurance, to exist in extremely unfavorable conditions, that is, in conditions where other species cannot survive, and therefore cannot compete with them. With the similarity of the age composition of cenopopulations in different ecological and cenotic areas, they differed from each other in terms of vitality composition. The vitality type of the studied cenopopulations changed from prosperous to depressive. The analysis of the age spectrum showed that all the studied populations are normal, incomplete, with a maximum in the generative fraction with a large proportion of plants of the generative period, with a small proportion of pregerative and senile individuals. For most individuals of the S. cretacea, normal development is common that described by the successive passage of individuals of all age states in their life cycle. Under optimal conditions, individuals of S. cretacea are characterized by slow development with slow rates of development in the middle generative age state. This is due to the specifics of the ecology of the habitat of S. cretacea (narrow ecological confinement, features of the soil substrate, etc.) and the biology of the species (seed renewal, prolonged stay of individuals in the generative state).

Distribution of orchids in the upper basin of the Ural River and questions of nature conservation

Aim. Conduct a botanical and geographical analysis of the species of the fam. Orchidaceae in the upper part of the Ural River basin and provide recommendations on the organization of specially protected natural areas.Material and Methods. The study of the distribution of orchids was carried out both on the basis of the results of our own field expeditions and on literature and herbarium collections stored in local and central herbaria (UFA, SWER, LE, MW). The coenopopulation studies were carried out in accordance with generally accepted methods.Results. The species composition of orchids was revealed and their arealogical, ecological-coenotic, coenopopulation analysis was undertaken in the upper part of the Ural River basin. Despite the wide range, most species of the fam. Orchidaceae are characterised by a narrow ecological-coenotic confinement. The low occurrence of orchids in the conditions of the steppe and forest-steppe zones of the territories under consideration is associated with both weather-climatic and anthropogenic impacts. The coenopopulations of most species are small and the ontogenetic spectra are incomplete.Conclusions. Species of the family Orchidaceae do not grow in economically developed territories. The remaining locations of orchids are mainly associated with landscapes that are difficult to access for anthropogenic impact. In order to preserve the steppe and forest-steppe landscapes of the Urals it is necessary to further develop the system of specially protected natural areas. The most promising for this purpose are the Krykty and Irendyk ranges, which are distinguished by their unique landscape and biological diversity.

Precipitation and potential evapotranspiration determine the distribution patterns of threatened plant species in Sichuan Province, China

A fundamental goal of ecologists is to determine the large-scale gradients in species richness. The threatened plants are the priority of such studies because of their narrow distribution and confinement to a specific habitat. Studying the distribution patterns of threatened plants is crucial for identifying global conservation prioritization. In this study, the richness pattern of threatened plant species along spatial and elevation gradients in Sichuan Province of China was investigated, considering climatic, habitat-heterogeneity (HHET), geometric constraint and human-induced factors. The species richness pattern was analyzed, and the predictor variables, including mean annual temperature (MAT), mean annual precipitation (MAP), potential evapotranspiration (PET), HHET, and disturbance (DIST), to species richness were linked using the geographical distribution data of threatened species compiled at a spatial resolution of 20 km × 20 km. Generalized linear models and structural equation modelling were used to determine the individual and combined effects of each variable on species richness patterns. Results showed a total of 137 threatened plant species were distributed between 200 and 4800 m.a.s.l. The central region of the province harbors the highest species diversity. MAP and PET profoundly explained the richness pattern. Moreover, the significant role of DIST in the richness patterns of threatened plants was elucidated. These findings could help determine the richness pattern of threatened plant species in other mountainous regions of the world, with consideration of the impact of climate change.

A meshless scheme on the electrokinetically driven flow of power-law fluid through nanochannel considering dual effects of heterogeneity in wall charge and surface wettability

The present article deals with the development of a meshless scheme to study the electrokinetically driven flow of non-Newtonian fluid through narrow confinement. Combined impact of patterned charge and hydrodynamic slip length along the channel walls is considered. The widely employed power-law model is adopted to consider non-Newtonian behaviour of the background electrolytic medium. The mathematical model to study the transport of ionized liquid consists of the Poisson equation for electrostatic potential, Nernst–Planck equations for conservation of mass of mobile electrolyte ions and the Cauchy momentum equations along with equations of continuity for the flow field. We further delineated the impact of complex flow physics on the mixing efficiency of the uncharged solute injected from the inlet. The present study has two different aspects, on one hand, the successful implementation of meshless scheme based on radial basis functions and on the other hand, to dictate the impact of patterned charge and hydrodynamic slip length on the overall electrokinetic transport of ionized liquid and its effect on the mixing of injected uncharged solute. Going beyond the widely employed Debye-Hückel approximation, we simulate the governing equations using meshless scheme based on Radial Basis Functions (RBF). The numerical results are found to be in close agreement with the available theoretical and experimental results. The computational results are further presented to indicate the impact of pertinent parameters on the flow modulation and mixing of uncharged solutes. • Combined impact of patterned charge and hydrodynamic slip length of channel walls on the electrokinetic flow modulation is considered. • Power-law model is adopted to consider the non-Newtonian rheology of the fluidic medium. • Radial basis function based meshless scheme is employed for the numerical simulation. • Impact of variable surface charge and slip length on flow modulation is analysed for maximum throughput. • Impact of modulated flow field on the mixing efficiency of injected uncharged solutes is further illustrated.

Unified dynamics of hydrogen–oxygen–diluent detonations in narrow confinements

The present work addresses the interesting question that whether universal relationships can be obtained for characterizing the dynamics of hydrogen–oxygen–diluent detonations in narrow channels and as well in small circular tubes. Theoretically, we first demonstrate the success of adopting the effective induction zone length, which accounts for the leading shock velocity deficits resulting from wall losses, in unifying the quasi-one-dimensional (quasi-1D) detonation dynamics, predicted by the first principles models. These theoretically unified quasi-steady dynamics, irrespective of the geometry dimensions as well as the mixture compositions, are found to be in very good agreement with the large scores of already published detonation experiments in narrow confinements. Moreover, the experimentally unified dynamics of detonations at the macro-scale excellently follow the geometrically expected scaling of 2:1 between the 3D circular tube diameter and the 2D thin channel width results. Such excellent agreement of scaling between theory and experiments not only confirms the negligible role of small-scale cellular structures in the macro-scale propagation mechanism of weakly unstable detonations, but also permits the successful establishment of the universal correlation for characterizing the dynamics of hydrogen detonations in narrow channels and tubes.

Escaping speed of bacteria from confinement

Microswimmers such as bacteria exhibit large speed fluctuation when exploring their living environment. Here, we show that the bacterium Escherichia coli with a wide range of length speeds up beyond its free-swimming speed when passing through narrow and short confinement. The speedup is observed in two modes: for short bacteria with L <20 μm, the maximum speed occurs when the cell body leaves the confinement, but a flagellar bundle is still confined. For longer bacteria (L ≥ 20 μm), the maximum speed occurs when the middle of the cell, where the maximum number of flagellar bundles locate, is confined. The two speed-up modes are explained by a vanishing body drag and an increased flagella drag—a universal property of an “ideal swimmer.” The spatial variance of speed can be quantitatively explained by a simple model based on the resistance matrix of a partially confined bacterium. The speed change depends on the distribution of motors, and the latter is confirmed by fluorescent imaging of flagellar hooks. By measuring the duration of slowdown and speedup, we find that the effective chemotaxis is biased in filamentous bacteria, which might benefit their survival. The experimental setup can be useful to study the motion of microswimmers near surfaces with different surface chemistry.

Nonconventional Fluorescent Hyperbranched Polymer Dots as Skin Nanocarriers Constructed from an Olefinic Aliphatic AB2-Type Monomer

We constructed an olefinic aliphatic AB2 monomer (π-AB2) for the synthesis of a nonconventional fluorescent hyperbranched polymers (π-HBPs) through self-polymerization. We obtained π-AB2 from N-(3-aminopropyl)diethanolamine and maleic anhydride in three steps with a total yield of 79%. The π-HBPs possessed hyperbranched poly(amido acid) structures with internal alkene moieties, branched amino groups, and carboxyl terminal units. With their nonconjugated hyperbranched structures, the π-HBPs functioned as water-soluble polymer dots. Inter- and intramolecular hydrogen bonding in the π-HBPs resulted in a physically cross-linked structures displaying nonconventional fluorescence. This fluorescence arose from spatial conjugation at the molecular level, leading to clustering-induced emission with the lone pairs of electrons and the π-electrons interacting in a narrow confinement space. The emission of π-HBP 03 occurred at 460 nm upon excitation of 390 nm, with quantum yields of 13.5 and 7.5% at pH 7 and 3, respectively. From an examination of the relationship between chemical structure and photoluminescence, we found that the fluorescence emissions of the HBP without internal alkene moieties and π-HBP 03 (with internal alkene moieties) were 395 and 460 nm, respectively (a red-shift of 65 nm when removing the olefinic units). The self-assembly of π-HBP 03 in aqueous solution produced nanosized (ca. 9.1 nm) particles, as determined through dynamic light scattering. π-HBP 03 is noncytotoxic, with a cell viability of >90% at 1500 μg mL–1. When applied to percutaneous absorption mouse skin, the penetration ability of the π-HBPs increased in various time profiles according to the cluster size and nanostructure of the polymer dots. When we incubated HaCaT cells with π-HBP 03 for 24 h, confocal microscopy revealed that π-HBP 03 became located within the cells. Furthermore, assays revealed that π-HBP 03 displayed effective antioxidant abilities when employed at concentrations of 0.6 and 1.5 mg mL–1.

Combined electromechanically driven pulsating flow of nonlinear viscoelastic fluids in narrow confinements.

Controlled microscale transport is at the core of many scientific and technological advancements, including medical diagnostics, separation of biomolecules, etc., and often involves complex fluids. One of the challenges in this regard is to actuate flows at small scales in an energy efficient manner, given the strong viscous forces opposing fluid motion. We try to address this issue here by probing a combined time-periodic pressure and electrokinetically driven flow of a viscoelastic fluid obeying the simplified linear Phan-Thien-Tanner model, using numerical as well as asymptotic tools, in view of the fact that oscillatory fields are less energy intensive. We establish that the interplay between oscillatory electrical and mechanical forces can lead to complex temporal mass flow rate variations with short-term bursts and peaks in the flow rate. We further demonstrate that an oscillatory pressure gradient or an electric field, in tandem with another steady actuating force can indeed change the net throughput significantly-a paradigm that is not realized in Newtonian or other simpler polymeric liquids. Our results reveal that the extent of augmentation in the flow rate strongly depends on the frequency of the imposed actuating forces along with their waveforms. We also evaluate the streaming potential resulting from an oscillatory pressure-driven flow and illustrate that akin to the volume throughput, the streaming potential also shows complex temporal variations, while its time average gets augmented in the presence of a time-periodic pressure gradient in a nonlinear viscoelastic medium.

Interplay of high zeta potential and steric factor on the slip thermofluidics of power law fluids through narrow confinements

Thermal transport in a non-Newtonian fluid flow through a parallel plate microchannel is investigated with an emphasis on the effects of high zeta potential and steric factor. The fluid viscosity is modelled using the power law and the flow is driven by a combination of electric field and pressure gradient in the form of a dimensionless flow actuation coefficient. The effects of joule heating, viscous dissipation and slip length at the wall are considered. A semi-analytical formulation for the temperature profile is developed which is solved numerically using the Galerkin Finite Element method. We find that the Nusselt number increases as the flow behaviour index is increased. Velocity slip is also found to have a positive impact on convective heat transfer. However, as the zeta potential and steric factor increase, the Nusselt number begins to decline as there is an increase in viscous dissipation. We highlight the importance of considering variable electrical conductivity in evaluating the effect of joule heating at high zeta potential and moderate steric factor. In this regime, joule heating dominates advective transport and heat flow is reversed which may be detrimental or even damaging to microfluidic devices. A comprehensive thermal map is developed for a wide range of zeta potentials and steric factors.

Slip hydrodynamics of combined electroosmotic and pressure driven flows of power law fluids through narrow confinements

Electroosmotic flows (EOF) in microfluidic devices can be greatly enhanced over superhydrophobic surfaces because the high shear rates within the electrical double layer can drive large slip velocities at the interface. Using the power law fluid model, we derive a novel formulation for the Helmholtz–Smoluchowski (HS) velocity and use it to examine the effect of slip on the hydrodynamics of a coupled pressure driven and EOF. Semi analytical relations for the velocity gradient are obtained for cases of a favourable pressure gradient but exact solutions of the velocity can be found only for certain power law indices. Cases of adverse pressure gradient and fractional power law indices are investigated using numerically using the Galerkin Finite Element Method. The validity of the semi analytical relations verified by comparison with the numerical method. The presence of velocity slip at the wall leads to an enhancement of the HS velocity that is most pronounced in shear thinning fluids. Adverse pressure gradients are observed to generate an inflection in the velocity profile and even a two-way flow for certain flow parameters. The strength of the adverse pressure gradient needed to setup a reverse flow at the channel centre reduces as the slip length is increased. The location of the point of inflection is found to depend on the channel height, pressure gradient, electric field, slip length, Debye length and non-Newtonian behaviour.

Electrokinetics of polymeric fluids in narrow rectangular confinements.

The flow of polymeric liquids in narrow confinements with a rectangular cross section, in the presence of electrical double layers is analyzed here. Our analysis is motivated by the fact that many of the previous studies on the flow of complex fluids tend to focus on highly idealized parallel plate channels, which are markedly different from the rectangular ducts, used in many experiments and devices. We consider the combined electroosmotic and pressure driven flows as well as the streaming potential resulting from a mechanically driven flow. We use two distinct constitutive relations to model the polymeric liquids, namely the simplified exponential Phan-Thien-Tanner (sePTT) model and the Giesekus model, both of which are non-linear viscoelastic models, capable of capturing the shear thinning behavior. We establish that the applied electric field may have a strong influence on the overall flow rate, which rapidly increases with the field strength as well as the extent of viscoelasticity of the fluid. Viscoelasticity and shear thinning behavior also enhance the streaming potential by several fold as compared to a Newtonian medium. We demonstrate that the aspect ratio of a channel has a bigger influence on the net throughput and the streaming potential, when the extent of viscoelasticity is relatively large. We illustrate that for sePTT fluids, the flow is strictly unidirectional, while for Giesekus fluids, secondary flows are inevitably present on account of their non-zero second normal stress coefficient. Although the electric field does not change the overall patterns of these secondary flows, their magnitude does depend on the imposed field strength for combined flows.

Notes on Salvia baldshuanica (Lamiaceae), an endemic species from Middle Asia

We present a critical revision of information about rare and endangered endemic species Salvia baldshuanica (Lamiaceae), included in the Red Books of the USSR and Tajikistan. As the nomenclatural type had been missing, we assembled information on the original herbarium material performed a proper typification of the species name. A chorological analysis of the species distribution in Middle Asia was carried out. To assess the state of the current natural populations, a topographic mapping of localities (Sanglok mountains, two isolated local populations; Sarsaryak ridge, one local population) was made. A narrow edaphic confinement of plants of this species to gypsum-bearing mountain soils has been established. A taxonomic assessment of the key morphological traits of S. baldshuanica confirmed at least the sectional level of its position within the subgenus Leonia. The species was found in nature only three times – in 1883, 1937 and 1979, which confirms its exceptional rarity and high scientific interest.

Book Reviews

The section opens with a review well written by a giant in the field of numerical solution of partial differential equations, Roland Glowinski. In this featured review, he analyzes the book Think Before You Compute: A Prelude to Computational Fluid Dynamics, by E. J. Hinch, in much detail and contributes his own thoughts on appraisal or possibilities for improvement to every chapter of the book. The reviewer's verdict on the book is: “The book is a gem.” The following three reviewed books, written in an earlier and different world, take on a whole new relevance against the background of the current pandemic situation. First, we have the book by Irina Kareva and Georgy Karev, Modeling Evolution of Heterogeneous Populations: Theory and Applications. This book is diligently reviewed by Karen Page, who rates the book as “enlightening" even if it still contains small annoying errors. The following book, Delay-Adaptive Linear Control, by Yang Zhu and Miroslav Krstic, also seems to anticipate some aspects of the current modeling and control of the COVID-19 pandemic. This book is reviewed in detail by Bozenna Pasik-Duncan and is classified as an important contribution to control in delay systems. For the classification and mining of numerous medical data, such as those being generated right now, Mehrshad Sadria and Anita Layton suggest reading Bioinformatics, edited by Andreas D. Baxevanis, Gary D. Bader, and David S. Wishart, and recommend it as an “easy to read, greatly informative, and highly timely” book. Finally, I would like to mention the book by Zhendong Luo and Goong Chen on Proper Orthogonal Decomposition Methods for Partial Differential Equations, which is reviewed by the expert Stefan Volkwein, who praises the book as providing “a really good recipe for the application of the POD method to many nonstationary PDEs,” and also the book Basic Calculus of Planetary Orbits and Interplanetary Flight: The Missions of the Voyagers, Cassini, and Juno, by Alexander J. Hahn, that allows the reader to escape the current narrow earthly confinement in mathematical thoughts and delve into interplanetary explorations.

The in-plane anisotropy of the effective g factors in Al0.25Ga0.75N/GaN based quantum point contacts with narrow channels

The effective g factors (g*) of the lowest three subbands of Al0.25Ga0.75N/GaN-based quantum point contacts (QPCs) are obtained in various magnetic field orientations. The g factors show an anisotropic enhancement compared to those in the two-dimensional electron gas, among which an in-plane anisotropy becomes manifested, when the QPC is depleted from the third to the first subband and the channel width shrinks from the order of 10−7 m–10−8 m. In the one-dimensional (1D) regime with only one subband in the QPC, the in-plane g* perpendicular to the current is evidently larger than the parallel one. The in-plane anisotropy can be attributed to the Rashba spin–orbit coupling (SOC) in the narrow confinement. The reason that the anisotropy can be observed in this work, but not in conventional III–V semiconductors studied previously, is due to the fact that the Al0.25Ga0.75N/GaN-based QPCs have larger polarization-field-induced Rashba SOC and much stronger 1D constriction.

Electroosmosis of a viscoelastic fluid over non-uniformly charged surfaces: Effect of fluid relaxation and retardation time

We investigate the electroosmotic flow of a quasi-linear viscoelastic fluid over a surface having charge modulation in narrow confinements. We obtain analytical solutions using a combination of regular and matched asymptotic expansions in order to describe the viscoelastic flow field and apparent slip velocity besides pinpointing variations of the flow rate and ionic currents due to the surface charge modulation. We demonstrate excellent agreement between the asymptotic analytical solution for the flow field and the full numerical solution in the limiting condition of a thin electrical double layer and weakly viscoelastic fluid. For a wide range of flow governing parameters, we analyze the flow velocity, vortex dynamics, flow rates, and streaming current. We demonstrate that the magnitude of the observed electroosmotic slip velocity is more sensitive to the thickness of the electrical double layer rather than the viscoelasticity of the fluid. We have observed that the contribution of fluid elasticity is prominent in breaking the axial symmetry in the electroosmotic flow with the presence of periodic charge distributions, which is in contrast to the symmetric electroosmotic flow field of a Newtonian fluid over the same charge modulated walls. The results hold the key toward understanding the flow of biological fluids in microfluidic flows by leveraging electrokinetic transport over charge modulated surfaces. We believe that the results of net throughput, streaming current, and vortex dynamics will aid our understanding of the complex fluid behavior and microfluidic mixers.

Densest helical structures of hard spheres in narrow confinement: An analytic derivation

The emergence of helicity from the densest possible packings of equal-sized hard spheres in narrow cylindrical confinement can be understood in terms of a density maximization of repeating microconfigurations. At any cylinder-to-sphere diameter ratio D∈(1+3/2,2), a sphere can only be in contact with its nearest and second nearest neighbors along the vertical z-axis, and the densest possible helical structures are results of a minimized vertical separation between the first sphere and the third sphere for every consecutive triplet of spheres. By considering a density maximization of all microscopic triplets of mutually touching spheres, we show, by both analytical and numerical means, that the single helix at D∈(1+3/2,1+43/7) corresponds to a repetition of the same triplet configuration and that the double helix at D∈(1+43/7,2) corresponds to an alternation between two triplet configurations. The resulting analytic expressions for the positions of spheres in these helical structures could serve as a theoretical basis for developing novel chiral materials.

Magnetohydrodynamic electro-osmotic flow of Maxwell fluids with patterned charged surface in narrow confinements

We study the magnetohydrodynamic electro-osmotic flow of Maxwell fluids through two microparallel plates with patterned charged surfaces. The combined influences of two imposed time periodic electric fields (one along the lateral direction and the other along the axial direction) and an external vertical magnetic field are taken into account. The flow is driven by Lorentz force and electric field force and is 2D due to charge modulated surfaces. Upon the assumptions of the Debye–Hückel linearization, the analytical solutions of the stream function and velocity field are derived. The variations in velocity with the dimensionless relaxation time De, the Hartmann number Ha, and the oscillating Reynolds number Re are depicted graphically. Furthermore, the parameters that influence the generation of vortexes in the flow field are also discussed.

Insights Into Pāhoehoe Lava Emplacement Using Visible and Thermal Structure‐From‐Motion Photogrammetry

AbstractWe present the evolution over 3 months of a 2016–2017 pāhoehoe flow at Kīlauea as it changed from a narrow sheet flow into a compound lava field fed by a stable system of tubes. The portion of the flow located on Kīlauea's coastal plain was characterized using helicopter‐based visible and thermal structure‐from‐motion photogrammetry to construct a series of georeferenced digital surface models and thermal maps on eight different days. Results reveal key influences on the emplacement and evolution of such long‐lived pāhoehoe flows. This region of the flow grew by ~12 × 106 m3 with a near‐constant time‐average discharge rate of 1.2–2.7 m3/s. The development of two tube systems is captured and shows an initial nascent tube enhanced by a narrow topographic confinement, which later inflated and created a topographic inversion that modulated the emplacement of a second flow lobe with its own tube system. The analysis of breakouts at various stages of the field's life suggests that the evolution of the thermal and morphological properties of the flow surface reflect its maturity. Thermal properties of breakouts were used to expand the empirical relationship of breakout cooling to longer timescales. This study contributes to the long‐term development and validation of more accurate predictive models for pāhoehoe, required during the management of long‐lasting lava flow crises in Hawai'i and elsewhere.

Entropy generation on electromagnetohydrodynamic flow through a porous asymmetric micro-channel

Abstract We analyze the heat transfer phenomena in a narrow confinement filled with Couple Stress fluid (taking into account molecule size effect) driven by the simultaneous influence of pressure gradient, electrical potential and the peristaltic pumping in the presence of magnetic field. The effects of Joule heating, permeability of the porous medium and dissipation of energy are taken into account. Entropy generation in terms of Bejan profile and the Nusselt number under different parameters are investigated. The analytical method has been invoked to find the closed from solution of the thermo-fluidic governing equations. The study reveals that the zeta potential has significant importance in controlling velocity and thermal response in the system. The Joule heating effect and Brinkman number both are equally responsible for enhancement of thermal irreversibility measured in terms of Bejan number profile. Thus the study bears potential applications in industrial and biomedical technology for developing microfluidic devices.