Pillar Array Research Articles

Direct laser writing of curved SERS for light-guided enhancement.

Flexible SERS substrates, typically used on irregular surfaces, have unexplored optomechanical effects that could enhance performance. We developed a micromechanically bending structure, i.e. microbender, to study how bending affects SERS substrates' performance. Optical simulations of nanopillar arrays on micro-curved surfaces showed a 25-134% improvement in mean-field localization at the pillar tips for arrays with pillar diameters of 0.4-1μm, pitches of 0.5-0.8μm, and heights of 0.5-4.5μm. Raman measurements showed that SERS intensity increases when in a curved state due to enhanced light scattering, guiding, and field localization. A curved array of 6μm tall pillars (0.5μm diameter, 1μm spacing) produced Raman intensities similar to dense single-voxel arrays with shorter 0.8μm pillars (0.2μm diameter, 0.2μm gaps) in the planar state. This finding suggests that low resolution fabrication technologies can produce curved SERS substrates with similar performance to high resolution planar SERS, offering an alternative to the current "smaller is better" trend through post-fabrication manipulation.

Knox-Saleem kinetic performance limits in liquid chromatography—A contemporary tutorial

The kinetic performance limits evaluated by Knox and Saleem in 1969 are reevaluated herein. Published 55 years ago, the original study did not address several key features of contemporary chromatography. The following features of chromatographic analyses were assumed in the source:•The static operations (isothermal isobaric GC, isocratic isothermal isobaric LC).•The columns packed with discrete particles.•The columns were optimized to deliver the smallest plate height.Additionally, currently obsolete parameters and notations were used complicating comprehension of the original study.In this tutorial focusing mostly on LC, the original Knox-Saleem study is extended to gradient elution LC, to the columns with arbitrary structure (open, packed, pillar array, monolithic, etc.) and to suboptimal operations – all expressed in contemporary notations. The study is based on previously published basic structure-independent equations of column kinetic performance.Some conclusions of this tutorial are different from previous ones. It has been concluded herein that at any pressure (no matter how low) any separation performance (no matter how high) can be achieved as long as the analysis time is acceptable. This seems to contradict with Knox-Saleem statement suggesting that there is “the critical pressure below which a separation number S cannot be achieved however much time is available.” Similar statement was also previously known from Giddings (1962): “critical pressure, pc, the inlet pressure below which a [required, LB] separation can never be obtained”.

Deep cryogenic silicon etching for 3D integrated capacitors: A numerical perspective

One promising approach to increase the capacity density of integral microcapacitors, microsupercapacitors, and microbatteries is three-dimensional structure design, where electrodes are exposed in three dimensions instead of conventional in-plane electrodes. Such structures include nanowires, nanotubes, nanopillars, nanoholes, nanosheets, and nanowalls. In this work, a cryogenic silicon etching process suitable for fabrication of structures with high electrode area is proposed. A numeric model of this process is experimentally calibrated and used for pillar array structure sidewall area optimization. The use of adaptive Runge–Kutta–Fehlberg time integrator allows to achieve almost linear overall computation complexity as a function of simulated etching time, despite the linear increase in conductance computation complexity with depth. A rule for choosing optimal geometric structure parameters under technological constraints is formulated. An optimized trefoil-like structure is proposed, resulting in a total 5.5% increase in sidewall area with respect to the hexagonal array of circular pillars, resulting in 20.33 sidewall area per unit chip area for 30 min long etch or 31.80 for 60 min long etch.

Polarization‐Controlled Diffractions of Submicron Pillar Arrays of Azo Molecular Glass for Image Recording and Reconstruction

Recording and manipulating optical waves with functional structures are crucially important for many applications. Herein, the submicron pillar arrays of an azo molecular glass (IA‐Chol) are explored to show functional synergy of a recording medium and a diffractive optical element. The image recording is achieved through the pillar deformation along the electric‐field oscillation direction of incident light. When illuminated with a polarized beam, the reconstructed images appear in the first‐order diffraction spots of the pillar array with the tailored intensity distributions depending on the states of polarization of the recording beam and the image reconstruction beam. This approach enables several images to be recorded in the adjacent zones of the same pillar array using lights with different polarization directions, and then the images are reconstructed separately or simultaneously upon the polarization directions of the illumination light. Furthermore, the topographic features of the pillar array after the recording are replicated by replica‐molding to the surfaces of polydimethylsiloxane (PDMS) slices as negative replicas and transformed to surfaces of poly(methylmethacrylate) (PMMA) films through hot‐embossing. The PDMS and PMMA replicas are highly transparent in the visible light range and able to produce the reconstructed images with light in a wide‐wavelength extent.

Enhanced Phase Change Heat Transfer with Fused Deposition Modeling (FDM) Printed Pit and Pillar (Pi2) Arrays

Phase change heat transfer, crucial in thermal management systems, can be significantly enhanced through optimized surface structures. This study investigates pool boiling heat transfer enhancement using 3D printed structures with carefully designed pillar and pit geometries. We present a novel approach combining the Dual Rise model with separate liquid–vapor pathways to improve Critical Heat Flux (CHF) and Heat Transfer Coefficients (HTC). Using copper-infused Polylactic Acid (PLA) filaments, we created and sintered structured surfaces featuring pit-assisted nucleation sites, interpillar spacing for vapor escape, and pillar roughness for enhanced liquid supply. Experiments with deionized water and ethanol under atmospheric pressure demonstrated substantial improvements over plain surfaces: water showed an 87% increase in CHF and 39% in maximum HTC, while ethanol exhibited even greater enhancements of 122% in CHF and 61% in HTC. These improvements are attributed to the synergistic effects of optimized surface geometry and separated liquid–vapor pathways, reducing counterflow resistance and improving hydrodynamic stability. A theoretical framework based on the Dual Rise model explains these enhancements, providing insights into coupled capillary action and hemiwicking effects in boiling heat transfer. The study introduces predictive models for CHF and HTC enhancement, offering valuable tools for future design optimization in applications ranging from electronics cooling to power plant thermal management and advanced heat exchangers.

Assessment of pillar-array electrodes for electrochemical flow reactors using a novel hydrodynamic electrode performance factor

This work introduces and validates a Hydrodynamic Electrode Performance Factor (HEPF) for flow reactors. Traditional approaches to electrode optimization often rely on separated mass transfer and pressure drop metrics, hindering comparisons. We address this issue by combining electrochemical and hydrodynamic parameters through a new mathematical expression. This formulation draws inspiration from established equations in heat transfer and the widely recognized Chilton-Colburn analogy, aiming to develop a quantification method independent of the experimental arrangement. The HEPF is complementary to the well-established volumetric mass transfer coefficient and to Storck’s energetic effectiveness postulates for electrochemical reactors. Additionally, this study validates the proposed equation experimentally and then applies it to evaluate pillar array electrodes using 2D computational fluid dynamics simulations for laminar flow conditions. Both experimental and simulation approaches are used to analyze the hydrodynamic behaviour of the electrodes, utilizing the Forchheimer and Hagen-Poiseuille numbers. Notably, preliminary turbulence effects are observed at Reynolds numbers as low as 50 to 125. Visualization of velocity streamlines revealed distinct wake formation behind the pillars at these low Reynolds numbers. This study also explores how reactor inlets, outlets, and tubing pressure losses affect electrode performance. Results emphasize the importance of considering pressure drop, which is integral to the new hydrodynamic performance factor. Analysis of pillar array electrodes demonstrates that reducing both interpillar distance and pillar radius leads to improved electrochemical performance

Uniform carbon pillars array grown on boron doped diamond for high-performance supercapacitors and hydrogen evolution reactions

Carbon materials have marvelous ability in energy storage and microelectronics as a result of the high specific surface area and electrical conductivity. However, the low stability and the low power density caused by low potential window make it particularly difficult for their application in aqueous electrolysis. In this study, boron doped diamond (BDD) with wide potential window is used as substrate and Ni as catalyst to grow uniform carbon pillars (CP) by microwave plasma chemical vapor deposition method. The composite structure (CP/BDD) yields significant specific capacity (91.64 mF cm−2 at 0.1 mA cm−2) and cycling stability (92.3 % retention rate after 20,000 cycles) when used as the electrode of supercapacitors, superior to most of BDD-based electrodes. The prepared symmetrical supercapacitor devices maintain their excellent electrochemical performance characteristics (power density of 4.4 mW cm−2 and energy density of 13.4 μW h cm−2), as well as high cycling stability. In addition, the electrode has considerable application potential in electrochemical hydrogen production with low hydrogen evolution potential and small Tafel slope value. These results illustrate the potential of BDD based composites for using as energy storage electrodes for electronic products and energy conversion equipment.

A GexSe1-x switch-only-memory technology through polarized atomic distribution

Ovonic threshold switching (OTS) materials that are frequently used with a resistor (1S1R) in memory devices have been found to show controllable and reversible memory properties, which could enable new memory architectures. Here, we examine the impact of composition on the polarity-dependent memory properties of GexSe1-x OTS materials and reveal that an increase in Se content results in a higher set voltage threshold (Vth), a lower reset current (IRST), and a higher set energy. Specifically, Ge56Se44 demonstrates two distinct Vth of 5.1 and 3.8 V, which retain after annealing at 85 ℃ for one day. We fabricated Ge56Se44 into 1000 by 1000 cross-point pillar arrays and tested 100 of them. The results demonstrated that these Ge56Se44 devices show similar memory properties with a reset speed of 1 μs, a set speed of 50 ns, and an endurance of over 105 cycles. Interestingly, the Ge56Se44 pillars’ reset and set states could be attributed to polarized atomic distributions. By utilizing GexSe1-x, we demonstrate a true cross-point switch-only-memory technology and provide mechanistic insights for self-selecting OTS materials.

Streamline-directed tunable deterministic lateral displacement chip: A numerical approach to efficient particle separation

In conventional Deterministic Lateral Displacement (DLD), the migration behavior of a particle of specific size is determined by the critical diameter (Dc), which is predefined by the device's geometry. In contrast to the typical approach that alters the angle between the pillar array and fluid streamlines by modifying the geometrical parameters, this study introduces a novel perspective that focuses on changing the direction of the streamlines. The proposed technique offers a tunable DLD chip featuring a straightforward design that allows for easy fabrication. This chip features one completely horizontal pillar array with two bypass channels on the top and bottom of the DLD chamber. The width of these bypass channels changes linearly from their inlet to their outlet. Two design configurations are suggested for this chip, characterized by either parallel or unparallel slopes of the bypass channels. This chip is capable of generating a wide range of Dc values by manipulating two distinct control parameters. The first control parameter involves adjusting the flow rates in the two bypass channels. The second control parameter entails controlling the slopes of these bypass channels. Both of these parameters influence the direction of particle-carrying streamlines resulting in a change in the path-line of the particles. By changing the angle of streamlines with pillar array, the Dc can be tuned. Prior to determining the Dc for each case, an initial estimation was made using a Python script that utilized the streamline coordinates. Subsequently, through FEM modeling of the particle trajectories, precise Dc values were ascertained and compared with the estimated values, revealing minimal disparities. By adjusting the flow rate and slope of the bypass channels, maximum Dc ranges of 4–10 μm and 8–13 μm can be achieved, respectively. This innovative chip enables the attainment of Dc values spanning from 0.5 to 14 μm.

Nondestructive Demolding of Structure-Designable High-Aspect-Ratio Nanoimprint Template.

Demolding is a crucial step in nanoimprint lithography (NIL) for successfully transferring template structures onto resist materials. The process, however, is often hindered by the adhesion and friction between the template and resist, leading to inevitable defects on the replicas and posing challenges in replicating templates with high-aspect-ratio (HAR) structures. Here, we introduce a novel approach using the dissolvable template method to achieve the nondestructive demolding of structure-designable HAR nanoimprint templates. The templates were fabricated by the 3D lithography technology, employing a positive photoresist that can be easily dissolved in alkaline solutions after exposure to ultraviolet (UV) radiation. By implementing this method, we successfully transferred dense arrays of pillars with a minimal diameter of 1.2 μm and a significant aspect ratio of 18, as well as a microlens array diffuser with randomly distributed structural parameters. The dissolvable template method paves the way for stress-free demolding, broadening NIL's application range.

Microfluidics and Chip Development

During the course of the summer, I had the privilege to work with Dr. Carlos Escobedo and his team of researchers on the topics of microfluidics and Lab-On-Chip (LOC) technology. Microfluidics is a branch of fluid dynamics which utilizes small volumes of fluid to perform tests under ideal conditions, and LOC is the process of using microfluidics for experiments in small-scale environments. I participated in two LOC projects, the first for bacterial analysis and the second for microplastic separation. The goal of the first project was to observe if Vibrio Cholerae bacteria was attracted to a variety of chemo attractants. To observe this interaction under microfluidic conditions, we developed a chip which when flooded with chemoattractant trapped a portion in the chip. We could then remove the non-entrapped chemoattractant from the sides and refill the chip with bacteria. Observations of the bacteria’s movement were then taken using a microscope attached to a digital camera. The second project focused on microplastics, which are plastic particulates under 5mm in diameter, our smallest sample being 10μm. Due to their size standard filtering techniques were ineffective at separating them, which led to us using Deterministic Lateral Displacement (DLD). DLD utilizes an array of pillars to create spots of changing pressure for passing particles. The array is designed so larger particles are unaffected while smaller particulates will be redirected and collected separately. To arrange the plastics into their types, a centrifugal design was used. This design functions similarly to a centrifuge, which by rapidly spinning a substance separates out materials based on density. The chip works under a similar theory, but instead uses a spiral channel to force the particles in a repeated circular spinning motion. The particles then exit with differing directionalities based on where they were in the channel, allowing for collection.

Biomimetic fractal pillars for the thermal–hydraulic enhancement of a vapor chamber

Owing to their remarkable thermal–hydraulic performance, vapor chambers have diverse applications, especially for cooling electronic devices. However, the performances of circular and noncircular pillars throughout the entire vapor chamber under identical wick volume conditions have been compared in very few studies. In this study, a series of noncircular pillar arrays featuring biomimetic tree-like fractal networks is introduced. The incorporation of fractal pillars significantly enhances the thermal–hydraulic performance of the vapor chamber because the gas–liquid interface area is extended. Compared to a vapor chamber with circular pillars, the maximum condensation surface temperature difference, total thermal resistance, and liquid pressure drop of this vapor chamber with fractal pillars are reduced by up to 57.8 %, 13.8 %, and 10.9 %, respectively. In particular, with large branch levels and pillar diameters, the fractal structure is pivotal for boosting the overall performance. When the number of pillars is increased, the fractal structure's impact on the thermal performance reaches a limit, whereas its boosting effect on the flow performance weakens. This study is a pioneering exploration of the application of stretched geometries in pillar-type vapor chambers, with fractal pillars utilized in showcase demonstrations.

Exploring three-dimensional photoinhibition to enhance vat photopolymerization: A preliminary study

Vat photopolymerization (VPP) based additive manufacturing (AM) technologies print 3D components by using light to selectively cure photosensitive resins. In VPP-based AM, one outstanding challenge remains in controlling the over-curing, which is mainly caused by the diffusive and/or excessive photo-induced species such as free radicals and can severely affect the geometric properties of as-printed parts. Common practices rely on formulating proper resins or optimizing exposure parameters to address the vertical over-curing but often ignore the lateral over-curing. In this work, we develop a new VPP process of photoinhibition aided photopolymer AM (PinPAM) to comprehensively address over-curing issues in both vertical and lateral dimensions for enhancing the properties of as-printed geometry. The PinPAM method incorporates an adaptive photoinhibition zone, generated both surrounding and underneath the curing zone on a layer basis. This differs from current literature approaches that utilize photoinhibition to create a higher deadzone to increase print speed or constrain vertical profiles for achieving volumetric VPP AM. We present several preliminary experimental study cases involving pillar array sample printing. By comparing part dimensions and shapes resulting from traditional VPP and PinPAM, our experiments prove the concept of PinPAM and demonstrate its potential to address over-curing in VPP. Furthermore, we present an initial case study on optimizing the PinPAM process for printing cylinder samples with targeted dimensions, illustrating the planning and implementation of PinPAM. A discussion on future research directions to establish PinPAM is included. The developed PinPAM opens up a new avenue for improving VPP printed parts’ geometrical properties and facilitating its adoption in precision fabrications that demand dimensional accuracy and resolution.

Selective dynamic band gap tuning in metamaterials using graded photoresponsive resonator arrays.

The introduction of metamaterials has provided new possibilities to manipulate the propagation of waves in different fields of physics, ranging from electromagnetism to acoustics. However, despite the variety of configurations proposed so far, most solutions lack dynamic tunability, i.e. their functionality cannot be altered post-fabrication. Our work overcomes this limitation by employing a photo-responsive polymer to fabricate a simple metamaterial structure and enable tuning of its elastic properties using visible light. The structure of the metamaterial consists of graded resonators in the form of an array of pillars, each giving rise to different resonances and transmission band gaps. Selective laser illumination can then tune the resonances and their frequencies individually or collectively, thus yielding many degrees of freedom in the tunability of the filtered or transmitted wave frequencies, similar to playing a keyboard, where illuminating each pillar corresponds to playing a different note. This concept can be used to realize low-power active devices for elastic wave control, including beam splitters, switches and filters.This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'.

Energy Dissipation during Wenzel Wetting via Roughness Scale Interface Dynamics.

A numerical method is proposed to simulate the roughness scale interface dynamics of a slow-moving fluid interface as it advances over a chemically homogeneous rough surface. Analysis of the governing augmented Navier-Stokes and Young's boundary condition equations shows how the local interface behavior can be represented via a series of incrementally advanced equilibrium interfacial morphologies. Combined with a roughness scale mechanical energy balance [Harvie, D. J. E. Contact-angle hysteresis on rough surfaces: mechanical energy balance framework. J. Fluid Mech. 2024, 986, A17], the simulations are used to calculate the energy dissipation associated with a surface decorated with a periodic array of round-edge square pillars. This dissipation is used to predict static contact angle hysteresis (CAH) from knowledge of just the surface roughness topography and equilibrium contact angle. We show that the energy dissipated varies approximately as ϕln ϕ (with ϕ being the area fraction), becoming zero as ϕ → 0. The CAH predicted by our method is in good agreement with the experimental results of Forsberg et al. [Forsberg, P. S.; Priest, C.; Brinkmann, M.; Sedev, R.; Ralston, J. Contact line pinning on microstructured surfaces for liquids in the Wenzel state. Langmuir 2010, 26, 860-865], thereby demonstrating that our numerical method of simulating interfacial dynamics adequately captures the real interface motion, as well as illustrating how far-field contact angle and energy dissipation approaches are consistent for this surface. We also compute CAH for an interface moving at 45° to the surface periodicity direction to show that the experimental measurements are bracketed by the 0° and 45° advance direction results. The proposed method opens up the field to quantitative analysis, surface functionalization, and design for different specific applications.

Microscopic Particle Image Velocimetry Analysis of Multiphase Flow in a Porous Media Micromodel.

Pore-scale oil displacement behavior was investigated in a porous media micromodel using microscopic particle image velocimetry (μPIV). Porous media micromodels consisting of an ordered square array of cylindrical pillars with 50 and 70% porosities were fabricated with photolithography. The oil displacement was performed with the injection of water at flow rates of 37.5, 75, and 150 μL/h. These flow rates correspond to Reynolds number of 1.1 × 10-2, 2.2 × 10-2, and 4.4 × 10-2, respectively in the 50% porous channel, and 1.84 × 10-3, 3.69 × 10-3, and 7.38 × 10-3, respectively in the 70% porous channel. The capillary numbers for these flow rates are 2.18 × 10-5, 4.36 × 10-5, and 8.72 × 10-5, respectively in the 50% porous channel, and 1.56 × 10-5, 3.12 × 10-5, and 6.23 × 10-5, respectively in the 70% porous channel. The micromodel is initially saturated with oil, with the invading water phase following the path of least resistance as it displaces the oil. The μPIV data were used to construct probability density functions (PDFs) which show an initial, nonzero, peak in transverse velocity as the water enters the micromodel. The PDFs broaden with time, indicating that the water is spreading, before retracting to a peak velocity of 0 mm/s, indicating that the water displacement has achieved equilibrium. We developed a model based on conservation of mass to describe the efficiency of the displacement process. All flow conditions demonstrate peak displacement efficiency when the amount of oil phase displacement is ∼9 pore volumes in 50% porous channel and ∼4 pore volumes in 70% porous channel.

Optimization of passive micromixers: effects of pillar configuration and gaps on mixing efficiency

Chemical bioreactions play a significant role in many of the microfluidic devices, and their applications in biomedical science have seen substantial growth. Given that effective mixing is vital for initiating biochemical reactions in many applications, micromixers have become increasingly prevalent for high-throughput assays. In this research, a numerical study using the finite element method was conducted to examine the fluid flow and mass transfer characteristics in novel micromixers featuring an array of pillars. The study utilized two-dimensional geometries. The impact of pillar configuration on mixing performance was evaluated using concentration distribution and mixing index as key metrics. The study explores the effects of pillar array design on mixing performance and pressure drop, drawing from principles such as contraction–expansion and split-recombine. Two configurations of pillar arrays, slanted and arrowhead, are introduced, each undergoing investigation regarding parameters such as pillar diameter, gap size between pillar groups, distance between pillars, and vertical shift in pillar groups. Subsequently, optimal micromixers are identified, exhibiting mixing efficiency exceeding 99.7% at moderate Reynolds number (Re = 1), a level typically challenging for micromixers to attain high mixing efficiency. Notably, the pressure drop remains low at 1102 Pa. Furthermore, the variations in mixing index over time and across different positions along the channel are examined. Both configurations demonstrate short mixing lengths and times. At a distance of 4300 μm from the inlet, the slanted and arrowhead configurations yielded mixing indices of 97.2% and 98.9%, respectively. The micromixers could provide a mixing index of 99.5% at the channel’s end within 8 s. Additionally, both configurations exceeded 90% mixing indices by the 3 s. The combination of rapid mixing, low pressure drop, and short mixing length positions the novel micromixers as highly promising for microfluidic applications.

Printing pillar array structure of electrodes facilitating ion diffusion and electron transport for high-performance asymmetric microsupercapacitors

The asymmetric microsupercapacitors (MSCs) are appealing power sources for miniaturized electronic devices owing to their high capacitance and wider working voltage window. However, the sluggish ion diffusion and poor electron transport in pseudocapacitive electrodes result in confined electrochemical performance of devices. In this work, we propose the pillar array structure of electrodes via 3D printing V2O5 (VN) nanosheets and graphene composite inks to boost the electrochemical performance of asymmetric MSCs. The V2O5 (VN) nanosheets and graphene sandwich each other can deliver a high electrical conductivity. The pillar array structure of electrodes shortens ion diffusion pathway to endow the electrodes with fast kinetics. The asymmetric MSCs achieve an impressive energy density of 44.86 μWh cm−2 and power density of 1.78 mW cm−2, powering a pressure sensor for 20 000 s. This strategy developed here is very helpful to promote the practical applications of MSCs.

Pillar Array Mixer for Postcolumn Derivatization Integrated into Liquid Chromatography-Based Microfluidic Device.

The chemical derivatization of target analytes can enhance the sensitivity and selectivity of separation-based methods for metabolite analysis using microfluidic devices. However, the development of chromatography-based microfluidic devices with integrated derivatization units is challenging. In this study, a novel derivatization unit with a pillar array (PA)-based mixing channel was developed for postcolumn derivatization during on-chip liquid chromatography (LC). The PA mixer enhanced mixing between the derivatization reagents and analytes in the transverse direction, while preventing analyte dispersion in the flow direction. After the concept was confirmed using computational fluid dynamics analysis, microfluidic devices with a LC column and PA mixer were fabricated on a 20 × 20 mm silicon plate. Fluid experiments were performed using a PA mixer with a pillar size of 5 or 10 μm or a hollow-channel mixer, which revealed that the PA mixer enhanced transverse mixing without increasing the width of the analyte peak. Moreover, the developed device enabled the analysis of three amino acids within 40 s by separation via hydrophilic interaction chromatography followed by postcolumn fluorogenic derivatization with naphthalene-2,3-dicarboxaldehyde and fluorescence detection. Our results demonstrate the potential of integrated derivatization units for the development of micrototal analysis systems for use in bioanalysis.

Behavioral transition of a fish school in a crowded environment.

In open water, social fish gather to form schools, in which fish generally align with each other. In this work, we study how this social behavior evolves when perturbed by artificial obstacles. We measure the behavior of a group of zebrafish in the presence of a periodic array of pillars. When the pillar density is low, the fish regroup with a typical interdistance and a well-polarized state with parallel orientations, similarly to their behavior in open-water conditions. Above a critical density of pillars, their social interactions, which are mostly based on vision, are screened and the fish spread randomly through the aquarium, orienting themselves along the free axes of the pillar lattice. The abrupt transition from natural to artificial orientation happens when the pillar interdistance is comparable to the social distance of the fish, i.e., their most probable interdistance. We develop a stochastic model of the relative orientation between fish pairs, taking into account alignment, antialignment, and tumbling, from a distribution biased by the environment. This model provides a good description of the experimental probability distribution of the relative orientation between the fish and captures the behavioral transition. Using the model to fit the experimental data provides qualitative information on the evolution of cognitive parameters, such as the alignment or the tumbling rates, as the pillar density increases. At high pillar density, we find that the artificial environment imposes its geometrical constraints to the fish school, drastically increasing the tumbling rate.