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Biomimetic crossflow filtration with wave minimal surface geometry for particulate biochar water treatment [1]

['Mason Anderson', 'Department Of Chemical', 'Biological Engineering', 'University Of Idaho', 'Moscow', 'Idaho', 'United States Of America', 'Vibhav Durgesh', 'Department Of Mechanical Engineering', 'Martin Baker']

Date: 2023-03

Wave minimal surfaces (WMSs) are mathematically defined structures that are commonly observed in nature. Their unique properties have allowed researchers to harness their potential for engineering applications. Since WMSs can be represented by mathematical equations, the geometry can be parametrized and studied using computational fluid dynamics (CFD) for particle separation. Low energy particle separation in water treatment can yield low-carbon footprint technology approaches such as biochar water treatment where removal and recovery of adsorbed N and P on biochar can address water pollution, climate change and food security. The objective of this work was to demonstrate the capability of WMS as a crossflow filtration system to remove particulates in water. For this purpose we used CFD to optimize WMS geometry and studied the performance of the 3D-Printed (3DP) optimized WMS using experimental fluid dynamics (EFD) in a water tunnel. CFD studies quantified planar vorticity, fluid filtrate flux, and particle behavior of WMS. For inflow velocities of 0.2–0.4 m/s, CFD results showed that a reverse wave filter design with convex shape leading-edge, angle of incidence of 90 o , and maximum width of n = 1.0 captured 15–25% of upstream velocity at the filter port. CFD analysis showed more than 95% separation efficiency at velocities and pressures of 0.2–0.32 m/s and 5–35 kPa, respectively. Particle Image Velocimetry (PIV) was used for EFD fluid flow measurements with an optimized wave minimal surface (OMWS). Comparison of OMWS CFD and PIV velocity fields showed good agreement with a root-mean-square error of less than 10%. Particle size analysis showed that the 3DP OMWS could filter particle sizes ranging from 1–30 μm with at least 50% particle count reduction in the filtrate. Thus, we successfully demonstrated a novel framework for analyzing a crossflow water filtration system from conceptual design to initial benchtop experiments using iterative CFD, 3DP, and EFD.

Funding: This publication was developed under Assistance Agreement No. R840087 (GM, MB), awarded by the U. S. Environmental Protection Agency and under Agreement No. 2020-69012-31871 (GM), funded by the U.S. Department of Agriculture to the University of Idaho. This work is also supported by the Idaho Agricultural Experiment Station (GM). It has not been formally reviewed by the funding agencies. The views expressed in this document are solely those of the authors and do not necessarily reflect those of the funding agencies. These agencies do not endorse any products or commercial services mentioned in this publication. The authors would also like thank David Thiessen for support for the water tunnel used in this work (GM). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Introduction

Particle filtration from water has been broadly explored as it has diverse applications encompassing biological, environmental, and industrial areas [1–7]. The science and engineering community has worked extensively in this area to address different aspects of the subject, such as mechanisms involved in solid-liquid interactions [8, 9], improved engineering designs to enhance filtration processes and systems [2, 3, 10] and understanding biological processes such as feeding mechanisms of animals [11–17]. Recently, researchers have explored new technological systems that are inspired by nature [11, 13, 18–21]. In this regard, the current study aims to develop a framework in utilizing computational, experimental fluid dynamics and 3D printing approaches to investigate the potential of minimal surfaces for particulate water treatment.

Novel particle filtration technologies, with lower carbon equivalent (CO 2 e) footprints, can concomitantly address a range of engineering grand challenges [22] and sustainable development goals [23]. Systems thinking in the design stage has shown that life cycle impacts are an increasingly important criteria during the technology innovation process [24, 25]. Addressing the global challenges of clean water, food security and the carbon sequestration required to mitigate climate change, granular and powdered biochar particulates have received considerable attention in adsorptive phosphate and nitrogen removal and recovery from water [26–28]. To this end, our laboratory’s ongoing work in the field of biochar water treatment, especially where the biochar particles can be used to remove and recover phosphorus from water, has demonstrated its potential as an emerging water treatment approach [28–31]. Removing and recovering phosphorus from water addresses the nutrient pollution linked to harmful algae blooms [32, 33] while also recovering non-renewable phosphorus, a vital nutrient for agriculture [34]. However, efficiently capturing back biochar particles with adsorbed phosphorus from the water stream after dosing with traditional dead-end filtration systems requires a considerable energy and pressure gradient, resulting in a significant CO 2 e footprint that can cancel the carbon sequestration benefits of biochar [35].

In nature, energy-efficient filter feeding mechanisms can yield an evolutionary advantage, such as is observed in Earth’s largest creature, the balaenid blue whales [36]. To design an efficient and non-clogging filter, researchers have looked at feeding mechanisms used by marine animals as the possible inspiration for particle filtration. Some of these initial studies have shown the unique design of the filter feeders, e.g., bivalves [16], American paddlefish [11], balaenid whales [12, 14, 15, 17], and manta rays [20, 21]. Wright et al. [16] investigated different filter-feeding bivalve mollusks and their ability to filter out particles as small as bacteria. They found that the bivalves were able to filter bacteria with great efficiency due to the designs of their cilia. Goldbogen et al. [12] and other researchers [14, 15, 17] have studied balaenid whales and their energy efficient feeding strategy despite their gigantic size. Divi et al. [20] studied manta rays’ feeding mechanisms and found that these fishes have wing-like structures to intercept particles (i.e., planktons) that ricochet away from the filter pores. Brooks et al. [11] investigated American paddlefishes’ feeding mechanisms and found that vortices generated in their branchial arches provide a novel mechanism for the suspension, concentration, and transport of particles in the suspension-feeding fish. These studies have shown filter feeding mechanisms have complex designs and even more complex fluid flows that allow for efficiently filtrating out nutrients.

Researchers have used biomimetic designs in several applications ranging from ion-mediated membranes [37, 38], oil-water emulsions filtration [39], and crossflow filtration [13, 19, 40]. Sanderson et al. [13] found that the vortices formed between the gills during crossflow enabled the fishes to capture particles without clogging. The continued efforts helped develop a new filter design such as a helical-shaped filter that transported the particles at the downstream end of the filter [40]. Similarly, Liao et al. [39] prepared a filter mesh inspired by armors and scales of shellfish, which effectively prevented them from marine oil contamination. The results of their mesh design have excellent superhydrophilic and underwater superoleophobic properties suitable for gravity-driven oil-water separations. In another similar study, Clark and San Miguel [19] used a lobe filtration design from a manta ray’s filter-feeding mechanism [20]. They proposed a scaled microfluidic device and showed that the device was capable of filtering particles on the order of 10 μm.

Despite the extensive research effort in using bio-inspired designs, there are several challenges in designing filters using bio-inspired geometries. One such challenge is the complex geometry and fabricating such models can be time and cost-intensive. Therefore, this study focuses on mathematically defined minimal surface geometry for filter design. The minimal surface geometry is commonly observed in nature, and the minimal surface geometries are one of the most energy-efficient designs for the given constraints. Another benefit of using mathematically defined minimal surface geometry design is that it allows for parametric studies and can be fabricated using 3D printing and advanced manufacturing technology.

Minimal surfaces are a widely researched area in mathematics literature [41–45], and are commonly observed in several natural patterns, designs, and fluid flow patterns. Different definitions arise when describing minimal surfaces, and a few are described here. The term minimal surface stems from the idea that a surface is minimal if and only if its mean curvature is zero [45]. Another definition of a minimal surface is the surface if and only if every point has a neighborhood with the least area relative to its boundary [42]. Minimal surfaces can be observed in nature and architecture from the structure of the cerebellum [46], nucleic acid folding in viruses [47], and structural buildings [48, 49]. Minimal surfaces have also been used in particle filtration, such as investigations performed by Sreedhar et al. [50], Thomas et al. [51], and Fu et al. [52] on triply periodic minimal surfaces.

Several researchers have attempted to provide different filtration approaches with varying success. However, there is a lack of comprehensive studies of filter designs that are mathematically defined and incorporate a framework to design filters from concept to a laboratory experiment. Therefore, this work aims to perform a feasibility study utilizing a bio-inspired filtration mechanism and a wave minimal surface (WMS) [44, 53]. For this study, a WMS was selected as it is mathematically defined, allowing for parametrization of the design space for systematic testing.

There are three main objectives for this study. First, computational fluid dynamics (CFD) parametric studies of the WMS were conducted to identify their vortex generation capabilities for particle filtration. Further CFD studies were conducted on the model to configure its increased mass flow rate at the filter pore, leading to the optimized wave minimal surface (OMWS) design. Second, a comparison of CFD studies with experimental fluid dynamics (EFD) measurements was performed for the OMWS. Lastly, the performance of the OMWS design was quantified in lab-scale experiments to assess its filtration capabilities. The initial results from this investigation showed that the OMWS has potential use in particle filtration for a certain range of velocities and particle diameters.

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[1] Url: https://journals.plos.org/water/article?id=10.1371/journal.pwat.0000055

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