382 research outputs found

    A pilot-scale study of dynamic response scenarios for the flexible operation of post-combustion CO2 capture

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    AbstractThe ability to operate flexibly is critical for the future implementation of carbon capture and storage (CCS) in thermal power plants. A dynamic test campaign examines the response of a CO2 absorption/desorption pilot-scale plant to realistic changes in flue gas flow rates and steam supply, representative of the operation of a Natural gas combined cycle (NGCC) plant fitted with post-combustion capture. Five scenarios, demonstrating the operational flexibility that is likely to be encountered in an energy market with significant penetration from intermittent renewables, are presented, with 30% monoethanolamine (MEA) as the absorbing solvent. It complements a wider effort on dynamic modelling of these systems where a lack of dynamic plant data has been reported.The campaign focuses on analysing critical plant parameters of the response of the pilot plant to a gas turbine shutdown, a gas turbine startup and three enhanced operational flexibility scenarios, including two for power output maximisation and one for frequency response with a rapid increase of steam supply to the reboiler. The campaign also demonstrates the use of continuous in situ solvent lean loading measurement with the use of a novel online continuous liquid sensor.It confirms that no significant barriers to flexible operation of amine post-combustion capture are found, although there remains scope for the improvement of plant response. Solvent inventory and circulation times are found to have a significant effect on capture rate during certain dynamic operations. A large solvent inventory increases total circulation times, which can result in additional time being required for the plant to return to steady state following a perturbation. The plant is forced to operate with a non-optimal capture rate while the solvent loading at the absorber inlet stabilises is identified as a potential impact.Use of interim solvent storage and continuous online measurement of solvent CO2 loading, combined with comprehensive knowledge of liquid circulation times and potential mixing effects, are suggested as methods for improving plant response to dynamic operation, thereby increasing CCS plant flexibility

    A Novel Immersed Boundary Method for Direct Numerical Simulations of Solid-Fluid Flows

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    This thesis has been submitted in fulfilment of the requirements for a postgraduate degree (e.g. PhD, MPhil, DClinPsychol) at the University of Edinburgh. Please note the following terms and conditions of use: • This work is protected by copyright and other intellectual property rights, which are retained by the thesis author, unless otherwise stated. • A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. • This thesis cannot be reproduced or quoted extensively from without first obtaining permission in writing from the author. • The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the author. • When referring to this work, full bibliographic details including the author, title, awarding institution and date of the thesis must be given

    Interfacial dynamics in counter-current gas-liquid flows

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    This dissertation considers the genesis and dynamics of interfacial instability in vertical laminar gas-liquid flows, using as a model the two-dimensional channel flow of a thin falling film sheared by counter-current gas. The methodology is linear stability theory by means of Orr-Sommerfeld analysis together with direct numerical simulation of the two-phase flow in the case of nonlinear disturbances. The influence of two main flow parameters on the interfacial dynamics, namely the film thickness and pressure drop applied to drive the gas stream, is investigated. To make contact with existing studies in the literature, the effect of various density and viscosity contrasts as well as surface tension is also examined. Energy budget analyses based on the Orr-Sommerfeld theory reveal various coexisting unstable modes (interfacial, shear, internal) in the case of high density contrasts, which results in mode coalescence and mode competition, but only one dynamically relevant unstable interfacial mode for low and intermediate density contrast. Furthermore, high viscosity contrast and increases in surface tension lead to some amount of mode competition for thin film. A study of absolute and convective instability for low density contrast shows that the system is absolutely unstable for all but two narrow regions of the investigated parameter space. These regions are extended at intermediate density contrast and exhibit only small changes with increased viscosity contrast or surface tension. Direct numerical simulations of the system with low density contrast show that linear theory holds up remarkably well upon the onset of large-amplitude waves as well as the existence of weakly nonlinear waves. For high density contrasts corresponding more closely to an air-water-type system, linear stability theory is also successful at determining the most-dominant features in the interfacial wave dynamics at early-to-intermediate times. Nevertheless, the short waves selected by the linear theory undergo secondary instability and the wave train is no longer regular but rather exhibits chaotic motion. Furthermore, linear stability theory also predicts when the direction of travel of the waves changes - from downwards to upwards. The practical implications of this change in terms of loading and flooding is discussed. The change in direction of the wave propagation is represented graphically for each investigated system in terms of a flow map based on the liquid and gas flow rates and the prediction carries over to the nonlinear regime with only a small deviation. Besides the semi-analytical and numerical analyses, experiments with an practically relevant setup and flow system have been carried out to benchmark and validate the models developed in this work

    Development of an integrated complex 3D fluidic device assembled from fully characterised functional blocks: Michaelis-Menten enzyme kinetics analysis as a case study

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    The work presented in this thesis demonstrates a new approach to the design of integrated uidic devices. Most `lab-on-a-chip' are in fact `chips-in-a-lab'. The equipment used to operate them, such as microscopes and syringe pumps, is bulky, expensive and the portability is non-existent. Fluidic devices operate on multiple domains, such a fludics, pneumatics, sensing, control, etc. By integrating the domains to a single device, cost can be reduced and portability increased. A new manufacturing process was developed to allow for the integration of multiple domains. The vast majority of fluidic devices are two-dimensional, made via soft lithography, which limits the complexity and integration of other components. Three- dimensional fluidic devices can be used to create complex intricate networks and can include sensors, actuators and optics. A negative mould was 3D printed in Acrylonitrile Butadiene Styrene (ABS), encased in Polydimethylsiloxane (PDMS) before being placed in an acetone bath. Because of the swelling properties of ABS in solvents, Acetone could reach the embedded ABS. ABS was liquefied in the presence of acetone, making it possible to be flushed from the PDMS, leaving a void. Following the development of the manufacturing process, functional fluidic blocks were developed to create more complex devices based on usage. Each block was designed to perform a given task, including a photometric sensor, a proportional valve, a turbulent flow mixer, and storage wells. Using the blocks that were developed, a device designed to perform Michaelis-Menten enzyme kinetics analysis was demonstrated. The device was operated by a combination of a custom PCB and a Matlab GUI, thus creating an integrated system. Enzyme kinetics were analysed by determining the initial reaction rate of the enzyme-catalysed reactions for various concentration of its substrate. In order to determine reaction rates, it is common to monitor the opacity of the reaction product over time. This is often achieved by using a substrate (or a substrate analogue) which produces a product with a unique optical absorbance, thus the opacity of the product can be monitored by absorption spectroscopy. The experiment was repeated for multiple concentrations before the kinetics were extrapolated. The device created can perform the same task, as well as automating the mixing of any concentration necessary for the kinetic analysis, at fraction of the cost of commercial equipment

    Fundamentals of dropwise wetting and evaporation phase-change of binary mixture droplets on micro-decorated surfaces

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    Almost every aspect of our daily lives involves liquid-surface interactions and is intimately related to the physicochemical properties of the substrate as well as those of the liquid. Understanding the mechanisms taking place at the initial state of the evaporation process i.e., wettability, and during the evaporation of droplets is of great interest to many industrial, biological, and medical applications. This research investigates experimentally the initial wettability states and the evaporation modes for droplets of pure water, pure ethanol and their binary mixture, accessing a wide range of surface tensions, on hydrophobic and hydrophilic micro-pillared surfaces with fixed height and diameter whilst varying the spacing between the pillars. On one hand, the initial wetting states of pure fluids and their binary mixtures on intrinsically hydrophobic micro-decorated surfaces are first studied and a wetting regime map is proposed. This regime map predicts the droplets’ symmetrical and asymmetrical shapes and wetting dependence on the fluid surface tension and the surface structure on the hydrophobic microstructured surfaces, which in turn govern the subsequent evolution of the droplet contact angle and contact radius. Four different evaporation modes have been observed which are consistent with the literature and further two evaporation modes have been revealed here for the first time, namely, increasing contact angle mixed-sick- slip mode and decreasing contact angle mixed-stick-slip mode. On the other hand, on intrinsically hydrophilic surfaces, the same systematic experimental study is applied using the same fluids and the same microstructured surfaces. It is remarked that the wettability and evaporation on hydrophilic structured surfaces can be affected by ambient exposure after subjecting the surfaces to air plasma cleaning, which eventually removes any deposition of hydrocarbons ever present in the ambient. Unlike the hydrophobic surfaces, the hemi-wicking and spreading regimes are further observed on these surfaces which, consequently, affect the evaporation process. The same six evaporation modes have been observed on these surfaces with different durations though. Investigating the initial wetting and the evaporation modes can lead to a better understanding of choosing the proper structure and wettability (and/or ambient exposure) combined with the correct binary mixture concentration to be specifically tailored to different applications

    Design and development of catalytic hollow fibre-based reactors for methane emission abatement under extreme conditions

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    Natural gas is playing a key role in the decarbonisation of our energy system. This transition fuel is the cleanest fossil fuel and its combustion produces 50% less carbon dioxide than coal and 30% less than oil per unit energy generated. However, natural gas is itself a greenhouse gas responsible for a third of all global warming since pre-industrial levels. Natural gas-powered processes such as electricity production, industrial operations, residential heating and natural gas-fuelled vehicles inevitably emit small concentrations of unburned methane. Due to their low concentration (i.e. 300-1500 ppmV), these residual methane emissions have long been overlooked. As a result, there is no direct legislation addressing them and, today, an effective technology to abate these emissions is unavailable. The objective of this work is to develop a residual methane after-treatment technology that is cost-effective, long-lived and compact. The technology must be effective under real conditions and be resistant to sulfur poisoning at low temperature (i.e. 450°C), the main limitation faced by traditional precious metal-based catalysts. In order to evaluate the performance of the technology presented herein, reaction studies under real and extreme conditions as well as thorough characterisation of the materials have been fulfilled. This work has successfully underpinned the first hollow fibre after-treatment for residual methane emission abatement. This technology combines a non-precious iron and chromium oxide catalyst with a ceramic hollow fibre-based support. The developed catalyst, which is a mixture of hematite, eskolaite and traces of iron (II) chromite, has shown high resistance to sulfur poisoning during the 1000 h reaction study under sulfur dioxide concentrations 20 to 100 times larger than normal levels. Even though the catalyst was initially deactivated, it retained a third of its original activity. The long-term activity of the catalyst has been attributed to the highly sulfur-resistant eskolaite phase. In comparison, state-of-the-art precious metal-based catalysts are deactivated within hours under similar conditions. In addition, when compared to packed bed reactors, hollow fibre reactors have proven to be 3 to 5 times more efficient in terms of methane catalytic oxidation per unit mass of catalyst. Moreover, the technology has proven to be effective under real operating cycles (i.e. 10 thermal shocks) making it the ideal candidate for the development of commercial residual methane emission after-treatments. Finally, this technology has the potential to reduce an estimated 5.6 billion cubic metres annual residual methane emissions arising from electricity production, industrial and residential heating as well as transportation [1,2]. The global warming effect of these annual emissions over 20 years is equivalent to 470 billion cubic metres of carbon dioxide, a volume similar to the water volume of Lake Erie, one of the five Great Lakes of North America. Furthermore, industrialising this technology will pressure legislators to include residual methane emissions in future greenhouse gas regulations

    Fading correlation of co-located transmitters

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    Fading or attenuation of a signal due to environment is a phenomenon often encountered in wireless communications. It is expected that co-located transmitters i.e. transmitters placed very close to each other show a high signal fading correlation due to the presence of similar fading environment. In this thesis, we present an experimental study of this phenomenon. Correlation of received signal strengths obtained from co-located transmitters in dynamically varying environments indicate that the large scale signal variations (shadow fading) are highly correlated while the small scale variations (multipath or fast fading) show a low correlation. Highly correlated large scale variations suggest a presence of same large shadowing elements in the transmit-receive path while a low correlation among the multipath variations is due to mutual coupling between the antennas at very close distances. This has two implications: it suggests that shadow fading variations can serve as an indicator of the co-location of closely spaced transmitters while the multipath variations cannot. However, low multipath signal correlations suggest that antenna diversity could be investigated for implementation in mobile handsets.M.S.Includes bibliographical referencesby Prashant Jadha

    Numerical study of microfluidic effects and red blood cell dynamics in 'deterministic lateral displacement' geometries

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    The last two decades have seen microfluidics gaining increasing interest from the fields of medical diagnostics and bio-chemical processes, due to its immense potential for point-of-care diagnostic applications. Since blood plays a crucial role in many physiological and diagnostic processes, red blood cells (RBCs) have been the focus of a large volume of microfluidics research. The isolation of red blood cells and other blood components, based on the manifest morphological characteristics, is required in many applications, e. g. flow cytometry. The deterministic lateral displacement (DLD) is one such popular microfluidic technique that has shown great promise toward cellular separations. The DLD technique separates particles based on their hydrodynamic size. It has been demonstrated for size-based separations down to unprecedented size resolutions of ~ 10 nm. The DLD consists of a large number of obstacle pillars placed in a microfluidic channel. The layout of these obstacles is such that the obstacle array presents a fixed angle to the average fluid flow through the microfluidic channel. Size-based separation comes about due to steric interaction of particles with the pillars. Particles larger than a ‘critical’ size are forced to move along the obstacle array incline. The larger particles, following the array incline, are displaced perpendicular to the average flow direction, and are said to be on the displacement mode. Particles smaller than this critical size flow along the average fluid flow direction, zigzagging around the obstacles. The trajectories followed by these smaller particles are classified as zigzag mode. Micro-particles therefore follow different trajectory modes based on their size, eventually leading to their spatial separation. The particles are separated passively, i. e. other than the pressure drop needed to drive the fluid flow through the DLD micro-channel, there is no need for any external forces for particle sorting. Numerous studies since the advent of the DLD have focussed on widening the scope of applications covered by the technique. In this thesis, I take a more physical approach, focussing on understanding the microhydrodynamics and RBC dynamics within the DLD geometries. For these investigations, I have used an in-house numerical solver that incorporates ingredients for fluid flow solution, RBC membrane deformation, and an explicit coupling algorithm between the two. The lattice Boltzmann method is used for obtaining a fluid flow solution at low Reynolds numbers, and the finite element method is used for computing the membrane energetics. The immersed boundary method explicitly couples these two solutions with non-matching boundaries, at each time step. Firstly, I investigate subtle flow hydrodynamic effects through DLD obstacle arrays. Here, fluid-only simulations uncover and map anisotropic flow permeability of the obstacle arrays. The research reveals that if the unit cell of the obstacle array geometrically forms a parallelogram, the array induces an anisotropic pressure gradient normal to the average flow direction. Contrarily, if the obstacle arrangement reflects a rotated square in its unit cell, anisotropy is entirely absent. Such anisotropic pressure conditions in the DLD cause local flow deviations and can lead to unintended particle motion arising from locally varying critical separation size. I find that elevated levels of such anisotropy are also brought about by pillar shape design and asymmetric array gaps. Furthermore, strategies to minimise anisotropic flow effects are proposed. The research on deformable RBC flow through the DLD tackles both single and collective cell dynamics in these arrays. Single cell dynamics is studied for special, non-cylindrical obstacle pillar shapes. In addition to the particle-obstacle steric contact, dynamic RBC motion leads to effects that influence cell trajectories in the DLD. Such effects are strongly tied to the interplay between RBC deformability, dynamic motion (such as tumbling and tank-treading) and the flow-field generated by the pillar shape. In certain cases, wall-induced hydrodynamic cell migration becomes significant enough such that the deformed tank-treading RBC undergoes displacement mode without steric contact with the pillars. Here, migration velocity experienced by the cells interacting with special pillar shapes causes a reversal of the phase-bifurcation trend. The uncovering of this mechanism, opens the door for research on novel DLD pillar designs that exploit wall-induced soft particle migration. Lastly, the research turns to collective RBC dynamics at high volume fractions, in standard DLD arrays with cylindrical pillars. Here, I research the effect of increasing cell volume fraction on the displacement and zigzag modes, with the help of appropriate statistical measures. I find that the displacement mode suffers a breakdown at higher volume fractions, while the zigzag mode remains robust. This has important implications for cell separation applications in the DLD, where smaller particles (e. g. platelets) need to be separated from a dense background of RBCs and vice versa. The investigations undertaken in this thesis identify subtle hydrodynamic and particle effects in DLD arrays that explain previously unresolved particle behaviour. This research should help improve the design and fabrication of DLD devices, especially those targeted at improved separation and manipulation of deformable RBCs

    Investigations into CO₂ immiscible displacements from pore scale to core scale

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    The flow of immiscible displacement in porous media is of great importance in many applications of subsurface transports, such as geological sequestration of CO₂ in saline aquifers and depleted oil/gas fields, enhanced oil recovery (EOR) and removal of nonaqueous phase liquids (NAPLs) from aquifer sediments. In this work, the investigation of immiscible displacement focuses on drainage process, in which wetting fluid residing in porous media is displaced by a non-wetting fluid. Fingering led by unstable displacement is one of the major reasons limiting the efficiency in drainage process. For example, in CO₂ sequestration, fingering of low-viscosity gaseous or supercritical CO₂ limits their access to reservoir rocks and thus only a fraction of reservoir is occupied by injected CO₂. In enhanced oil recovery by CO₂ or water, less than half of original oil in place is recovered due to viscous fingers. The immiscible displacement process in CO₂ injection into the geological formations and reservoirs involves complex cross-scale flow from pore scale to core scale and eventually reservoir scale. Pore-scale flow can provide the most fundamental information of microscopic factors that have significant effects on macroscopic process, which cannot be captured by current continuum-scale models. Simulating a reservoir-scale flow with pore-scale modelling is not possible as it requires enormous computation. Instead, core-scale model is a brilliant option to characterize the flow dynamics of the reservoir to obtain upscaled flow functions (e.g., relative permeability and capillary pressure) for reservoir-scale models. A solid understanding of immiscible displacement from both pore-scale and core-scale perspectives is critically important in evaluating the impacts and efficiencies of displacement processes and providing accurate flow information for the reservoir model. In this PhD project, immiscible displacements were investigated in the core sample and pore-scale network to evaluate the effect of key factors (namely fluid pressure, temperature, CO₂ phase and injection flowrate) on crucial flow parameters, such as differential pressure, flow patterns, phase saturation, relative permeability and displacement efficiency. The study sheds more light on the impact of capillary and viscous forces on multiphase flow characteristics and explores the conditions where capillary or viscous forces dominate the flow. In addition, immiscible displacements in homogenous and physical rock networks are compared by numerical simulation. CO₂-water core flooding experiments were carried out in a sandstone under different subsurface temperature and pressure conditions by considering the effects of CO₂ phase, pressure and CO₂ injection rate. The pressure fluctuation behaviours, capillary displacement pressure, relative permeability and water recovery are investigated for gas CO₂-water, supercritical CO₂-water and liquid CO₂-water displacements. Pressure fluctuations during the displacements are analysed by wavelet decomposition method. The pressure fluctuations are affected by the CO₂ phase but is almost independent of injection rate. The capillary displacement pressure is quantified by the pressure jump occurring at the beginning of CO₂ invasion into the core sample, which agrees well with the value estimated based on Kozeny model. The relative permeability is calculated by the JBN method, and it is found that liquid CO₂-water displacement has a higher relative permeability. Uncertainty of the relative permeability caused by the assumption of incompressible fluids is quantified. Flow instability in immiscible displacements is predominately affected by the interactions between capillary and viscous forces, which can determine the displacement efficiency and CO₂ storage capacity. CO₂-water and CO₂-oil core flooding experiments with various viscosity ratios and capillary numbers were implemented to understand the interplay of capillary and viscous effects during the displacements by analysis of the pressure behaviours, and the experimental results are further demonstrated by macroscopic capillary number and the Log Nca-Log M phase diagram. In viscous-dominated displacement, differential pressure evidently depends on the injection rate and the pressure decline curve is fitted by a power function. The exponent of the function is found to be significantly larger at the crossover between capillary-dominated and viscous-dominated regions. In capillary-dominated displacement, the pressure profile is characterized by a pressure jump at the beginning and intermittent fluctuations during displacement. Further analysis by wavelet decomposition indicates a transition point existing in standard deviation of pressure fluctuations when the displacement is transformed from capillary-dominated to viscous-dominated. The experiment results agree well with the macroscopic capillary number, which characterizes the interaction between capillary and viscous forces at a critical value of ᵐᵃᶜʳᵒ꜀ₐ~1. For further understanding of the effects of capillary and viscous forces on the immiscible displacements occurring on the scale of individual pores and of how these processes determine the invasion patterns, CO₂-water and water-oil immiscible displacements were conducted in the pore-scale network with physical rock structures. Viscosity ratio and capillary number for the displacements were varied by employing different fluid pairs and injection flowrates. The pressure behaviour, flow pattern, invading phase saturation, trapped oil cluster size and macroscopic capillary number were investigated for displacements transforming from viscous-dominated to capillary-controlled. The behaviour of differential pressure is similar to that in core flooding experiments. A transition point exists on the relationship between standard deviation of pressure fluctuations and capillary number when displacement varies from viscous-dominated to capillary-controlled, which is also in accord with the results from core flooding experiments except for the value of the transition point. The non-wetting phase saturation shows great dependence on the capillary number. When capillary force dominates the flow, the non-wetting phase saturation hardly increases with increasing the amount of injection after breakthrough while it increases greatly when viscous force is the dominating force. With increasing capillary number, the trapped oil cluster size become smaller while the interfacial length between two fluids gets larger. The calculated value of macroscopic capillary number accurately predicts the viscous-dominated flow with ᵐᵃᶜʳᵒ꜀ₐ~1, but the value maybe underestimated for capillary-controlled flow due to the underestimation of trapped oil cluster size. Another key issue considered in the project is the effect of pore structure on the immiscible displacement. A direct numerical simulation method is employed by COMSOL Multiphysics 5.6 software to simulate the immiscible displacement in two microfluidic networks, one with a homogeneous structure and the other with a physical rock structure. The numerical model is first validated by immiscible displacement in a single capillary. The simulated results are in good agreement with the theoretical solution calculated based on Darcy-Weisbach equation. Then, flow dynamics, such as flow patterns, differential pressure and phase saturation were investigated in these two networks when the displacement is transformed from capillary-controlled to viscous-dominated. Early breakthrough resulted by viscous fingering is observed in both networks and more obviously in physical rock network. Capillary fingering is not clearly detected, properly due to the limitation of the network scale. In both networks, the flow patterns become compact at equilibrium compared with that at breakthrough in displacements with high injection flowrate (or capillary number) while they remain almost unchanged for displacements with low injection flowrate. The behaviours of differential pressure are similar in these two networks other than pressure achieving equilibrium more quickly in homogeneous network under the same injection flowrate condition. The pressure behaviours are in accord with the results from pore-scale experiments except obvious inertia effect at the beginning of displacements. Transition points are discovered on the relationships between pressure fluctuations and capillary number in both networks and are nearly the same, which are around Log Nca = -3.2. The dynamic, breakthrough-time, equilibrium-time saturation of non-wetting phase is evaluated. It is discovered that the saturation is larger in homogeneous network at high injection flowrates while it is about the same at low injection flowrates. The trend of saturation in physical rock network is in good agreement with pore-scale experimental result

    From wetting to withering: the life and times of droplets on microstructured terrains

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    This thesis presents a detailed exploration into the dynamics of droplet wetting and evaporation on microstructured surfaces, bridging the interdisciplinary fields of physics, chemistry, and surface engineering. Each chapter methodically delves into a distinct facet of this complex interplay, ranging from non-spherical droplet morphologies and nanoparticle deposition patterns to the novel phenomenon of droplet spawning within binary fluid mixtures. The investigation begins with pure fluids and progressively extends to nanofluids and binary mixtures, offering a comprehensive view of fluid behaviour on structured surfaces. Initially, the research is anchored in understanding the morphological control of droplets on textured surfaces. It places significant emphasis on the influence of surface roughness and microscale topography in shaping droplet wetting and evaporation dynamics. A pivotal finding is how micropillar spacing and geometry critically affect droplet shapes, inducing distinct morphologies and modulating evaporation rates, thereby revealing the nuanced interaction of fluid physics with surface characteristics. As the thesis progresses, the focus shifts to complex fluids, particularly the behaviour of aluminium oxide nanofluid droplets. Here, the role of interpillar spacing, geometry, and nanofluid concentration is systematically examined. The research uncovers the formation of sophisticated nanoparticle networks, highlighting concentration-dependent self-assembly processes significantly influenced by the geometric constraints of microstructured surfaces. The study concludes with an innovative investigation into the behaviour of binary ethanol-water mixtures in a hemiwicking state on microtextured surfaces. This research unveils the spontaneous emergence of mini-droplets, a phenomenon driven by the differential volatility of the fluid components and the resultant changes in local surface tension. Collectively, this thesis offers novel insights into droplet behaviour on microstructured surfaces and lays the groundwork for potential technological applications. By bridging theoretical principles with experimental observations, the research opens new avenues for technological advancements and sets a foundation for future explorations in the evolving landscape of fluid dynamics
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