Influence of evaporation rate on cracks’ formation of a drying drop of whole blood

Asymmetric Deposits and Crack Formation during Desiccation of a Blood Droplet on an Inclined Surface

We study the combined effect of varying droplet volume and inclination angles on the desiccation patterns left behind evaporating sessile droplets of human blood. We systematically varied the droplet volume in a range of [1-10 μL] and inclination angles between [0-70°]. Microstructural characterization of the deposits was performed using optical microscopy and surface profilometry. On a horizontal surface, typical deposits of toroidal shape with cracks oriented in radial and azimuthal directions were observed. With an increase in the droplet volume and inclination, the interplay between the gravitational and surface tension effects leads to an asymmetric liquid-vapor interface shape, resulting in a differential evaporative mass flux pattern across the interface. Subsequently, we observe elongation of the overall desiccation patterns along with asymmetric mass deposits between the advancing and receding fronts. As a consequence, the crack morphology on the two fronts exhibits pronounced differences. The distinct regimes of asymmetric mass deposits and crack morphology were quantitatively examined as a characteristic of varying droplet volume and inclinations, parametrized in terms of the mean radial crack spacing and width. These findings are qualitatively analyzed by a first-order theoretical model that is based on the energy conservation principle incorporating the release of mechanical stress energy by contraction of the deposit at the last stage of the desiccation process and the consumed surface energy upon formation of the new surfaces during crack evolution.

Front-Tracking and Gelation in Sessile Droplet Suspensions: What Can They Tell Us about Human Blood?

Recently developed imaging techniques have been used to examine the redistribution of human red blood cells and comparator particles dispersed in carrier fluids within evaporating droplets. We demonstrate that progressive gelation initiates along an annular front, isolating a central pool that briefly remains open to particulate advection before gelation completes across the droplet center. Transition to an elastic solid is evidenced by cracking initiating proximal to front locations. The arrested flow of cellular components, termed a "halted front", has been investigated using a time-lapse analysis "signature". The presence of a deformable biocellular component is seen to be essential for front-halting. We show a dependence of front-halt radius on cell volume-fraction, potentially offering a low-cost means of measuring hematocrit. A simple model yields an estimate of the gel zero-shear yield-stress. This approach to understanding the drying dynamics of blood droplets may lead to a new generation of point-of-care diagnostics.

Scalloped pattern deposition during the spreading and drying of polymer droplets

Droplets containing polyvinylpyrrolidone (PVP) dissolved in ethanol display a distinctive scalloped pattern at the rim while spreading and drying on a high-energy surface. Two distinct spreading regimes are observed, leading to the formation of a thin film with a uniform height that extends from the original droplet. An experimental study indicates polymer accumulation at the edge containing trace water, resulting in a surface tension gradient across the droplet, enhancing the droplet's spreading. This fast-spreading film develops a ridge at the contact line and becomes unstable. The influence of evaporation within the droplet shows no significant effect on the wavelength of the instability. Instead, the magnitude of the surface tension gradient and the surface energy of the substrate emerge as the dominant factors influencing the instability. This observation is validated by saturating the environment surrounding the droplet with ethanol vapour to reduce evaporation or employing solvents with low vapour pressure. Additionally, PVP in ethanol droplets deposited on hydrophobic substrates demonstrate a stable and pinned contact line, contrasting the behaviour observed on high-energy surfaces. By identifying the critical overlap concentration of the polymer, the transitional threshold between the scalloped instability and ringlike morphology is determined. The scalloped instability can be suppressed by removing residual water from the solution, eliminating the surface tension gradient, indicating that Marangoni forces are the underlying cause of the observed instability. The long-wave evolution equation, assuming a constant Marangoni shear flow, accurately predicts the most unstable wavelength, demonstrating good agreement with experimental observations.

Liquid-Liquid Phase Separation Induced by Vapor Transfer in Evaporative Binary Sessile Droplets

Drying of binary sessile droplets consisting of ethanol and octamethyltrisiloxane on a high-energy surface is investigated. During the process of evaporation, the droplets undergo liquid-liquid phase separation, resulting in the appearance of microdroplets at the liquid-air interface, which subsequently violently burst. This phase separation is attributed to water vapor transfer into the droplet, which modifies the solubility and leads to the formation of a ternary mixture. The newly formed ternary mixture may undergo nucleation and growth or spinodal decomposition, depending on the droplet composition path. By control of the relative humidity of air, phase separation can be mitigated or even eliminated. The droplets also display high mobility and complex wetting behavior due to phase separation, with two contracting and two spreading stages. The mass loss experiments reveal that the droplets undergo three distinct drying stages with an enhanced evaporation rate observed during the phase separation stage. A modified diffusion-limited model was employed to predict the evaporation rate, accounting for the physiochemical changes during evaporation and proved to be consistent with experimental observations. The findings of this work enhance our understanding of a coupled fundamental process involving the evaporation of multicomponent mixtures, wetting, and phase separation.

Drying of bio-colloidal sessile droplets: Advances, applications, and perspectives

Drying of biologically-relevant sessile droplets, including passive systems such as DNA, proteins, plasma, and blood, as well as active microbial systems comprising bacterial and algal dispersions, has garnered considerable attention over the last decades. Distinct morphological patterns emerge when bio-colloids undergo evaporative drying, with significant potential in a wide range of biomedical applications, spanning bio-sensing, medical diagnostics, drug delivery, and antimicrobial resistance. Consequently, the prospects of novel and thrifty bio-medical toolkits based on drying bio-colloids have driven tremendous progress in the science of morphological patterns and advanced quantitative image-based analysis. This review presents a comprehensive overview of bio-colloidal droplets drying on solid substrates, focusing on the experimental progress during the last ten years. We provide a summary of the physical and material properties of relevant bio-colloids and link their native composition (constituent particles, solvent, and concentrations) to the patterns emerging due to drying. We specifically examined the drying patterns generated by passive bio-colloids (e.g., DNA, globular, fibrous, composite proteins, plasma, serum, blood, urine, tears, and saliva). This article highlights how the emerging morphological patterns are influenced by the nature of the biological entities and the solvent, micro- and global environmental conditions (temperature and relative humidity), and substrate attributes like wettability. Crucially, correlations between emergent patterns and the initial droplet compositions enable the detection of potential clinical abnormalities when compared with the patterns of drying droplets of healthy control samples, offering a blueprint for the diagnosis of the type and stage of a specific disease (or disorder). Recent experimental investigations of pattern formation in the bio-mimetic and salivary drying droplets in the context of COVID-19 are also presented. We further summarized the role of biologically active agents in the drying process, including bacteria, algae, spermatozoa, and nematodes, and discussed the coupling between self-propulsion and hydrodynamics during the drying process. We wrap up the review by highlighting the role of cross-scale in situ experimental techniques for quantifying sub-micron to micro-scale features and the critical role of cross-disciplinary approaches (e.g., experimental and image processing techniques with machine learning algorithms) to quantify and predict the drying-induced features. We conclude the review with a perspective on the next generation of research and applications based on drying droplets, ultimately enabling innovative solutions and quantitative tools to investigate this exciting interface of physics, biology, data sciences, and machine learning.

Surfactant Control of Coffee Ring Formation in Carbon Nanotube Suspensions

The coffee ring effect regularly occurs during the evaporation of colloidal droplets and is often undesirable. Here we show that adding a specific concentration of a surfactant can mitigate this effect. We have conducted experiments on aqueous suspensions of carbon nanotubes that were prepared with cationic surfactant dodecyltrimethylammonium bromide added at 0.2, 0.5, 1, 2, 5, and 10 times the critical micelle concentration. Colloidal droplets were deposited on candidate substrates for printed electronics with varying wetting characteristics: glass, polyethylene terephthalate, fluoroethylene propylene copolymer, and polydimethylsiloxane. Following drying, four pattern types were observed in the final deposits: dot-like, uniform, coffee ring deposits, and combined patterns (coffee ring with a dot-like central deposit). Evaporation occurred predominantly in constant contact radius mode for most pattern types, except for some cases that led to uniform deposits in which early stage receding of the contact line occurred. Image analysis and profilometry yielded deposit thicknesses, allowing us to identify a coffee ring subfeature in all uniform deposits and to infer the percentage coverage in all cases. Importantly, a critical surfactant concentration was identified for the generation of highly uniform deposits across all substrates. This concentration resulted in visually uniform deposits consisting of a coffee ring subfeature with a densely packed center, generated from two distinct evaporative phases.

The Effect of the Physical Morphology of Dried Biofluids on the Chemical Stability of Analytes Stored in Paper and Direct Analysis by Mass Spectrometry

Three-dimensional (3D) dried blood spheroids formed on hydrophobic paper are a new microsampling platform that can stabilize labile molecules in whole blood stored in ambient air at room temperature. In this study, we define the ideal conditions for preparing the dried blood spheroids. The physical morphology of 3D dried blood spheroids is found to be largely impacted by the unregulated relative humidity of the surrounding environment. A solution of KOH placed in an enclosed chamber offers a facile way to control humidity. We also report a general polymer coating strategy that serves to stabilize dried biofluids when prepared under ordinary ambient conditions without regulation of humidity. Dried blood spheroids coated in xanthan gum polymer exhibited enhanced chemical and physical stability. The same xanthan gum polymer provided chemical stability for 2D dried blood spots when compared with the conventional noncoated samples. We have expanded the application of xanthan gum to less viscous biofluids such as urine to induce an artificial protective barrier that also provides enhanced stability for labile performance-enhancing drugs stored at room temperature. The impact of polymer coating on direct biofluid analysis via paper spray mass spectrometry was determined by comparing the relative ionization efficiency, percent difference of ionization efficiency, and matrix effects of performance-enhancing drugs that were spiked in undiluted raw urine. Acceptable analytical performance was recorded for all three criteria, including high ionization efficiencies that ranged from 77 to 93% in the presence of the xanthan gum polymer.

Drying-induced stresses in poroelastic drops on rigid substrates

We develop a theory for drying-induced stresses in sessile, poroelastic drops undergoing evaporation on rigid surfaces. Using a lubrication-like approximation, the governing equations of three-dimensional nonlinear poroelasticity are reduced to a single thin-film equation for the drop thickness. We find that thin drops experience compressive elastic stresses but the total in-plane stresses are tensile. The mechanical response of the drop is dictated by the initial profile of the solid skeleton, which controls the in-plane deformation, the dominant components of elastic stress, and sets a limit on the depth of delamination that can potentially occur. Our theory suggests that the alignment of desiccation fractures in colloidal drops is selected by the shape of the drop at the point of gelation. We propose that the emergence of three distinct fracture patterns in dried blood drops is a consequence of a nonmonotonic drop profile at gelation. We also show that depletion fronts, which separate wet and dry solid, can invade the drop from the contact line and localize the generation of mechanical stress during drying. Finally, the finite element method is used to explore the stress profiles in drops with large contact angles.

Pattern formation in drying blood drops

Patterns in dried droplets are commonly observed as rings left after spills of dirty water or coffee have evaporated. Patterns are also seen in dried blood droplets and the patterns have been shown to differ from patients afflicted with different medical conditions. This has been proposed as the basis for a new generation of low-cost blood diagnostics. Before these diagnostics can be widely used, the underlying mechanisms leading to pattern formation in these systems must be understood. We analyse the height profile and appearance of dispersions prepared with red blood cells (RBCs) from healthy donors. The red cell concentrations and diluent were varied and compared with simple polystyrene particle systems to identify the dominant mechanistic variables. Typically, a high concentration of non-volatile components suppresses ring formation. However, RBC suspensions display a greater volume of edge deposition when the red cell concentration is higher. This discrepancy is caused by the consolidation front halting during drying for most blood suspensions. This prevents the standard horizontal drying mechanism and leads to two clearly defined regions in final crack patterns and height profile. This article is part of a discussion meeting issue 'A cracking approach to inventing new tough materials: fracture stranger than friction'.

Transient Prediction of Nanoparticle-Laden Droplet Drying Patterns through Dynamic Mode Decomposition

Nanoparticle-laden sessile droplet drying has a wide impact on applications. However, the complexity affected by the droplet evaporation dynamics and particle self-assembly behavior leads to challenges in the accurate prediction of the drying patterns. We initiate a data-driven machine learning algorithm by using a single data collection point via a top-view camera to predict the transient drying patterns of aluminum oxide (Al₂O₃) nanoparticle-laden sessile droplets with three cases according to particle sizes of 5 and 40 nm and Al₂O₃ concentrations of 0.1 and 0.2 wt %. Dynamic mode decomposition is used as the data-driven learning model to recognize each nanoparticle-laden droplet as an individual system and then apply the transfer learning procedure. Along 270 s of droplet drying experiments, the training period of the first 100 s is selected, and then the rest of the 170 s is predicted with less than a 10% error between the predicted and the actual droplet images. The developed data-driven approach has also achieved the acceptable prediction for the droplet diameter with less than 0.13% error and a coffee-ring thickness over a range of 2.0 to 6.7 μm. Moreover, the proposed machine learning algorithm can recognize the volume of the droplet liquid and the transition of the drying regime from one to another according to the predicted contact line and the droplet height.

Concentration-driven phase transition and self-assembly in drying droplets of diluting whole blood

Multi-colloidal systems exhibit a variety of structural and functional complexity owing to their ability to interact amongst different components into self-assembled structures. This paper presents experimental confirmations that reveal an interesting sharp phase transition during the drying state and in the dried film as a function of diluting concentrations ranging from 100% (undiluted whole blood) to 12.5% (diluted concentrations). An additional complementary contact angle measurement exhibits a monotonic decrease with a peak as a function of drying. This peak is related to a change in visco-elasticity that decreases with dilution, and disappears at the dilution concentration for the observed phase transition equivalent to 62% (v/v). This unique behavior is clearly commensurate with the optical image statistics and morphological analysis; and it is driven by the decrease in the interactions between various components within this bio-colloid. The implications of these phenomenal systems may address many open-ended questions of complex hierarchical structures.

Crack density in bloodstains

We construct a theoretical framework to understand the crack density of bloodstains by modeling whole blood as a suspension of binary size colloid particles. Our analysis based upon theories of soft capillarity and porous flows explains the observed increase of the crack density with increase of blood viscosity and decrease of environmental humidity. The results have direct implications on forensic science and medical diagnosis.

Machine Learning Analysis for Quantitative Discrimination of Dried Blood Droplets

One of the most interesting and everyday natural phenomenon is the formation of different patterns after the evaporation of liquid droplets on a solid surface. The analysis of dried patterns from blood droplets has recently gained a lot of attention, experimentally and theoretically, due to its potential application in diagnostic medicine and forensic science. This paper presents evidence that images of dried blood droplets have a signature revealing the exhaustion level of the person, and discloses an entirely novel approach to studying human dried blood droplet patterns. We took blood samples from 30 healthy young male volunteers before and after exhaustive exercise, which is well known to cause large changes to blood chemistry. We objectively and quantitatively analysed 1800 images of dried blood droplets, developing sophisticated image processing analysis routines and optimising a multivariate statistical machine learning algorithm. We looked for statistically relevant correlations between the patterns in the dried blood droplets and exercise-induced changes in blood chemistry. An analysis of the various measured physiological parameters was also investigated. We found that when our machine learning algorithm, which optimises a statistical model combining Principal Component Analysis (PCA) as an unsupervised learning method and Linear Discriminant Analysis (LDA) as a supervised learning method, is applied on the logarithmic power spectrum of the images, it can provide up to 95% prediction accuracy, in discriminating the physiological conditions, i.e., before or after physical exercise. This correlation is strongest when all ten images taken per volunteer per condition are averaged, rather than treated individually. Having demonstrated proof-of-principle, this method can be applied to identify diseases.

Pattern Formation in Drying Sessile and Pendant Droplet: Interactions of Gravity Settling, Interface Shrinkage, and Capillary Flow

We reported the interactions of the gravitational sedimentation, interface shrinkage, and outward capillary flow in drying droplets. This coupling effect is the inference we draw from deposition patterns of both sessile and pendant droplets, which contain particles of different sizes, evaporating on a patterned substrate. The deposition difference between sessile and pendant droplets containing microparticles indicated that gravitational sedimentation has a significant influence on the deposition morphology. The phase diagram shows that the particle deposition process can be divided into two stages: in the first stage, the competition between the interface shrinkage and the gravitational sedimentation determines whether the particles can be captured by the liquid-air interface; in the second stage, the capillary flow takes the particles inside the droplet toward the edge. The deposition morphology is the result of competition and cooperation interactions of the free setting, interface shrinkage, and outward capillary flow.

Controlling the contact angle of biological sessile drops for study of their desiccated cracking patterns

Current exploration of cracking patterns of desiccated biological sessile drops as a new approach of scientific research is progressing rapidly. It has been proposed that biological fluids are naturally capable of storing information. Cracking patterns of desiccated biological sessile drops have the potential to provide a facile means to study the links between compositions of biofluids, their structures and their functions. This potential is, however, limited by our current inability to control the influences of non-pathological factors on cracking patterns. Among the non-pathological factors, the initial sessile drop contact angle has a strong influence on cracking patterns through affecting the material transport and stress distributions within the drop. In this work, we developed a method to control the initial drop contact angle on a glass surface to enable the investigation of the contact angle-induced pattern changes in a biological sessile drop. Human blood was selected as the biofluid in this study, because of its richness in cracking patterns. It has been found that the increase in the initial contact angle enlarges the orthoradial cracks close to the drop edge and compresses the width of the peripheral region. We have also concluded that the number of cracks in the central region of the desiccated pattern can be correlated with the drop contact angle. This work also provides a novel protocol for fabricating standardized substrates for studies of desiccation patterns of biological and other complex colloidal fluids.

Pattern formation of stains from dried drops to identify spermatozoa motility

We study how cell motility affects the stains left by the evaporation of droplets of a biofluid suspension containing mouse spermatozoa. The suspension, which contains also a high concentration of salts usually needed by motile cells, forms, upon drying, a crystallized pattern. We examine the structural characteristics of such patterns by optical microscopy. The analysis reveals that cell motility affects the formation of elongated crystals with lateral tips, as well as the creation of interlocked aggregates. We prove that a lacunarity algorithm based on polar symmetry, distinguishes among deposits generated by motile and non-motile cells with an accuracy greater than 95%.

Mechanisms of pattern formation from dried sessile drops

The formation of patterns after the evaporation of colloidal droplets deposited on a solid surface is an everyday natural phenomenon. During the past two decades, this topic has gained broader audience due to its numerous applications in biomedicine, nanotechnology, printing, coating, etc. This paper presents a detailed review of the experimental studies related to the formation of various deposition patterns from dried droplets of complex fluids (i.e., nanofluids, polymers). First, this review presents the fundamentals of sessile droplet evaporation including evaporation modes and internal flow fields. Then, the most observed dried patterns are presented and the mechanisms behind them are discussed. The review ends with the categorisation and exhaustive investigation of a wide range of factors affecting pattern formation.

Biofluid spectroscopic disease diagnostics: A review on the processes and spectral impact of drying

The complex patterns observed from evaporated liquid drops have been examined extensively over the last 20 years. Complete understanding of drop deposition is vital in many medical processes, and one which is essential to the translation of biofluid spectroscopic disease diagnostics. The promising use of spectroscopy in disease diagnosis has been hindered by the complicated patterns left by dried biological fluids which may inhibit the clinical translation of this technology. Coffee-ring formation, cracking and gelation patterns have all been observed in biofluid drops, and with surface homogeneity being a key element to many spectroscopic techniques, experimental issues have been found to arise. A better understanding of the fundamental processes involved in a drying droplet could allow efficient progression in this research field, and ultimately benefit the population with the development of a reliable cancer diagnostic.

Evaporation of Nanosuspensions on Substrates with Different Hydrophobicity

Liquid drop evaporation on surfaces is present in many industrial and medical applications, e.g., printed electronics, spraying of pesticides, DNA mapping, etc. Despite this strong interest, a theoretical description of the dynamic of the evaporation of complex liquid mixtures and nanosuspensions is still lacking. Indeed, one of the aspects that have not been included in the current theoretical descriptions is the competition between the kinetics of evaporation and the adsorption of surfactants and/or particles at the liquid/vapor and liquid/solid interfaces. Materials formed by an electrically isolating solid on which a patterned conducting layer was formed by the deposits left after drop evaporation have been considered as very promising for building electrical circuits on flexible plastic substrates. In this work, we have done an exhaustive study of the evaporation of nanosuspensions of latex and hydrophobized silver nanoparticles on four substrates of different hydrophobicity. The advancing and receding contact angles as well as the time dependence of the volume of the droplets have been measured over a broad range of particle concentrations. Also, mixtures of silver particles and a surfactant, commonly used in industrial printing, have been examined. Furthermore, the adsorption kinetics at both the air/liquid and solid/liquid interfaces have been measured. Whereas the latex particles do not adsorb at the solid/liquid and only slightly reduce the surface tension, the silver particles strongly adsorb at both interfaces. The experimental results of the evaporation process were compared with the predictions of the theory of Semenov et al. (Evaporation of Sessile Water Droplets: Universal Behavior in the Presence of Contact Angle Hysteresis. Colloids Surf. Physicochem. Eng. Asp. 2011, 391 (1-3), 135-144) and showed surprisingly good agreement despite that the theory was developed for pure liquids. The morphology of the deposits left by the droplets after total evaporation was studied by scanning electronic microscopy, and the effects of the substrate, the particle nature, and their concentrations on these patterns are discussed.

Generation of strength in a drying film: How fracture toughness depends on dispersion properties

The fracture toughness of colloidal films is measured by characterizing cracks which form during directional drying. Images from a confocal microscope are processed to measure the crack width as a function of distance from the crack tip. Applying theory for thin elastic films the fracture toughness is extracted. It is found that the fracture toughness scales with the particle size to the -0.8 power and that the critical energy release rate scales with the particle size to the -1.3 power. In addition, the fracture toughness is found to increase at lower evaporation rates, but the film thickness does not have a significant effect.

Ultrasonic monitoring of droplets' evaporation: Application to human whole blood

During a colloidal droplet evaporation, a sol-gel transition can be observed and is described by the desiccation time τD and the gelation time τG. These characteristic times, which can be linked to viscoelastic properties of the droplet and to its composition, are classically rated by analysis of mass droplet evolution during evaporation. Even if monitoring mass evolution versus time seems straightforward, this approach is very sensitive to environmental conditions (vibrations, air flow…) as mass has to be evaluated very accurately using ultra-sensitive weighing scales. In this study we investigated the potentialities of ultrasonic shear reflectometry to assess τD and τG in a simple and reliable manner. In order to validate this approach, our study has focused on blood droplets evaporation on which a great deal of work has recently been published. Desiccation and gelation times measured with shear ultrasonic reflectometry have been perfectly correlated to values obtained from mass versus time analysis. This ultrasonic method which is not very sensitive to environmental perturbations is therefore very interesting to monitor the drying of blood droplets in a simple manner and is more generally suitable for complex fluid droplets evaporation investigation.

Blood drop patterns: Formation and applications

The drying of a drop of blood or plasma on a solid substrate leads to the formation of interesting and complex patterns. Inter- and intra-cellular and macromolecular interactions in the drying plasma or blood drop are responsible for the final morphologies of the dried patterns. Changes in these cellular and macromolecular components in blood caused by diseases have been suspected to cause changes in the dried drop patterns of plasma and whole blood, which could be used as simple diagnostic tools to identify the health of humans and livestock. However, complex physicochemical driving forces involved in the pattern formation are not fully understood. This review focuses on the scientific development in microscopic observations and pattern interpretation of dried plasma and whole blood samples, as well as the diagnostic applications of pattern analysis. Dried drop patterns of plasma consist of intricate visible cracks in the outer region and fine structures in the central region, which are mainly influenced by the presence and concentration of inorganic salts and proteins during drying. The shrinkage of macromolecular gel and its adhesion to the substrate surface have been thought to be responsible for the formation of the cracks. Dried drop patterns of whole blood have three characteristic zones; their formation as functions of drying time has been reported in the literature. Some research works have applied engineering treatment to the evaporation process of whole blood samples. The sensitivities of the resultant patterns to the relative humidity of the environment, the wettability of the substrates, and the size of the drop have been reported. These research works shed light on the mechanisms of spreading, evaporation, gelation, and crack formation of the blood drops on solid substrates, as well as on the potential applications of dried drop patterns of plasma and whole blood in diagnosis.

A mechanistic view of drying suspension droplets

When a dispersion droplet dries, a rich variety of spatial and temporal heterogeneities emerge. Controlling these phenomena is essential for many applications yet requires a thorough understanding of the underlying mechanisms. Although the process of film formation from initially dispersed polymer particles is well documented and is known to involve three main stages - evaporation, particle deformation and coalescence - it is impossible to fully disentangle the effects of particle deformation and coalescence, as these stages are closely linked. We circumvent this problem by studying suspensions of colloidal rubber particles that are incapable of coalescing. Varying the crosslink density allows us to tune the particle deformability in a controlled manner. We develop a theoretical framework of the main regimes and stresses in drying droplets of these suspensions, and validate this framework experimentally. Specifically, we show that changing the particle modulus by less than an order of magnitude can completely alter the stress development and resulting instabilities. Scanning electron microscopy reveals that particle deformability is a key factor in stress mitigation. Our model is the suspension equivalent of the widely used Routh-Russel model for film formation in drying dispersions, with additional focus on lateral nonuniformities such as cracking and wrinkling inherent to the droplet geometry, thus adding a new dimension to the conventional view of particle deformation.

Crack patterns over uneven substrates

Cracks in thin layers are influenced by what lies beneath them. From buried craters to crocodile skin, crack patterns are found over an enormous range of length scales. Regardless of absolute size, their substrates can dramatically influence how cracks form, guiding them in some cases, or shielding regions from them in others. Here we investigate how a substrate's shape affects the appearance of cracks above it, by preparing mud cracks over sinusoidally varying surfaces. We find that as the thickness of the cracking layer increases, the observed crack patterns change from wavy to ladder-like to isotropic. Two order parameters are introduced to measure the relative alignment of these crack networks, and, along with Fourier methods, are used to characterise the transitions between crack pattern types. Finally, we explain these results with a model, based on the Griffith criteria of fracture, that identifies the conditions for which straight or wavy cracks will be seen, and predicts how well-ordered the cracks will be. Our metrics and results can be applied to any situation where connected networks of cracks are expected, or found.