Color Gradient Research Articles

Local and Hierarchical Refinement for Subdivision Gradient Meshes

AbstractGradient mesh design tools allow users to create detailed scalable images, traditionally through the creation and manipulation of a (dense) mesh with regular rectangular topology. Through recent advances it is now possible to allow gradient meshes to have arbitrary manifold topology, using a modified Catmull‐Clark subdivision scheme to define the resultant geometry and colour [LKSD17]. We present two novel methods to allow local and hierarchical refinement of both colour and geometry for such subdivision gradient meshes. Our methods leverage the mesh properties that the particular subdivision scheme ensures. In both methods, the artists enjoy all the standard capabilities of manipulating the mesh and the associated colour gradients at the coarsest level as well as locally at refined levels. Further novel features include interpolation of both position and colour of the vertices of the input meshes, local detail follows coarser‐level edits, and support for sharp colour transitions, all at any level in the hierarchy offered by subdivision.

Uncovering the Formation of Color Gradients for Glucose Colorimetric Assays on Microfluidic Paper-Based Analytical Devices by Mass Spectrometry Imaging.

This study describes the use of mass spectrometry imaging with matrix-assisted laser desorption/ionization (MALDI) and desorption electrospray ionization (DESI) to understand the color gradient generation commonly seen in microfluidic paper-based analytical devices (μPADs). The formation of color gradients significantly impacts assay sensitivity and reproducibility with μPADs but the mechanism for formation is poorly understood. The glucose enzymatic assay using potassium iodide (KI) as a chromogenic agent was selected to investigate the color gradient generated across a detection spot. Colorimetric measurements revealed that the relative standard deviation for the recorded pixel intensities ranged between 34 and 40%, compromising the analytical reliability. While a variety of hypotheses have been generated to explain this phenomenon, few studies have attempted to elucidate the mechanisms associated with its formation. Mass spectrometry imaging using MALDI and DESI was applied to understand the nonuniform color distribution on the detection zone. MALDI experiments were first explored to monitor the spatial distribution of the glucose oxidase and horseradish peroxidase mixture, before and after lateral flow assay with and without KI. MALDI(+)-TOF data revealed uniform enzyme distribution on the detection spots. On the other hand, after the complete assay DESI(-) measurements revealed a heterogeneous shape indicating the presence of iodide and triiodide ions at the zone edge. The reaction product (I3-) is transported by lateral flow toward the zone edge, generating the color gradient. Mass spectrometry imaging has been used for the first time to prove that color gradient forms as result of the mobility small molecules and not the enzyme distribution on μPAD surface.

Color gradients reflect an inside-out growth in early-type galaxies of the cluster MACS J1206.2-0847

Aims. Color gradients of galaxies are a powerful tool for resolving the variations of stellar populations within galaxies. We use this approach to explore the evolution of early-type galaxies in the core of the massive galaxy cluster MACS J1206.2-0847 at z = 0.44. Methods. We used imaging data in 12 filters (covering a wavelength range from 400 to 1600 nm) from the Hubble Space Telescope provided by the CLASH survey, as well as additional spectral information from its follow-up program, CLASH-VLT. We performed multiwavelength optimized model fitting using Galapagos-2 from the MegaMorph project to measure their photometric parameters (total integrated magnitudes, effective radii re, and Sérsic indices n). We used them to derive color gradients for the colors g475 − I814, r625 − Y105, I814 − H160, and Y105 − H160 at radii ranging between 0.1 and 2re for 79 early-type cluster galaxies. From synthetic spectral models that use simple star formation recipes, we inferred ages and metallicities of the stellar population at different locations within each galaxy and characterized their influence on the radial color trends. Results. Early-type galaxies show a substantial decrease in effective radii re with wavelength. We measure that galaxy sizes are ~25% smaller in the red H160 filter than in the blue r625 filter but maintain a constant (within 3σ) Sérsic index n with wavelength. We find negative color gradients in all colors with slopes ranging between −0.07 and −0.17 mag dex−1 and with no obvious dependence on total magnitude, stellar mass, or location inside the cluster core. We explain the observed radial trends of color gradients as a result of the ages and metallicities of the respective stellar populations. Red galaxy cores are typically ~3 Gyr older and more enriched in metals than the galaxy outskirts, which are of solar metallicity. Conclusions. Our results support the predictions from hydrodynamical cosmological simulations, which describe a passive evolution combined with an inside-out-growth of early-type galaxies. In this scenario, galaxies assemble their stellar mass primarily in the outskirts through the accretion of mass-poor satellites and thus manifest the observed trends of color-, metallicity- and age gradients.

Lattice Boltzmann Simulation of Immiscible Two-Phase Displacement in Two-Dimensional Berea Sandstone

Understanding the dynamic displacement of immiscible fluids in porous media is important for carbon dioxide injection and storage, enhanced oil recovery, and non-aqueous phase liquid contamination of groundwater. However, the process is not well understood at the pore scale. This work therefore focuses on the effects of interfacial tension, wettability, and the viscosity ratio on displacement of one fluid by another immiscible fluid in a two-dimensional (2D) Berea sandstone using the colour gradient lattice Boltzmann model with a modified implementation of the wetting boundary condition. Through invasion of the wetting phase into the porous matrix, it is observed that the viscosity ratio plays an important role in the non-wetting phase recovery. At the viscosity ratio ( λ ) of unity, the saturation of the wetting fluid is highest, and it linearly increases with time. The displacing fluid saturation reduces drastically when λ increases to 20; however, when λ is beyond 20, the reduction becomes less significant for both imbibition and drainage. The front of the bottom fingers is finally halted at a position near the inlet as the viscosity ratio increases to 10. Increasing the interfacial tension generally results in higher saturation of the wetting fluid. Finally, the contact angle is found to have a limited effect on the efficiency of displacement in the 2D Berea sandstone.

Probing the Limits of Egg Recognition Using Egg Rejection Experiments Along Phenotypic Gradients.

Brood parasites lay their eggs in other females' nests, leaving the host parents to hatch and rear their young. Studying how brood parasites manipulate hosts into raising their young and how hosts detect parasitism provide important insights in the field of coevolutionary biology. Brood parasites, such as cuckoos and cowbirds, gain an evolutionary advantage because they do not have to pay the costs of rearing their own young. However, these costs select for host defenses against all developmental stages of parasites, including eggs, their young, and adults. Egg rejection experiments are the most common method used to study host defenses. During these experiments, a researcher places an experimental egg in a host nest and monitors how hosts respond. Color is often manipulated, and the expectation is that the likelihood of egg discrimination and the degree of dissimilarity between the host and experimental egg are positively related. This paper serves as a guide for conducting egg rejection experiments from describing methods for creating consistent egg colors to analyzing the findings of such experiments. Special attention is given to a new method involving uniquely colored eggs along color gradients that has the potential to explore color biases in host recognition. Without standardization, it is not possible to compare findings between studies in a meaningful way; a standard protocol within this field will allow for increasingly accurate and comparable results for further experiments.

Proposal and validation of colour index for Kinnow mandarin (Citrus nobilis × Citrus deliciosa)

Kinnow (Citrus nobilis Lour × Citrus deliciosa Tenora) acceptability by consumer and processors depends on their bright orange colour, size and other quality traits like TSS and acidity. More bright orange coloured Kinnow fruits are preferred. The objective of this study is to propose an index for growers and researchers to know the harvesting date and better quality of fruits respectively. Kinnow fruits of varying colour gradient were harvested from ten treatments. These ten treatments were different doses of N: P: K. They acted as a source to produce variability in Kinnow peel colour, which was utilized for index formulation and validation. They were compared with a standard. Standard comprised of most uniform bright orange coloured fruits of Kinnow orange. The observations for L, a and b were recorded by Hunterlab. There were total eleven colour indexes studied. Out of eleven indexes, seven were previously validated by other workers for different fruit crops. Four indexes were formulated in this study to validate them for Kinnow along with remaining seven indexes. Index a/b showed highest positive correlation with total carotenoid content of peel (0.548 and 0.519 respectively). It recorded minimum value for standard (0.52±0.02) indicates that lower values for these indices will represent brighter colour of kinnow.

The properties of bright globular clusters, ultra-compact dwarfs and dwarf nuclei in the Virgo core: hints on origin of ultra-compact dwarf galaxies (UCDs)

AbstractBased on the data from the Next Generation Virgo cluster Survey (NGVS), we statistically study the photometric properties of globular clusters (GCs), ultra-compact dwarfs (UCDs) and dwarf nuclei in the Virgo core (M87) region. We found an obvious negative color (g - z) gradient in GC system associate with M87, i.e. GCs in the outer regions are bluer. However, such color gradient does not exist in UCD system, neither in dwarf nuclei system around M87. In addition, we found that many UCDs are surrounded by extended, low surface brightness envelopes. The dwarf nuclei and UCDs show different spatial distributions from GCs, with dwarf nuclei and UCDs (especially for the UCDs with visible envelopes) lying at larger distances to the Virgo center. These results support the view that UCDs (at least for a fraction of UCDs) are more tied to dwarf nuclei than to GCs.

Using Eye Tracking to Evaluate the Usability of Flow Maps

Flow maps allow users to perceive not only the location where interactions take place, but also the direction and volume of events. Previous studies have proposed numerous methods to produce flow maps. However, how to evaluate the usability of flow maps has not been well documented. In this study, we combined eye-tracking and questionnaire methods to evaluate the usability of flow maps through comparisons between (a) straight lines and curves and (b) line thicknesses and color gradients. The results show that curved flows are more effective than straight flows. Maps with curved flows have more correct answers, fixations, and percentages of fixations in areas of interest. Furthermore, we find that the curved flows require longer finish times but exhibit smaller times to first fixation than straight flows. In addition, we find that using color gradients to indicate the flow volume is significantly more effective than the application of different line thicknesses, which is mainly reflected by the presence of more correct answers in the color-gradient group. These empirical studies could help improve the usability of flow maps employed to visualize geo-data.

Metallicity gradients in the globular cluster systems of early-type galaxies: in situ and accreted components?

Massive early-type galaxies typically have two subpopulations of globular clusters (GCs) which often reveal radial colour (metallicity) gradients. Collating gradients from the literature, we show that the gradients in the metal-rich and metal-poor GC subpopulations are the same, within measurement uncertainties, in a given galaxy. Furthermore, these GC gradients are similar in strength to the {\it stellar} metallicity gradient of the host galaxy. At the very largest radii (e.g. greater than 8 galaxy effective radii) there is some evidence that the GC gradients become flat with near constant mean metallicity. Using stellar metallicity gradients as a proxy, we probe the assembly histories of massive early-type galaxies with hydrodynamical simulations from the Magneticum suite of models. In particular, we measure the stellar metallicity gradient for the in-situ and accreted components over a similar radial range as those observed for GC subpopulations. We find that the in-situ and accreted stellar metallicity gradients are similar but have a larger scatter than the metal-rich and metal-poor GC subpopulations gradients in a given galaxy. We conclude that although metal-rich GCs are predominately formed during the in-situ phase and metal-poor GCs during the accretion phase of massive galaxy formation, they do not have a strict one-to-one connection.

Exploiting aggregate channel features for urine sediment detection

Urine sediment examination refers to the use of microscopes to examine various tangible components in urine sediment, e.g. red blood cells (RBCs), white blood cells (WBCs), tube, and crystal, etc., having a very important role in infectious diseases and circulatory diseases diagnosis. The traditional method about urine sediment analysis depends on the observation of medical staffs. So the workload is particularly large and inefficient, and relevant staff need to own some experience. Recently, the automation of urine sediment analysis can be realized. However, due to the complexity of the urine sediment microscopic image, the accuracy and efficiency of the automatic recognition for the tangible components are still very low. To solve this problem, we investigate channel features to urine sediment detection which include diverse feature types like color channel features and gradient magnitude, etc. We propose aggregate channel features plus (ACF+) detector which is based on aggregate channel features (ACF) for urine sediment detection. We adopt improved Adaboost classifier. The input image does not require any preprocessing and the specific ingredients such as RBCs can be detected directly with a high precision and efficiency. On the testing set, our proposed ACF+ detector suppresses several competitive baselines e.g. Support Vector Machine (SVM) combined with Histogram of Oriented Gradient (HOG), vanilla ACF, and ACDS. In terms of speed, it runs 3FPS on 2592 × 2048 images.

On the Transition of the Galaxy Quenching Mode at 0.5 < z < 1 in CANDELS

Abstract We investigate the galaxy quenching process at intermediate redshift using a sample of ∼4400 galaxies with M * > 109 M ⊙ between redshift 0.5 and 1.0 in all five CANDELS fields. We divide this sample, using the integrated specific star formation rate (sSFR), into four subgroups: star-forming galaxies (SFGs) above and below the ridge of the star-forming main sequence (SFMS), transition galaxies and quiescent galaxies. We study their UVI (U − V versus V − I) color gradients to infer their sSFR gradients out to twice effective radii. We show that on average both star-forming and transition galaxies at all masses are not fully quenched at any radii, whereas quiescent galaxies are fully quenched at all radii. We find that at low masses (M * = 109–1010 M ⊙) SFGs both above and below the SFMS ridge generally have flat sSFR profiles, whereas the transition galaxies at the same masses generally have sSFRs that are more suppressed in their outskirts. In contrast, at high masses (M * > 1010.5 M ⊙), SFGs above and below the SFMS ridge and transition galaxies generally have varying degrees of more centrally suppressed sSFRs relative to their outskirts. These findings indicate that at z ∼ 0.5–1.0 the main galaxy quenching mode depends on its already formed stellar mass, exhibiting a transition from “the outside-in” at M * ≤ 1010 M ⊙ to “the inside-out” at M * > 1010.5 M ⊙. In other words, our findings support that internal processes dominate the quenching of massive galaxies, whereas external processes dominate the quenching of low-mass galaxies.

Spectral reflectance estimation from one RGB image using self-interreflections in a concave object.

Light interreflections occurring in a concave object generate a color gradient that is characteristic of the object's spectral reflectance. In this paper, we use this property in order to estimate the spectral reflectance of matte, uniformly colored, V-shaped surfaces from a single RGB image taken under directional lighting. First, simulations show that using one image of the concave object is equivalent to, and can even outperform, the state-of-the-art approaches based on three images taken under three lightings with different colors. Experiments on real images of folded papers were performed under unmeasured direct sunlight. The results show that our interreflection-based approach outperforms existing approaches, even when the latter are improved by a calibration step. The mathematical solution for the interreflection equation and the effect of surface parameters on the performance of the method are also discussed in this paper.

Nearby Early-type Galactic Nuclei at High Resolution: Dynamical Black Hole and Nuclear Star Cluster Mass Measurements

Abstract We present a detailed study of the nuclear star clusters (NSCs) and massive black holes (BHs) of four of the nearest low-mass early-type galaxies: M32, NGC 205, NGC 5102, and NGC 5206. We measure the dynamical masses of both the BHs and NSCs in these galaxies using Gemini/NIFS or VLT/SINFONI stellar kinematics, Hubble Space Telescope (HST) imaging, and Jeans anisotropic models. We detect massive BHs in M32, NGC 5102, and NGC 5206, while in NGC 205, we find only an upper limit. These BH mass estimates are consistent with previous measurements in M32 and NGC 205, while those in NGC 5102 and NGC 5206 are estimated for the first time and both found to be <106 M ⊙. This adds to just a handful of galaxies with dynamically measured sub-million M ⊙ central BHs. Combining these BH detections with our recent work on NGC 404's BH, we find that 80% (4/5) of nearby, low-mass ( M ⊙; km s−1) early-type galaxies host BHs. Such a high occupation fraction suggests that the BH seeds formed in the early epoch of cosmic assembly likely resulted in abundant seeds, favoring a low-mass seed mechanism of the remnants, most likely from the first generation of massive stars. We find dynamical masses of the NSCs ranging from 2 to 73 × 106 M ⊙ and compare these masses to scaling relations for NSCs based primarily on photometric mass estimates. Color gradients suggest that younger stellar populations lie at the centers of the NSCs in three of the four galaxies (NGC 205, NGC 5102, and NGC 5206), while the morphology of two are complex and best fit with multiple morphological components (NGC 5102 and NGC 5206). The NSC kinematics show they are rotating, especially in M32 and NGC 5102 ( ).

Formation of ultra-compact dwarf galaxies from supergiant molecular clouds

The origin of ultra-compact dwarf galaxies (UCDs) is not yet clear. One possible formation path of UCDs is the threshing of a nucleated elliptical dwarf galaxy (dE, N), however, it remains unclear how such massive nuclear stellar systems were formed in dwarf galaxies. To better establish the early history of UCDs, we investigate the formation of UCD progenitor clusters from super giant molecular clouds (SGMCs), using hydrodynamical simulations. In this study we focus on SGMCs with masses $10^{7} - 10^{8} \rm M_{\odot}$ that can form massive star clusters that display physical properties similar to UCDs. We find that the clusters have extended star formation histories with two phases, producing multiple distinct stellar populations, and that the star formation rate is dependent on the feedback effects of SNe and AGB stars. The later generations of stars formed in these clusters are more compact, leading to a clearly nested structure, and these stars will be more He-rich than those of the first generation, leading to a slight colour gradient. The simulated clusters demonstrate scaling relations between $R_{\rm eff}$ and $M$ and $\sigma_{v}$ and $M$ consistent with those observed in UCDs and strongly consistent with those of the original SGMC. We discuss whether SGMCs such as these can be formed through merging of self-gravitating molecular clouds in galaxies at high-z.

Watercolor Woodblock Printing with Image Analysis

AbstractWatercolor paintings have a unique look that mixes subtle color gradients and sophisticated diffusion patterns. This makes them immediately recognizable and gives them a unique appeal. Creating such paintings requires advanced skills that are beyond the reach of most people. Even for trained artists, producing several copies of a painting is a tedious task. One can resort to scanning an existing painting and printing replicas, but these are all identical and have lost an essential characteristic of a painting, its uniqueness. We address these two issues with a technique to fabricate woodblocks that we later use to create watercolor prints. The woodblocks can be reused to produce multiple copies but each print is unique due to the physical process that we introduce. We also design an image processing pipeline that helps users to create the woodblocks and describe a protocol that produces prints by carefully controlling the interplay between the paper, ink pigments, and water so that the final piece depicts the desired scene while exhibiting the distinctive features of watercolor. Our technique enables anyone with the resources to produce watercolor prints.

Visibility enhancement of color images using Type-II fuzzy membership function

Images taken in poor environmental conditions decrease the visibility and hidden information of digital images. Therefore, image enhancement techniques are necessary for improving the significant details of these images. An extensive review has shown that histogram-based enhancement techniques greatly suffer from over/under enhancement issues. Fuzzy-based enhancement techniques suffer from over/under saturated pixels problems. In this paper, a novel Type-II fuzzy-based image enhancement technique has been proposed for improving the visibility of images. The Type-II fuzzy logic can automatically extract the local atmospheric light and roughly eliminate the atmospheric veil in local detail enhancement. The proposed technique has been evaluated on 10 well-known weather degraded color images and is also compared with four well-known existing image enhancement techniques. The experimental results reveal that the proposed technique outperforms others regarding visible edge ratio, color gradients and number of saturated pixels.

The galaxy environment in GAMA G3C groups using the Kilo Degree Survey Data Release 3

We aim to investigate the galaxy environment in GAMA Galaxy Groups Catalogue (G3C) using a volume-limited galaxy sample from the Kilo Degree Survey Data Release 3. The k-Nearest Neighbour technique is adapted to take into account the probability density functions (PDFs) of photometric redshifts in our calculations. This algorithm was tested on simulated KiDS tiles, showing its capability of recovering the relation between galaxy colour, luminosity and local environment. The characterization of the galaxy environment in G3C groups shows systematically steeper density contrasts for more massive groups. The red galaxy fraction gradients in these groups is evident for most of group mass bins. The density contrast of red galaxies is systematically higher at group centers when compared to blue galaxy ones. In addition, distinct group center definitions are used to show that our results are insensitive to center definitions. These results confirm the galaxy evolution scenario which environmental mechanisms are responsible for a slow quenching process as galaxies fall into groups and clusters, resulting in a smooth observed colour gradients in galaxy systems.

Engineering composition-tunable 3D hierarchical bismuth oxyiodides heterojunctions: Ionic liquid-assisted fabrication with strong adsorption ability and enhanced photocatalytic properties

In this work, we report the fabrication of composition-tunable heterostructured bismuth oxyiodides photocatalysts using a facile ionic liquid-assisted precipitation method at room temperature. Through elaborately governing the reaction parameters, two groups of bismuth oxyiodide hybrids (Group 1: BiOI/Bi4O5I2, and Group 2: Bi4O5I2/Bi5O7I) with different components were prepared. The DRS spectra shows that the absorption edges of the hybrids were gradually tuned from 550 to 660 nm, which was in accordance with the color gradient from light yellow (Bi5O7I) to brick red (BiOI). The SEM images show that the products mainly exhibited 3D hierarchical architecture, which was beneficial for the adsorption of contaminants over the catalyst’s surface. The two groups of heterojunction photocatalysts all exhibited remarkably improved photocatalytic activity in decomposing o-phenylphenol (OPP) and 4-tert-butylphenol (PTBP) under visible light irradiation respect to single phase photocatalyst (BiOI, Bi4O5I2, or Bi5O7I). For BiOI/Bi4O5I2 hybrids, the S5 sample exhibited the optimal activity, which was approximately 5.35 and 1.85 times higher than that of pristine BiOI and Bi4O5I2, respectively. For the second group of Bi4O5I2/Bi5O7I, the optimal activity was observed for S9 hybrid, which was approximately 2.43 and 2.12 times higher than that of bare Bi4O5I2 and Bi5O7I under identical conditions. This activity enhancement should be attributed to the balanced band levels of the components, which facilitates the fast interfacial charge transmigration of photo-generated carriers, resulting in highly promoted charge separation efficiency. This deduction was proved by the photocurrent, electrochemical impedance spectroscopy, and photoluminescence measurements. The possible degradation mechanisms for BiOI/Bi4O5I2 and Bi4O5I2/Bi5O7I hybrids were proposed based on the band potentials and trapping experiment results.

317 Patient Engagement through Advanced Pressure Visualization as a Component of Pressure Injury Prevention

Hospital acquired pressure ulcers represent one of the most frequent health care problems in clinical practice. Burn patients specifically pose a greater challenge due to loss of skin integrity, post-op positioning requirements and high levels of moisture. As an adjunct to unit based standard of care, a new technology was initiated to identify if pressure visualization will encourage patient engagement in repositioning as a component of pressure injury prevention. The purpose of this project is to evaluate the impact of a new advanced pressure visualization (APV) system on patient engagement through visual feedback where body areas are exposed to pressure. The definition of engagement for this purpose is from Gruman, et al, as “actions individuals must take to obtain the greatest benefit from the health care services available to them.” Patients in the Burn Center with intact cognitive awareness and the ability to see and respond to a color screen at the foot of the bed were included. An APV was installed on all beds, which included a pressure sensor mat inside the mattress connected to a display tablet mounted at the foot of the bed. This tablet displays their body image with continuous pressure readings utilizing a color gradient to exhibit pressure values. Patients were educated on the colors reflective of high- low pressures on their individual body image. The color display indicates specific pressure measurements: ‘red’ is >75mmHg, orange is 60-74mmgHg, yellow is 45-59mmHg, green is 30-44mmHg, light blue is 15-29mmHg and dark blue 1-14mmHg. Patients were asked to reposition themselves, or request repositioning assistance from the health care team, to an area of lesser pressure color when areas of high pressure colors (red, orange or yellow) were noted. Data from the APV device was utilized to determine reduction in peak pressure with patient repositioning. Data from 10 patients and 20 repositions were identified. Initial peak pressures shown by APV images, averaged 73.5 mmHg. The average reduction in peak pressure after the ten patients self-repositions was 41.25 mmHg. The National Pressure Ulcer Advisory Panel prevention and treatment guidelines encourage patients to work with the health care team to develop an individualized pressure ulcer prevention plan. With APV, the patient can easily identify high areas of pressure and actively participate in pressure reduction measures. While patient engagement in this population resulted in reduced pressure, further research related to APV and patient engagement for the prevention of pressure injury is warranted.

Wetting boundary condition for the color-gradient lattice Boltzmann method: Validation with analytical and experimental data

Abstract In the color gradient lattice Boltzmann model (CG-LBM), a fictitious-density wetting boundary condition has been widely used because of its ease of implementation. However, as we show, this may lead to inaccurate results in some cases. In this paper, a new scheme for the wetting boundary condition is proposed which can handle complicated 3D geometries. The validity of our method for static problems is demonstrated by comparing the simulated results to analytical solutions in 2D and 3D geometries with curved boundaries. Then, capillary rise simulations are performed to study dynamic problems where the three-phase contact line moves. The results are compared to experimental results in the literature (Heshmati and Piri, 2014). If a constant contact angle is assumed, the simulations agree with the analytical solution based on the Lucas–Washburn equation. However, to match the experiments, we need to implement a dynamic contact angle that varies with the flow rate.