Stokes-Einstein Equation Research Articles

Mesoporous Silica Microparticle-Protein Complexes: Effects of Protein Size and Solvent Properties on Diffusion and Loading Efficiency.

Oral administration of protein-based therapeutics is highly desirable due to lower cost, enhanced patient compliance, and convenience. However, the harsh pH environment of the gastrointestinal tract poses significant challenges. Silica-based carriers have emerged as potential candidates for the delivery of protein molecules, owing to their tuneable surface area and pore volume. We explored the use of a commercial mesoporous silica carrier, SYLOID, for the delivery of octreotide and bovine serum albumin (BSA) using a solvent evaporation method in three different solvents. The loading of proteins into SYLOID was driven by diffusion, as described by the Stokes-Einstein equation. Various parameters were investigated, such as protein size, diffusion, and solubility. Additionally, 3D fluorescence confocal imaging was employed to identify fluorescence intensity and protein diffusion within the carrier. Our results indicated that the loading process was influenced by the molecular size of the protein as octreotide exhibited a higher recovery rate (71%) compared to BSA (32%). The methanol-based loading of octreotide showed uniform diffusion into the silica carrier, whereas water and ethanol loading resulted in the drug being concentrated on the surface, as shown by confocal imaging, and further confirmed by scanning electron microscopy (SEM). Pore volume assessment supported these findings, showing that octreotide loaded with methanol had a low pore volume (1.2cc/g). On the other hand, BSA loading was affected by its solubility in the three solvents, its tendency to aggregate, and its low solubility in ethanol and methanol, which resulted in dispersed particle sizes of 223 and 231μm, respectively. This reduced diffusion into the carrier, as confirmed by fluorescence intensity and diffusivity values. This study underscores the importance of protein size, solvent properties, and diffusion characteristics when using porous carriers for protein delivery. Understanding these factors allows for the development of more effective oral protein-based therapeutics by enhancing loading efficiency. This, in turn, will lead to advances in targeted drug delivery and improved patient outcomes.

Influence of temperature and dry density coupled effects on HTO, 36Cl, 85Sr and 133Ba diffusion through compacted bentonite

This study investigated the combined impact of temperature (from 25 to 80 °C) and dry density of bentonite (from 1.2 to 1.65 g·cm−3) on the apparent diffusion coefficient, Da, of four radionuclides (HTO, 36Cl, 85Sr and 133Ba) in a Ca-Mg bentonite. In this study, the different porewater chemistry, present under the specific experimental conditions -- a factor often overlooked in diffusion studies -- was explicitly considered. As a support to diffusion studies, batch sorption tests were carried out at different temperatures (25, 40, 60, and 80 °C) with the sorbing elements (85Sr and 133Ba).The planar source method was used for the determination of apparent diffusion coefficients, Da, which demonstrated its efficacy for both conservative (HTO and Cl) and sorbing elements. For all the investigated radionuclides, Da values decreased with increasing the clay dry density and increased with increasing temperature. Notably, the highest Da value (1·10−9 m2 s−1) was attained for HTO diffusion in the clay at 1.2 g cm−3 and 80 °C, while the lowest Da (3.6·10−12 m2 s−1) value was determined for Ba diffusion at 1.65 g cm−3 and 25 °C.The experimental Da values were analysed employing the Arrhenius law and the Stokes-Einstein equations. Results revealed that diffusion data are in a reasonable agreement with Arrhenius behaviour, but deviations from the Stokes-Einstein equation were observed for compaction densities higher than 1.4 g cm−3.

Effect of radius-dependent diffusion behavior of various gold nanoparticles on photothermal therapy

Among the various anti-cancer treatments, photothermal therapy (PTT) is gaining traction as it is a non-invasive treatment. PTT is a treatment technique involving the use of a laser to raise the temperature of the target tumor until it dies. In this study, the effects of PTT under various conditions of squamous cell carcinoma (SCC) occurring in the skin were numerically analyzed and optimized. Gold nanoparticles (AuNPs) with different radii were injected into the center of the SCC. Subsequently, the diffusion behavior of the AuNPs was analyzed to calculate the distribution area of the AuNPs that changed over time. Furthermore, at each elapsed time point after injection, the temperature distribution in the tissue was calculated, as treatment was performed using varying laser intensities. The diffusion coefficient of AuNPs was calculated using the Stokes–Einstein equation, and diffusion behavior of AuNPs in biological tissues was analyzed using the convection–diffusion equation. Additionally, temperature distribution was analyzed using the Pennes bioheat equation. The effect of PTT under each condition was quantitatively analyzed using apoptotic variables. As a result, As the radius of AuNPs increased, the optimal treatment start time was derived as 2 h, 8 h, 8 h, and 12 h, respectively, and the laser intensity at that time was derived as 0.44 W, 0.46 W, 0.42 W, and 0.42 W, respectively. The study findings will provide reference for the optimization of the efficacy of PTT.

Numerical analysis of the viscosity of ZrF4–BeF2 molten salts for nuclear transmutation using fusion neutron sources

This study analyzed the influence of ZrF4 on the viscosity of a ZrF4–BeF2 binary salt towards developing BeF2-based molten salts for nuclear transmutation targets. Specifically, we performed molecular dynamics simulation using a polarization ion model and evaluated the viscosity, static structure, and applicability of the Stokes–Einstein equation for ZrF4–BeF2 compared with LiF–BeF2. Our study revealed that ZrF4–BeF2 exhibits higher viscosity than LiF–BeF2 because each ionic bond's longer lifetime extends the structural relaxation time. Furthermore, it is suggested that the ZrF and BeF relaxations contribute to the viscosity mechanism of ZrF4–BeF2. Most of the elements in long-lived fission products (LLFPs) are multivalent ions such as Zr, Pd, and Sn, which bind strongly to anions and are not expected to contribute much to reducing the viscosity of BeF2 mixed salts. In contrast, Cs, also an LLFP, is a monovalent ion, and CsF can reduce the viscosity of these salts. Mixing particular LLFPs with CsF will be one of the principles in designing BeF2-based salts for transmutation.

Einstein–Stokes relation for small bubbles at the nanoscale

As the physicochemical properties of ultrafine bubble systems are governed by their size, it is crucial to determine the size and distribution of such bubble systems. At present, the size or size distribution of nanometer-sized bubbles in suspension is often measured by either dynamic light scattering or the nanoparticle tracking analysis. Both techniques determine the bubble size via the Einstein–Stokes equation based on the theory of the Brownian motion. However, it is not yet clear to which extent the Einstein–Stokes equation is applicable for such ultrafine bubbles. In this work, using atomic molecular dynamics simulation, we evaluate the applicability of the Einstein–Stokes equation for gas nanobubbles with a diameter less than 10 nm, and for a comparative analysis, both vacuum nanobubbles and copper nanoparticles are also considered. The simulation results demonstrate that the diffusion coefficient for rigid nanoparticles in water is found to be highly consistent with the Einstein–Stokes equation, with slight deviation only found for nanoparticle with a radius less than 1 nm. For nanobubbles, including both methane and vacuum nanobubbles, however, large deviation from the Einstein–Stokes equation is found for the bubble radius larger than 3 nm. The deviation is attributed to the deformability of large nanobubbles that leads to a cushioning effect for collision-induced bubble diffusion.

Nuclear induction line shape: Non-Markovian diffusion with boundaries.

The dynamics of viscoelastic fluids are governed by a memory function, essential yet challenging to compute, especially when diffusion faces boundary restrictions. We propose a computational method that captures memory effects by analyzing the time-correlation function of the pressure tensor, a viscosity indicator, through the Stokes-Einstein equation's analytic continuation into the Laplace domain. We integrate this equation with molecular dynamics simulations to derive necessary parameters. Our approach computes nuclear magnetic resonance (NMR) line shapes using a generalized diffusion coefficient, accounting for temperature and confinement geometry. This method directly links the memory function with thermal transport parameters, facilitating accurate NMR signal computation for non-Markovian fluids in confined geometries.

Self-diffusion and shear viscosity of pure 1-alkanol unary system: molecular dynamics simulation and review of experimental data.

Self-diffusion coefficients and shear viscosity coefficients of pure 1-alkanol liquids from methanol to 1-hexanol were predicted using molecular dynamics (MD) simulations. These coefficients have been calculated using the Green-Kubo and Einstein methods at a range of temperatures of 200-330 K with increments of 10 K. Two force fields, TraPPE-UA and OPLS-AA were applied. The predicted results were compared to the experimental data, and the activation energies for self-diffusion and shear viscosity were calculated using the Arrhenius equation. The Stokes-Einstein equation was used to examine its capability in predicting the relationship between self-diffusion and shear viscosity, and the effective hydrodynamic radius was determined using both the experimental data and the results from MD simulations. The TraPPE-UA force field showed better results for the transport properties of methanol, while the OPLS-AA force field performed well for predicting shear viscosity but weakly for self-diffusion, particularly at low temperatures and for 1-alkanol with higher methylene numbers. Using the mean squared displacement method for self-diffusion was found to be more accurate than the Green-Kubo method, while the Green-Kubo method was slightly better for calculating shear viscosity. The Stokes-Einstein equation is valid for pure 1-alkanol liquids with temperature-dependent effective hydrodynamic radius.

Permeability of C-S-H

Hydrodynamics in calcium silicate hydrates nanopores are crucial to concrete’s durability and confinement performance. Here, Non-Equilibrium Molecular Dynamics simulations of water confined in-between C-S-H layers are reported considering slit pore sizes spanning interlayer and gel pores. These simulations enable the computation of the permeability of C-S-H and the quantification of the boundary conditions associated with the flow. A tensorial formalism is applied to describe this forced flow accounting for the pore wall texture and resulting stick/slip boundary conditions. As for other properties, shear viscosity also shows a significant pore-size dependence at the nanoscale. The adoption of slip boundary conditions and confinement-dependent viscosity is crucial to capturing the water permeability of the C-S-H gel. The fundamental link between self-diffusion and viscosity (following the Einstein–Stokes equation) describes the temperature dependence of hydrodynamics.

Analysis of Brownian motion trajectories of non-spherical nanoparticles using deep learning

As nanoparticles are being put to practical use as useful materials in the medical, pharmaceutical, and industrial fields, the importance of technologies that can evaluate not only nanoparticle populations of homogeneous size and density but also those of rich diversity is increasing. Nano-tracking analysis (NTA) has been commercialized and widely used as a method to measure individual nanoparticles in liquids and evaluate their size distribution by analyzing Brownian motion. We have combined deep learning (DL) for NTA to extract more property information and explored a methodology to achieve an evaluation for individual particles to understand their diversity. Practical NTA always assumes spherical shape when quantifying particle size using the Stokes–Einstein equation, but it is not possible to verify whether the measured particles are truly spherical. We developed a DL model that predicts the shape of nanoparticles using time series trajectory data of BM obtained from NTA measurements to address this problem. As a result, we were able to discriminate with ∼80% accuracy between spherical and rod-shaped gold nanoparticles of different shapes, which are evaluated to have nearly equal particle size without any discrimination by conventional NTA. Furthermore, we demonstrated that the mixing ratio of spherical and rod-shaped nanoparticles can be quantitatively estimated from measured data of mixed samples of nanoparticles. This result suggests that it is possible to evaluate particle shape by applying DL analysis to NTA measurements, which was previously considered impossible, and opens the way to further value-added NTA.

Diffusion coefficient and tortuosity: Brownian Motion

The objective of this research is to determine the chloride ion diffusion through Brownian motion using images. The research also aims at the search for diffusional physical tortuosity due to Brownian motion to understand the transport flow of the chloride ion. Through micro-CT scanned images of concrete samples, a 3D reconstruction is performed for the representative element and define its microscopic properties. The implementation of the Brownian motion of the chloride ion particles in the porous network of the representative element considered the initial diffusion coefficient defined by the Stokes-Einstein equation. The diffusion coefficient is an important parameter for predicting the depth of attack of the chloride ion and its displacement due to Brownian motion helps to define the tortuosity of this diffusive transport. The research used computational modeling with MATLAB® software. The results show diffusion due to Brownian motion and tortuousness.

Development of Numerical Analysis Model for New Magnesium Electrolysis Process Using COMSOL

Magnesium (Mg) has good physical properties including light weight, excellent specific strength and high stiffness, and Mg is used in many fields. But current production methods of Mg have disadvantages, such as the generation of sulfur oxide and chlorine gas. In this situation, The Korea Institute of Geoscience and Mineral Resources (KIGAM) developed a Molten Salt Electrolysis Using Liquid Metal Cathode (MSELMC) method to produce high-purity magnesium. The MSE-LMC method can obtain 99.998-99.999% highpurity magnesium by the electrolysis of MgO dissolved in (MgF2)-LiF molten salt at 1053-1083 K, and by vacuum distilling an alloy generated by reacting with a metallic liquid cathode at 1200-1300 K. This study developed a numerical analysis model using COMSOL Multiphysics electrodeposition module to optimize the design of the electrolysis process. The model temperature was 1053K and molten salt was 54MgF2-46LiF with a 0.6wt% MgO system. 10A constant current was applied at the anode. This model uses the Butler-Volmer equation and the Nernst equation for the electric reaction. The Stokes-Einstein equation and Nernst-Einstein relation were used to calculate the diffusivity and electric mobility of salts. Unlike the experiment, in this model chlorine gas was generated. However, this model satisfied Faraday’s law. Therefore we define a new parameter using electric flux and voltage to conduct a quantitative evaluation according to the electrode shape, and compared that parameter by the changing angle of the anode.

Anomalous Dependence of Translational Diffusion on the Water Mole Fraction for Solute Molecules Dissolved in a 1-Butyl-3-methylimidazolium Tetrafluoroborate/Water Mixture.

Translational diffusion coefficients of carbon monoxide (CO), diphenylacetylene (DPA), and diphenylcyclopropenone (DPCP) were determined in mixtures of 1-butyl-3-methylimidazolium tetrafluoroborate ([C4mim]BF4) and water using transient grating spectroscopy at different mole fractions of water (xw). While DPA exhibited a larger diffusion coefficient than DPCP at low water mole fractions (xw < 0.7), as observed for conventional liquids and ionic liquids (ILs), it was smaller at high mole fractions (xw > 0.9). The apparent molecular radius of DPA determined using the Stokes-Einstein equation at xw > 0.9 is close to the radius of an IL cluster in a water pool as determined from small-angle neutron scattering experiments (J. Bowers et al., Langmuir, 2004, 20, 2192-2198), suggesting that the DPA molecules are trapped in IL clusters in the water pool and move together. The solvation state of DPCP in the mixture was studied using Raman spectroscopy. Dramatically strong water/DPCP hydrogen bonding was observed at higher water mole fractions, suggesting that DPCP is located near the cluster interfaces. The large diffusion coefficient of DPCP suggests that hopping of DPCP between IL clusters occurs through hydrogen bonding with water.

Kinetics of the complexation reaction of iron with dissolved oxygen in liquid sodium

This work aims to study the kinetics of pure iron corrosion by liquid sodium in the presence of dissolved oxygen. The corrosion rate of pure iron in liquid sodium was estimated from the mass loss in the samples as a function of immersion time. The parameters tested were dissolved oxygen content, temperature and velocity of the liquid sodium. The rate of pure iron dissolution in liquid sodium increases with dissolved oxygen content and follows a power law of order 2 as a function of the initial oxygen content (50−400ppm). The mechanism of iron corrosion by liquid sodium is activated in the temperature range between 525∘C and 600∘C. The experimental activation energy is estimated to be 168±10kJ/mol. The dissolution rate also increases with the liquid sodium agitation rate.Under the same experimental conditions, S. Meddeb et al. in [J. Nucl. Mater. 566 (2022) 153785] demonstrated that the iron dissolution is homogeneous and is explained by the formation of the NaFeO2 complex at the iron/liquid sodium interface. The corrosion kinetics measured is limited by the transfer of this complex through the mass transfer boundary layer. In the case of static sodium, the associated transfer coefficient is equal to (2.2 ± 0.8)·10−8 m/s. The proposed kinetic corrosion model estimates an excellent order of magnitude for our measurements of average iron thickness loss. Based on our experimental measurements, calculations lead to a diffusivity of the NaFeO2 complex in static liquid sodium of (1.6 ± 0.6)·10−9 m2/s. The Stokes-Einstein law can then be used to estimate an equivalent complex molecule radius of 2 · 10−9 m. These data, combined with the Stokes-Einstein equation, can be used in industrial applications to simulate the mechanism of iron corrosion in non-isothermal heat transfer loop systems.

The heterogeneous nature of the lithium-ion diffusion in highly concentrated sulfolane-based liquid electrolytes

Experimental data on Li-ion transport have indicated that cation hopping, or ligand-exchange mechanism contribute considerably to the Li ion conduction in highly concentrated electrolyte regimes. In this work we performed molecular dynamics simulations of solutions of LiBF4 in sulfolane, up to [LiBF4] = 5.8 mol.L−1 (mole fraction of sulfolane = 0.57), to better understand the solution structure and the nature of the Li ion diffusion. The radial distribution functions, aggregation and connectivity analyses revealed that as the concentration of salt increases, the Li ions can be pictured as nodes of a network shared by BF4− and sulfolane molecules. The formation of these two different continuous networks sharing the cation seems to reach a sweet spot when the mole fraction of sulfolane is ca. 0.67, where the Li+ transference number achieves its maximum value in LiBF4–sulfolane mixtures. The autocorrelation functions of cation-anion and cation-sulfolane pair separations exhibit a non-exponential behaviour. Also, the relaxation dynamics of these solutions at and above room temperature recalls to the supercooled glass-forming liquids at temperatures near the glass transition. The relaxation process of the Li-anion pair is the major contributor to deviations from the Stokes-Einstein equation seen in the highly concentrated LiBF4–sulfolane solutions. These results showing the role played by the primary relaxation steps of Li ions in highly concentrated electrolytes can pave the way to innovative energy storage devices.

Polymer Molecular Weights via DOSY NMR

Diffusion-ordered spectroscopy (DOSY) 1H nuclear magnetic resonance (1H NMR) has become a powerful tool to characterize the molecular weights of polymers. Compared to common characterization techniques, such as size exclusion chromatography (SEC), DOSY is faster, uses less solvent, and does not require a purified polymer sample. Poly(methyl methacrylate) (PMMA), polystyrene (PS), and polybutadiene (PB) molecular weights were determined by the linear correlation between the logarithm of their diffusion coefficients (D) and the logarithm of their molecular weights based on SEC molecular weights. Here, we emphasize the importance of the preparation needed to generate the calibration curves, which includes choosing the correct pulse sequence, optimizing parameters, and sample preparation. The limitation of the PMMA calibration curve was investigated by increasing the dispersity of PMMA. Additionally, by accounting for viscosity in the Stokes-Einstein equation, a variety of solvents were used to produce a "universal" calibration curve for PMMA to determine molecular weight. Furthermore, we place a spotlight on the increasing importance of DOSY NMR being incorporated into the polymer chemist's toolbox.

Single-Molecule Tracking of Reagent Diffusion during Chemical Reactions

Recent experiments have shown that the diffusion of reagent molecules is inconsistent with what the Stokes-Einstein equation predicts during a chemical reaction. Here, we used single-molecule tracking to observe the diffusion of reactive reagent molecules during click and Diels-Alder (DA) reactions. We found that the diffusion coefficient of the reagents remained unchanged within the experimental uncertainty upon the DA reaction. Yet, diffusion of reagent molecules is faster than predicted during the click reaction when the reagent concentration and catalyst concentration exceed a threshold. A stepwise analysis suggested that the fast diffusion scenario is due to the reaction but not the involvement of the tracer with the reaction itself. The present results provide experimental evidence on the faster-than-expected reagent diffusion during a CuAAC reaction in specific conditions and propose new insights into understanding this unexpected behavior.

Electrochemistry and Mass Transport of Ytterbium(III) in Bis(trifluoromethylsulfonyl)imide-Based Room-Temperature Ionic Liquids: Effects of Temperature, Viscosity, and Electrode Materials

Cyclic staircase voltammetry, rotating disk electrode voltammetry, controlled potential coulometry, and electrochemical impedance spectroscopy were used to probe the electrochemistry and mass transport of Yb3+ in the six room temperature ionic liquids based on the bis(trifluoromethylsulfonyl)imide (Tf2N−) anion with, 1-(1-butyl)−3-methylimidazolium (BuMeIm+), 1-(1-butyl)−1-methylpyrrolidinium (BuMePyro+), 1-(1-butyl)pyridinium (BuPy+), 1-butyltrimethylammonium (BuMe3N+), 1-ethyl-3-methylimidazolium (EtMeIm+), and tri(1-butyl)methylammonium (Bu3MeN+) cations. These investigations were carried out at glassy carbon as well as polycrystalline gold, platinum, and tungsten electrodes. The heterogeneous electron transfer rate of the quasireversible Yb3+/2+ redox couple was found to depend strongly on the electrode materials with the fastest rate observed at gold and the slowest rate found at tungsten, but was independent of the physicochemical properties of the various ionic liquids, in particular, the absolute viscosity. However, the mass transport of Yb3+ was dependent on the viscosity, and the temperature dependence of the diffusion coefficients was well represented by a Vogel-Tammann-Fulcher type expression for glass-forming ionic liquids. Analysis of the diffusion coefficient data with the Stokes-Einstein equation indicated that the solvodynamic radius of the diffusing Yb3+ was constant and independent of the structure and properties of the ionic liquid cations. The solvodynamic radius of Yb3+ was estimated from the “stick model” for the Stokes-Einstein equation. Application of the Random Closest Packing (RCP) model for spheres in consideration of the solvodynamic radius of the diffusing Yb3+ and the ionic radii of Yb3+ and Tf2N−, indicated that the former must diffuse in association with ∼5–6 of the anions.

Applicability of the Generalized Stokes-Einstein Equation of Mode-Coupling Theory to Near-Critical Polyelectrolyte Complex Solutions.

We examine whether the mode-coupling theory of Kawasaki and Ferrell (KF) [Kawasaki, K. Kinetic Equations and Time Correlation Functions of Critical Fluctuations. Ann. Phys. 1970, 61 (1), 1-56; Ferrell, R. A. Decoupled-Mode Dynamical Scaling Theory of the Binary-Liquid Phase Transition. Phys. Rev. Lett. 1970, 24 (21), 1169-1172] can describe dynamic light scattering (DLS) measurements of the dynamic structure factor of near-critical polyelectrolyte complex (PC) solutions that have been previously shown to exhibit a theoretically unanticipated lower critical solution temperature type phase behavior, i.e., phase separation upon heating, and a conventional pattern of static critical properties (low angle scattering intensity and static correlation, ξs) as a function of reduced temperature. Good qualitative accord is observed between our DLS measurements and the KF theory. In particular, we observe that the collective diffusion coefficient Dc of the PC solutions obeys the generalized Stokes-Einstein equation (GSE), Dc = kBT/6πηξs, where ξs is specified from our previous measurements and where η is measured by capillary rheometry under the same thermodynamic conditions as in our previous study of these solutions, allowing for a no-free-parameter test of the GSE. We also find that even the wavevector (q)-dependent collective diffusion coefficient Dc(q), measured by varying the scattering angle in the DLS measurements over a large range, is also well-described by the mean-field version of the KF theory. We find it remarkable that the KF theory provides such a robust description of collective diffusion in these complex charged polyelectrolyte blends under near-critical conditions given that charge fluctuations and association of the polymers might be expected to lead to physical complications that would invalidate the standard model of uncharged fluid mixtures.

Measurement and correlation of diffusion coefficients of vitamin K3 in a fluid mixture of carbon dioxide and decane at 313–343 K and 10–30 MPa

The diffusion coefficients D1m of vitamin K3 in a dense fluid mixture of carbon dioxide and decane were measured by the Taylor dispersion method at temperatures from (313.2–343.2) K and pressures from (10−30) MPa, over the entire range of decane composition. The D1m values of vitamin K3 increased with increasing temperature and decreasing pressure under isocratic conditions. In addition, the measured D1m values were found to be correlated with the hydrodynamic (HD) equation based on the Stokes–Einstein equation, with an average relative deviation of 4.9% for 110 conditions over a wide range of fluid viscosities ranging from that of supercritical carbon dioxide to that of compressed liquid decane, apparently irrespective of the decane composition and solvent species.

Fluorescent single particle tracking enables high sensitivity viscometry measurements of micro-volume samples.

Measuring the viscosities of high-value materials at the microscale with minimal waste is essential for increasing turnaround times during drug development in the pharmaceutical industry. Currently, viscometers on the market fail to meet these needs as they can only process a limited number of samples at a time and still require large (>100 μL) loading volumes for accurate readings. Previously, researchers have parameterized fluorescence correlation spectroscopy (FCS) at low volumes to predict antibody behaviors at higher concentrations using the generalized Stokes-Einstein equation. However, these methods lack the ability to produce measurements at a fast turnaround rate. Here, we use a wide field camera-based fluorescence microscope modality and particle tracking system in parallel with a Python PT software to measure the viscosities of multiple solutions using a 10-μL working volume. We applied the generalized Stokes-Einstein equation to the coefficient output of the PT Python software to obtain our final viscosity values. We obtained values of viscosity with an overall error of +-4cP, and the sample preparation method resulted in consistent readings for up to 5 hours after initial preparation. Viscosity readouts obtained using this method will allow for multi-sample imaging on a single chip using minuscule (10 μL) volumes, revolutionizing the efficiency of sample selection during drug development.