Unveiling nutrient flow-mediated stress in plant roots using an on-chip phytofluidic device.

The initial emergence of the primary root from a germinating seed is a pivotal phase that influences a plant's survival. Abiotic factors such as pH, nutrient availability, and soil composition significantly affect root morphology and architecture. Of particular interest is the impact of nutrient flow on thigmomorphogenesis, a response to mechanical stimulation in early root growth, which remains largely unexplored. This study explores the intricate factors influencing early root system development, with a focus on the cooperative correlation between nutrient uptake and its flow dynamics. Using a physiologically as well as ecologically relevant, portable, and cost-effective microfluidic system for the controlled fluid environments offering hydraulic conductivity comparable to that of the soil, this study analyzes the interplay between nutrient flow and root growth post-germination. Emphasizing the relationship between root growth and nitrogen uptake, the findings reveal that nutrient flow significantly influences early root morphology, leading to increased length and improved nutrient uptake, varying with the flow rate. The experimental findings are supported by mechanical and plant stress-related fluid flow-root interaction simulations and quantitative determination of nitrogen uptake using the total Kjeldahl nitrogen (TKN) method. The microfluidic approach offers novel insights into plant root dynamics under controlled flow conditions, filling a critical research gap. By providing a high-resolution platform, this study contributes to the understanding of how fluid-flow-assisted nutrient uptake and pressure affect root cell behavior, which, in turn, induces mechanical stress leading to thigmomorphogenesis. The findings hold implications for comprehending root responses to changing environmental conditions, paving the way for innovative agricultural and environmental management strategies.

Maximizing blue energy: the role of ion partitioning in nanochannel systems.

This study describes a numerical analysis on blue energy generation using a charged nanochannel with an integrated pH-sensitive polyelectrolyte layer (PEL), considering ion partitioning effects due to permittivity differences. The mathematical model for ionic and fluidic transport is solved using the finite element method, and the model validation is performed against existing theoretical and experimental results. The study investigates the influence of electrolyte concentration, permittivity ratio, and salt types (KCl, BeCl2, AlCl3) on the energy conversion process. The findings illustrate the substantial role of ion partitioning in modulating ionic concentration and potential fields, thereby affecting current profiles and energy conversion efficiencies. Remarkably, overlooking ion partitioning leads to significant overestimations of power density, highlighting the necessity of this consideration for accurate device performance predictions. This work introduces a promising configuration that achieves higher power densities, paving the way for the next generation of efficient energy-harvesting devices. The findings offer valuable insights into the development of state-of-the-art blue energy harvesting nanofluidic devices, advancing sustainable energy production.

Evaluating the potential of ethyl cellulose/eudragit-based griseofulvin loaded nanosponge matrix for topical antifungal drug delivery in a sustained release pattern.

Fungal infections are very alarming nowadays and are common throughout the world. Severe fungal infections may lead to a significant risk of mortality and morbidity worldwide. Sustained delivery of antifungal agents is needed to mitigate this problem. In the current study, an attempt has been made to formulate griseofulvin-loaded nanosponges using the quasi-emulsion solvent diffusion technique. For characterization, griseofulvin loaded nanosponges were tested by different instrumental techniques such as optical microscopy, scanning electron microscopy (SEM), powder X-ray diffractometer (PXRD), Fourier transform infrared spectroscopy (FT-IR), differential scanning calorimetry (DSC), and transmission electron microscopy (TEM). The antifungal activity of the nanosponges was assessed against Candida albican strain using the agar well-diffusion method. Finally, the drug-loaded nanosponges' in vitro sustained release activity was evaluated. FTIR spectra showed no chemical interference between the drug and polymers. Some of the peaks of the drug are not visible in the FTIR spectrum, which suggests drug entrapment. PXRD data showed that the drug lost its high crystallinity when entrapped in the nanosponge matrix. From the morphological studies via SEM and TEM, a brief idea of the surface morphology of the nanosponges was obtained. The small pores throughout the structure proved its high porosity. The antifungal sensitivity assay was successful, and a zone of inhibition was observed in all the formulations. The in-vitro drug release study showed sustained behaviour. The sustaining effect was due to the polymer and cross-linker used, which gave rise to a porous scaffold matrix. From the results, it can be concluded that griseofulvin-loaded nanosponges can be used for antifungal drug delivery against various topical skin infections.

AC Electrothermal Effect Promotes Enhanced Solute Mixing in a Wavy Microchannel.

For liquids used in biological applications, a smaller diffusion coefficient results in a longer mixing time. We discuss, in this endeavor, the promising potential of the AC electrothermal (ACET) effect toward modulating enhanced mixing of electrolytic liquids with higher convective strength in a novel wavy micromixer. To this end, we develop a modeling framework and numerically solve the pertinent transport equations in a three-dimensional (3D) configuration numerically. By benchmarking the developed modeling framework with the experimental results available in this paradigm, we aptly demonstrate the maximum temperature rise, flow topology, species concentration field, and mixing efficiency in the proposed configuration for a set of parameters pertinent to this analysis. We find that the maximum temperature increase in the wavy micromixer, owing to the electrothermal effect, is less than 10 K even for the higher strength of the applied voltage, implying nondegradation of biological substances within the liquid sample. We report that the formation of significant lateral flow closer to the electrodes leads to a highly three-dimensional ACET flow field, which has a significant impact on the mixing efficiency for the range of diffusive Peclet numbers considered. We also report that the wave amplitude of the mixer, when intervening with the diffusive Peclet number, strongly impacts the mixing efficiency. As witnessed in this endeavor, for the smaller diffusive Peclet number, the mixing efficiency increases with amplitude, while the effect becomes the opposite for the higher Peclet number. The results of this study seem to provide an adequate basis for the design of a novel micromixer intended for enhanced solute mixing in realistic microfluidic applications.

Salinity Gradient-Induced Power Generation in Nanochannels: The Role of pH-Sensitive Polyelectrolyte Layers.

By varying the pH values (pHR) and types of salt solution, we investigate the salinity gradient-induced electrical and mechanical flow energies inside a reservoir-connected charged nanochannel with a grafted pH-sensitive polyelectrolyte layer (PEL) on the inner surfaces. The aqueous solutions of KCl, LiCl, BaCl2, BeCl2, AlCl3, and Co(en)3Cl3 salts are used as the working fluid in the current investigation. We examine the associated ionic transport and flow field, aiming to understand the underlying physics behind the generation of electrical and hydraulic energy through alterations in pHR and types of salt solution. Our results reveal that the PEL space charge density decreases with increasing pHR at lower values, while it remains almost insensitive to higher pHR values. The electrical conductance and maximum pore power of the Co(en)3Cl3 solution are significantly higher compared to salts with monovalent and divalent cations. Furthermore, the magnitude of these two parameters decreases with lower pHR and becomes insensitive to higher pHR values. The results illustrate that the maximum electrical energy conversion efficiency enhances with pHR, reaching its highest level for the Co(en)3Cl3 solution. We expect that the findings of the current work will have a significant bearing on the design and development of a state-of-the-art salinity gradient-based energy convertor as a potential candidate for renewable energy sources.

Dielectric polarization-mediated efficient solute mixing: Effect of the geometrical configuration of polarizing blocks.

We propose a novel technique, consistent with the induced charge electrokinetic (ICEK) phenomenon, for the efficient mixing of solute species at a microfluidic scale. A nonuniform bipolar electric double layer develops in the presence of an external electric field over a polarizable object is better known as the ICEK phenomenon. This ICEK is one of the most favorable techniques preferred for enhanced solute mixing in on-chip microfluidic platforms. In the purview of the ICEK phenomenon, instead of using perfectly conducting polarizable objects, for the first time in this study, we employ polarizable dielectric objects of different sizes and shapes for efficient mixing of solute species. We show that different types of vortices developed in the flow pathway adjacent to the polarizable dielectric blocks help in yielding efficient mixing in the proposed configuration. The novelty of our work is embellished in two different perspectives, that is, first, concentrating on the influences of the physical properties of the polarizable dielectric block on the underlying mixing, and, second, focusing on their sizes, shapes, and the arrangements in tuning the underlying mixing phenomena.

Vortex-assisted electroosmotic mixing of Carreau fluid in a microchannel.

Pertaining to the mixing of the non-Newtonian Carreau fluid under electrokinetic actuation inside a plane microchannel, we propose a new design of micromixer that involves inserting a two-part cylinder bearing zeta potential of the same sign but different magnitude in the upstream and downstream directions. We numerically solve the transport equations to predict the underlying mixing characteristics. We demonstrate that a substantial momentum difference between the microchannel's plane wall and cylinder leads to the development of a vortex in the flow pathway, which in turn, enhances mixing substantially. As shown, for a fluid having a highly shear-thinning nature, the vortex-assisted convection mixing strength increases with diffusivity of the candidate fluids. Moreover, it is shown that for the higher shear-thinning nature of the candidate fluid, an increase in cylinder radius enhances mixing efficiency and flow rate simultaneously, resulting in a "quick and efficient" mixing condition. Additionally, the fluid rheology significantly alters the kinetics of shear-induced binary aggregation. Our findings show that the shear-induced aggregation characteristic time sharply increases with increasing shear-thinning behavior of the fluid.

Chemiosomotic flow in a soft conical nanopore: harvesting enhanced blue energy.

The salinity gradient energy or the 'blue energy' is one of the most promising inexpensive and abundant sources of clean energy, having immense capabilities to serve modern-day society. In this article, we overlay an extensive analysis of reverse electrodialysis (RED) for harvesting salinity gradient energy in a single conical nanochannel, grafted with a pH-tunable polyelectrolyte layer (PEL) on the inner surfaces. We primarily focus on the distinctiveness of the solution pH of the connecting reservoirs. In spite of acquiring a maximum power density of ∼1.2 kW m-2 in the chosen configuration, we notice a counter-intuitive patterning of the ion transport for a certain span of pH, leading to diminishing power. To this end, we discuss the possible strategic avenues essentially to achieve a higher amount of power density. In order to achieve a desirable outcome within that pH zone, we employ two separate approaches intending to counter the underlying physics. Results reveal a great enhancement in the power density as well as in the efficiency even under the framework of both strategies proposed herein. Moreover, as shown, the window of solution pH has increased by three times, implicating the maximum power density mentioned above. We expect that the strategic procedure of augmented energy harvesting as discussed in this analysis can be of importance from the perspective of fabricating state-of-the-art nanodevices aimed at blue energy harvesting.

Influence of viscoelectric effect on diffusioosmotic transport in nanochannel.

We have investigated the role of viscoelectric effect on diffusioosmotic flow (DOF) through a nanochannel connected with two reservoirs. The transport equations governing the flow dynamics are solved numerically using the finite element technique. We have extensively analyzed the variation of induced field due to electric double layer (EDL) phenomenon, relative viscosity as modulated by the viscoelectric effect as well as reservoir's concentration difference, and their eventual impact on the underlying flow characteristics. It is revealed that the induced electric field in the EDL enhances fluid viscosity substantially near the charged wall at a higher concentration. We have shown that neglecting viscoelectric effect in the paradigm of diffusioosmotic transport overestimates the net throughput, particularly at a higher concentration difference. Furthermore, we show that pertaining to chemiosmosis dominated regime, the average flow velocity modifies with the increase in concentration difference up to a critical value. In comparison, the rise in the strength of resistive electroosmotic actuation by the accumulation of anions in the upstream reservoir reduces the average flow velocity at a higher concentration difference. We have reported a reduction in critical concentration with the increase in viscoelectric effect. The inferences of this analysis are deemed pertinent to reveal the bearing of viscoelectric effect as a flow control mechanism pertaining to DOF at nanoscale.

RAV1 mediates cytokinin signaling for regulating primary root growth in Arabidopsis.

Root growth dynamics is an outcome of complex hormonal crosstalk. The primary root meristem size, for example, is determined by antagonizing actions of cytokinin and auxin. Here we show that RAV1, a member of the AP2/ERF family of transcription factors, mediates cytokinin signaling in roots to regulate meristem size. The rav1 mutants have prominently longer primary roots, with a meristem that is significantly enlarged and contains higher cell numbers, compared with wild-type. The mutant phenotype could be restored on exogenous cytokinin application or by inhibiting auxin transport. At the transcript level, primary cytokinin-responsive genes like ARR1, ARR12 were significantly downregulated in the mutant root, indicating impaired cytokinin signaling. In concurrence, cytokinin induced regulation of SHY2, an Aux/IAA gene, and auxin efflux carrier PIN1 was hindered in rav1, leading to altered auxin transport and distribution. This effectively altered root meristem size in the mutant. Notably, CRF1, another member of the AP2/ERF family implicated in cytokinin signaling, is transcriptionally repressed by RAV1 to promote cytokinin response in roots. Further associating RAV1 with cytokinin signaling, our results demonstrate that cytokinin upregulates RAV1 expression through ARR1, during post-embryonic root development. Regulation of RAV1 expression is a part of secondary cytokinin response that eventually represses CRF1 to augment cytokinin signaling. To conclude, RAV1 functions in a branch pathway downstream to ARR1 that regulates CRF1 expression to enhance cytokinin action during primary root development in Arabidopsis.

Leveraging spreadsheet analysis tool for electrically actuated start-up flow of non-Newtonian fluid in small-scale systems.

In this article, we demonstrate the solution methodology of start-up electrokinetic flow of non-Newtonian fluids in a microfluidic channel having square cross-section using Spreadsheet analysis tool. In order to incorporate the rheology of the non-Newtonian fluids, we take into consideration the Ostwald-de Waele power law model. By making a comprehensive discussion on the implementation details of the discretized form of the transport equations in Spreadsheet analysis tool, and establishing the analytical solution for a special case of the start-up flow, we compare the results both during initial transience as well as in case of steady-state scenario. Also, to substantiate the efficacy of the proposed spreadsheet analysis in addressing the detailed flow physics of rheological fluids, we verify the results for several cases with the corresponding numerical results. It is found that the solution obtained from the Spreadsheet analysis is in good agreement with the numerical results-a finding supporting spreadsheet analysis's suitability for capturing the fine details of microscale flows. We strongly believe that our analysis study will open up a new research scope in simulating microscale transport process of non-Newtonian fluids in the framework of cost-effective and non-time consuming manner.

Blue energy generation by the temperature-dependent properties in funnel-shaped soft nanochannels.

Salinity energy generation (SEG) studies have only been done under isothermal conditions at ambient temperature. The production of salinity energy can be improved under non-isothermal conditions, albeit preserving the energy efficiency. In the current study, the effects of gradients of temperature and concentration on the salinity energy generation process were examined simultaneously. Based on the temperature-dependent properties resulting from both temperature and concentration gradients, a numerical study was carried out to determine the maximum efficiency of salinity energy generation in funnel-shaped soft nanochannels. It was presumed that a dense layer of negative charge, called a polyelectrolyte layer (PEL), is coated on the walls of the nanochannels. Co-current and counter-current modes were used to obtain temperature and concentration gradients. Under steady-state conditions, the Poisson-Nernst-Planck, Stokes-Brinkman, and energy equations were numerically solved using equivalent approaches. The results revealed that by increasing the temperature and concentration ratios in both co-current and counter-current modes of operation, the salinity energy generation increased appreciably. The salinity energy generation increased from 30 to 80 pW upon increasing the temperature ratio from 1 to 8 at a constant concentration ratio of 1000 in counter-current mode. As verified from this analysis, low-grade heat sources (<100 °C) provide considerable energy conversion in PEL grafted nanofluidic confinement when placed between electrolyte solutions of different temperatures.

Characterization of condensation on nanostructured surfaces and associated thermal hydraulics using a thermal lattice Boltzmann method.

The dynamics of the condensation process on nanostructured surfaces can be modulated substantially by tuning the surface architecture. Present study uses the mesoscopic framework of lattice Boltzmann method (LBM) to explore the role of surface morphology and cold spot temperature in determining the visual state of the condensate droplet, mode of nucleation, and associated rates of energy and mass interactions. A multiple relaxation time-(MRT)-based LBM solver, coupled with pseudopotential model, has been developed to simulate a rectangular domain of saturated vapor, housing a cold spot on the bottom rough surface. Superhydrophobicity has been achieved for certain combinations of surface parameters, with the intercolumn spacing being the most influential one. Gradual increase in the spacing modifies the nucleation mode from top through side to bottom, while the droplet changes from Cassie to Wenzel state. The Cassie drop in top nucleation mode exhibits the largest contact angle and least rate of surface heat transfer. Both types of Wenzel drops display large rate of condensation and two peaks in heat transfer, along with very short nucleation time in comparison with Cassie drops. Couple of phase diagrams have been developed combining all four scenarios of condensation predicted by the present model. One important novelty of the present study is the consideration of nonisothermal condition within LB structure. Enhancement in the degree of subcooling at the cold spot encourages greater condensation and Cassie-to-Wenzel transition.

Quantitative model for predicting the imbibition dynamics of viscoelastic fluids in nonuniform microfluidic assays.

We develop a mathematical model to quantitatively describe the imbibition dynamics of an elastic non-Newtonian fluid in a conical (nonuniform cross section) microfluidic assay. We consider the simplified Phan-Thien-Tanner viscoelastic model to represent the rheology of the elastic non-Newtonian fluid. Our model accounts for the geometrical features of the fluidic assay, the key parameters affecting the rheological behavior of the fluid, and predicts the imbibition dynamics effectively. By demonstrating the temporal advancement of the filling length in the conical capillary graphically, obtained for pertinent parametric values belonging to their physically permissible range, we report an underlying balance between capillary and viscous forces during imbibition resulting in three distinct regimes of filling. Nonuniformity in the capillary cross section gives rise to an alteration in the viscous force being applied at the contact line (manifested through the alteration in shear rate) during the imbibition process, which upon maintaining a balance with the dominant capillary force results in three different regimes of filling. We believe that the present analysis has a twofold significance. First, this work will enhance the understanding of underlying imbibition dynamics of viscoelastic fluids (most of the biofluids exhibit viscoelastic rheology) in nonuniform fluidic pathways. Second, the developed model is of significant practical relevance for the optimum design of microfluidic assays, primarily used for sample diagnostics in biochemical and biomedical applications.

Algorithmic augmentation in the pseudopotential-based lattice Boltzmann method for simulating the pool boiling phenomenon with high-density ratio.

The pseudopotential-based lattice Boltzmann method (LBM), despite enormous potential in facilitating natural development and migration of interfaces during multiphase simulation, remains restricted to low-density ratios, owing to inherent thermodynamic inconsistency. The present paper focuses on augmenting the basic algorithm by enhancing the isotropy of the discrete equation and thermodynamic consistency of the overall formulation, to expedite simulation of pool boiling at higher-density ratios. Accordingly, modification is suggested in the discrete form of the updated interparticle interaction term, by expanding the discretization to the eighth order. The proposed amendment is successful in substantially reducing the spurious velocity in the vicinity of a static droplet, while allowing stable simulation at a much higher-density ratio under identical conditions, which is a noteworthy improvement over existing Single Relaxation Time (SRT)-LBM algorithms. Various pool boiling scenarios have been explored for a reduced temperature of 0.75, which itself is significantly lower than reported in comparable literature, in both rectangular and cylindrical domains, and also with micro- and distributed heaters. All three regimes of pool boiling have aptly been captured with both plain and structured heaters, allowing the development of the boiling curve. The predicted value of critical heat flux for the plain heater agrees with Zuber correlation within 10%, illustrating both quantitative and qualitative capability of the proposed algorithm.

Multifunctional liquid marbles to stabilize and transport reactive fluids.

The self-organized transport and delivery of reactive liquids without spillage or loss of activity have been among the most daunting challenges for a long time. In this direction, we employ the concept of forming "liquid marbles" (LMs) to encapsulate and transport reactive hydrogen peroxide (H2O2) coated with functional microparticles. For example, peroxide marbles coated with a toner ink display remote-controlled magnetotactic movement inside a fluidic medium, thus overcoming the weaknesses associated with use of the bare droplets. Interestingly, in such a scenario, the coating of the marbles could also be removed or reformed by bringing the magnet towards or away from the marble. In this way, this process could ensure an on-demand remotely guided coating on the peroxide droplet or its removal. The liquid marbles carrying peroxide solutions are found to preserve the activity of the peroxide and exhibit a low evaporation rate compared with the uncoated peroxide fuel. Interestingly, oil droplets floating on the water could be recovered by introducing the armoured LMs into water under magnetic guidance. Further, the functionalized marbles could be employed as suicide bags for the on-demand delivery of reactive materials in targeted locations. Preliminary research on the antibacterial activity of such liquid marbles has proven to be effective in bacterial killing, which may create new avenues for emerging antibacterial and antibiofilm applications. Finally, such functionalized LMs have been employed to investigate the effects of surface charge on attachment of recombinant Escherichia coli bacteria expressing green fluorescent protein and monitoring the real-time imaging of bacterial death attached to the marble surface.

Spreadsheet analysis of the field-driven start-up flow in a microfluidic channel.

We discuss, in this article, the solution method of the unsteady electroosmotic flow of Newtonian fluid in a square microfluidic channel cross-section in the framework of spreadsheet analysis. We demonstrate the implementation of the finite difference scheme, which is used for the discretization of the transport equations governing the flow dynamics of the present problem, in the spreadsheet tool. Also, we have shown the implementation details of different boundary conditions, which are typically used for the underlying electrohydrodynamics in a microfluidic channel, in the spreadsheet analysis tool. We show that the results obtained from the spreadsheet analysis match accurately with the numerical solutions for both the electrostatic potential distribution and the flow velocity. Our results of this analysis justify the credibility of the spreadsheet tool for capturing the intricate details of the electrically actuated microflows during the initial transiences, that is, for the start-up flows and the phenomenon due to the electrical double layer effect, quite effectively. The inferences of this analysis will open up a new research paradigm of microfluidics and microscale transport processes by providing the potential applicability of the spreadsheet tools to obtain the flow physics of our interest in a very intuitive and less expensive manner.

Autofocusing in digital holography using eigenvalues.

A new autofocusing algorithm for digital holography is proposed based on the eigenvalues of the images reconstructed at different distances in the measurement volume. An image quality metric evaluated based on the distribution of its eigenvalues is compared in function of the reconstruction distance to identify the location of the focal plane. The proposed automatic focal plane detection algorithm is capable of working with amplitude objects, phase objects, and mixed type objects. A performance comparison of the proposed algorithm with some previously reported representative algorithms is provided. The simulation and experimental results demonstrate the practical applicability of the proposed algorithm.

Numerical study of the vortex-induced electroosmotic mixing of non-Newtonian biofluids in a nonuniformly charged wavy microchannel: Effect of finite ion size.

We propose a micromixer for obtaining better efficiency of vortex induced electroosmotic mixing of non-Newtonian bio-fluids at a relatively higher flow rate, which finds relevance in many biomedical and biological applications. To represent the rheology of non-Newtonian fluid, we consider the Carreau model in this study, while the applied electric field drives the constituent components in the micromixer. We show that the spatial variation of the applied field, triggered by the topological change of the bounding surfaces, upon interacting with the non-uniform surface potential gives rise to efficient mixing as realized by the formation of vortices in the proposed micromixer. Also, we show that the phase-lag between surface potential leads to the formation of asymmetric vortices. This behavior offers better mixing performance following the appearance of undulation on the flow pattern. Finally, we establish that the assumption of a point charge in the paradigm of electroosmotic mixing, which is not realistic as well, under-predicts the mixing efficiency at higher amplitude of the non-uniform zeta potential. The inferences of the present analysis may guide as a design tool for micromixer where rheological properties of the fluid and flow actuation parameters can be simultaneously tuned to obtain phenomenal enhancement in mixing efficiency.

Investigations into the Complete Spreading Dynamics of a Viscoelastic Drop on a Spherical Substrate.

We study the spreading dynamics of a sphere-shaped elastic non-Newtonian liquid drop on a spherical substrate in the capillary-driven regime. We use the simplified Phan-Thien-Tanner model to represent the rheology of the elastic non-Newtonian drop. We consider the drop to be a crater on a flat substrate to calculate the viscous dissipation near the contact line. Following the approach compatible with the capillary-viscous force balance, we establish the evolution equation for describing the temporal evolution of the contact line during spreading. We show that the contact line velocity obtained from the theoretical calculation matches well with our experimental observations. Also, as confirmed by the present experimental observations, our analysis deems efficient to capture the phenomenon during the late stage of spreading for which the effect of line tension becomes dominant. An increment in the viscoelastic parameter of the fluid increases the viscous dissipation effect at the contact line. It is seen that the higher dissipation effect leads to an enhancement in the wetting time of the drop on the spherical substrate. Also, we have shown that the elastic nature of the fluid leads to an increment in the dynamic contact angle at any temporal instant as compared to its Newtonian counterpart. Finally, we unveil that the phenomenon of the increasing contact angle results in the time required for the complete wetting of drop, which becomes higher with increasing viscoelasticity of the fluid. This article will fill a gap still affecting the existing literature because of the unavailability of experimental investigations of the spreading of the elastic non-Newtonian drop on a spherical substrate.