Konstantin Kolegov | Astrakhan State University (original) (raw)
Papers by Konstantin Kolegov
Physics of Fluids, 2024
The continuing development of evaporative lithography is important for many areas such as the cre... more The continuing development of evaporative lithography is important for many areas such as the creation of photonic crystals for optronics and microelectronics, the development of biosensors for medical applications and biotechnology, and for the formation of functional coatings for nanotechnology, including the application of thin, protective polymer coatings. The article proposes a mathematical model that allows us to explain the basic mechanisms of the formation of thin polymer films (less than 50 μm thick) during their deposition onto a composite substrate by methanol evaporation from a solution. If the thermal conductivity of the substrate is spatially non-uniform, this results in inhomogeneous evaporation along the free film surface. Therefore, as the film dries, a patterned polymer coating is left behind on the substrate. The mathematical model described here is based on the lubrication approximation and takes into account the dependence of the solution density on the concentration. The numerical computation results are in qualitative agreement with the experimental data of other authors. The article shows that solutal Marangoni flow plays a primary role in the process under consideration. This study allows us to better understand the mechanisms that can be used in evaporative lithography.
arXiv (Cornell University), Jan 17, 2023
Journal of Physics: Conference Series, 2021
In this work, we continue to study the formation of particle chains (clusters) inside the annular... more In this work, we continue to study the formation of particle chains (clusters) inside the annular sediment during the drying of a colloidal droplet on a substrate. The average value of the cluster size was determined after processing experimental data from other authors. We performed a series of calculations and found the value of the model parameter allowed to get numerical results agreed with the experiment. Also, a modification of the previously proposed algorithm is analyzed here.
Advances in Colloid and Interface Science, 2020
The review covers experimental results of evaporative lithography and analyzes existing mathemati... more The review covers experimental results of evaporative lithography and analyzes existing mathematical models of this method. Evaporating droplets and films are applied in different fields, such as cooling of heated surfaces of electronic devices, diagnostics in health care, creation of transparent conductive coatings on flexible substrates, surface patterning. A method called evaporative lithography emerged after establishing the connection between the coffee ring effect taking place in drying colloidal droplets, and naturally occuring inhomogeneous vapor flow densities from fluid-vapor interfaces. Essential control of the colloidal particle deposit patterns is achieved in this method by producing ambient conditions that induce a nonuniform evaporation profile from the colloidal liquid surface. Evaporative lithography is part of a wider field, which is known as "Evaporative-induced self-assembly" (EISA). EISA involves methods based on the contact line processes, methods employing particle interaction effects and evaporative lithography. As a rule, evaporative lithography is a flexible and single-stage process with such advantages as simplicity, low price and possibility of application to almost any substrate without pretreatment. Since no mechanical impact on a template is present in evaporative lithography, the template integrity is preserved in the process. The method is also useful for creating materials with localized functions, such as slipperiness and self-healing. For these reasons, evaporative lithography attracts increasing attention and has a number of noticeable achievements at present. We also analyze limitations of the approach and ways of its further development.
Computer Research and Modeling, 2012
Выведены основные уравнения нестационарной математической модели одномерных (осредненных по высот... more Выведены основные уравнения нестационарной математической модели одномерных (осредненных по высоте капли) течений в высыхающей капле, покоящейся на твердом основании. В результате численных расчетов показано, что процессы в капле определяются законом испарения и значением капиллярного числа. При малых значениях капиллярного числа результаты, полученные с использованием нестационарной модели, мало отличаются от полученных при квазистационарном описании явления. При больших значениях капиллярного числа необходимо пользоваться полной формой записи уравнения. Ключевые слова: испаряющаяся капля, одномерное уравнение движения, нестационарная модель Работа выполнена при финансовой поддержке Министерства образования и науки Российской Федерации, проект 1.588.2011 «Математическое моделирование процессов самоорганизации в системах микро-и наночастиц».
Journal of Physics: Conference Series, 2019
The work is devoted to particles dynamics simulation in a colloidal drop, when it dries on a subs... more The work is devoted to particles dynamics simulation in a colloidal drop, when it dries on a substrate and the triple-phase boundary is fixed. Experimental observations [Deegan R. D. et. al., 2000] show a ring deposition on a solid substrate after full droplet desiccation. This phenomenon of macrolevel is known as coffee ring effect. There are other experiments that show a co-effect at the microlevel. We are talking about the formation of a quasicrystalline structure on the outer part of the ring and occurrence of an amorphous inner zone of ring [MarínÁ. G. et. al., 2011]. The goal of this work is to check the hypothesis of other authors that this phenomenon is explained by the competition between the characteristic times of diffusional displacement of particles and their transfer by a compensation flow [MarínÁ. G. et. al., 2011]. Numerical calculations using a two-dimensional model built on the basis of such assumptions and effects did not show formation of the amorphous zone. Probably, it is necessary to take into account the possibility of forming a multilayer structure of particles (3D-model).
Microgravity Science and Technology, 2017
The paper theoretically studies the method of evaporative lithography in combination with externa... more The paper theoretically studies the method of evaporative lithography in combination with external infrared heating. This method makes it possible to form solid microstructures of the required relief shape as a result of evaporation of the liquid film of the colloidal solution under the mask. The heated particles are sintered easier, so there are no cracks in the obtained structure, unlike the structure obtained employing the standard method of evaporative lithography. The paper puts forward a modification of the mathematical model which allows to describe not only heat and mass transfer at the initial stage of the process, but also the phase transition of colloidal solution into glass. Aqueous latex is taken as an example. The resulting final form of solid film is in good agreement with the experimental data of other authors.
Выведены основные уравнения нестационарной математической модели одномерных (осредненных по высот... more Выведены основные уравнения нестационарной математической модели одномерных (осредненных по высоте капли) течений в высыхающей капле, покоящейся на твердом основании. В результате численных расчетов показано, что процессы в капле определяются законом испарения и значением капиллярного числа. При малых значениях капиллярного числа результаты, полученные с использованием нестационарной модели, мало отличаются от полученных при квазистационарном описании явления. При больших значениях капиллярного числа необходимо пользоваться полной формой записи уравнения. The work aims to study the admissibility of the quasi-steady approach application in fluid flow modeling inside of evaporating drops placed on a solid horizontal substrate. Non-steady model has been developed to compare results with a quasi-steady model. For the first time one-dimensional motion equation of fluid in a drop is proposed from a momentum conservation law. We have shown that inward flow is possible on the edge of drop in one-dimensional models. It may be explained by existence of stagnation points.
Physics of Fluids, 2022
Colloidal droplets are used in a variety of practical applications. Some of these applications re... more Colloidal droplets are used in a variety of practical applications. Some of these applications require particles of different sizes. These include medical diagnostic methods, the creation of photonic crystals, the formation of supraparticles, and the production of membranes for biotechnology. A series of earlier experiments had shown the possibility of particle separation near the contact line, depending upon their size. A mathematical model has been developed to describe this process. Bi-dispersed colloidal droplets evaporating on a hydrophilic substrate are taken into consideration. A particle monolayer is formed near the periphery of such droplets due to the small value of the contact angle. The shape of the resulting deposit is associated with the coffee ring effect. The model takes into account both particle diffusion and transfers caused by capillary flow due to liquid evaporation. Monte Carlo simulations of such particle dynamics have been performed at several values of the particle concentration in the colloidal solution. The numerical results agree with the experimental observations, in which small particles accumulate nearer to the contact line than do the large particles. However, the particles do not actually reach the contact line but accumulate at a small distance from it. The reason for this is the surface tension acting on the particles in areas, where the thickness of the liquid layer is comparable to the particle size. Indeed, the same mechanism affects the observed separation of the small and large particles.
Journal of Physics: Conference Series, 2019
The work is devoted to particles dynamics simulation in a colloidal drop, when it dries on a subs... more The work is devoted to particles dynamics simulation in a colloidal drop, when it dries on a substrate and the triple-phase boundary is fixed. Experimental observations [Deegan R. D. et. al., 2000] show a ring deposition on a solid substrate after full droplet desiccation. This phenomenon of macrolevel is known as coffee ring effect. There are other experiments that show a co-effect at the microlevel. We are talking about the formation of a quasicrystalline structure on the outer part of the ring and occurrence of an amorphous inner zone of ring [Marín Á. G. et. al., 2011]. The goal of this work is to check the hypothesis of other authors that this phenomenon is explained by the competition between the characteristic times of diffusional displacement of particles and their transfer by a compensation flow [Marín Á. G. et. al., 2011]. Numerical calculations using a two-dimensional model built on the basis of such assumptions and effects did not show formation of the amorphous zone. Probably, it is necessary to take into account the possibility of forming a multilayer structure of particles (3D-model).
Physics of Fluids, 2022
Colloidal droplets are used in a variety of practical applications. Some of these applications re... more Colloidal droplets are used in a variety of practical applications. Some of these applications require particles of different sizes. These include medical diagnostic methods, the creation of photonic crystals, the formation of supraparticles, and the production of membranes for biotechnology. A series of earlier experiments had shown the possibility of particle separation near the contact line, depending upon their size. A mathematical model has been developed to describe this process. Bi-dispersed colloidal droplets evaporating on a hydrophilic substrate are taken into consideration. A particle monolayer is formed near the periphery of such droplets due to the small value of the contact angle. The shape of the resulting deposit is associated with the coffee ring effect. The model takes into account both particle diffusion and transfers caused by capillary flow due to liquid evaporation. Monte Carlo simulations of such particle dynamics have been performed at several values of the particle concentration in the colloidal solution. The numerical results agree with the experimental observations, in which small particles accumulate nearer to the contact line than do the large particles. However, the particles do not actually reach the contact line but accumulate at a small distance from it. The reason for this is the surface tension acting on the particles in areas, where the thickness of the liquid layer is comparable to the particle size. Indeed, the same mechanism affects the observed separation of the small and large particles.
Вестник Самарского государственного технического университета. Серия «Физико-математические науки»
Массоперенос в высыхающих каплях и пленках интересен с практической точки зрения, так как применя... more Массоперенос в высыхающих каплях и пленках интересен с практической точки зрения, так как применяется в задачах испарительной литографии. При создании условий неравномерного испарения с поверхности жидкого слоя возникают компенсационные потоки, перемещающие коллоидные частицы в области интенсивного испарения. Это позволяет получать на твердой поверхности микро- и наноструктуры требуемой формы. В работе описана нестационарная модель массопереноса в капельно-пленочных системах. Особенность модели заключается в совместном учете вязких, гравитационных и капиллярных сил. Для решения неустойчивой дискретной задачи о высыхающей капле (пленке) предложена регуляризованная разностная схема, на базе которой разработан комплекс программ. По результатам проведенных вычислительных экспериментов предложен способ получения кольцевых структур из микро- и наночастиц методом испарительной литографии.
Physics of Fluids, 2021
This work is devoted to a method to generate particle cluster assemblies and connected to evapora... more This work is devoted to a method to generate particle cluster assemblies and connected to evaporative lithography. Experiments are carried out using nonuniform evaporation of an isopropanol film containing polystyrene microspheres in a cylindrical cell. The local inhomogeneity of the vapor flux density is achieved by exploiting the temperature gradient. A copper rod is mounted in the central part of the bottom of the cell for further heating. The thermocapillary flow resulting from the surface tension gradient, due in turn to the temperature drop, transfers the particles that were originally at rest at the bottom of the cell. The effect of the initial thickness of the liquid layer on the height and base area of the cluster formed in the central region of the cell is studied. The velocity is measured using particle image velocimetry. A model describing the initial stage of the process is developed. The equations of heat transfer and thermal conductivity are used to define the temperature distribution in the liquid and in the cell. The fluid flow is simulated using the lubrication approximation. The particle distribution is modeled using the convection–diffusion equation. The evaporation flux density is calculated using the Hertz–Knudsen equation. The dependence of the liquid viscosity on the particle concentration is described by Mooney's formula. Numerical results show that the liquid film gradually becomes thinner in the central region, as the surface tension decreases with the increasing temperature. The liquid flow is directed to the heater near the substrate, and it transfers the particles to the center of the cell. The volume fraction of the particles increases over time in this region. The heat flow from the heater affects the geometry of the cluster for two reasons: First, the Marangoni flow velocity depends on the temperature gradient, and second, the decrease in film thickness near the heater depends on the temperature. The results of the simulation are in general agreement with the experimental data.
Journal of Physics: Conference Series, 2021
In this work, we continue to study the formation of particle chains (clusters) inside the annular... more In this work, we continue to study the formation of particle chains (clusters) inside the annular sediment during the drying of a colloidal droplet on a substrate. The average value of the cluster size was determined after processing experimental data from other authors. We performed a series of calculations and found the value of the model parameter allowed to get numerical results agreed with the experiment. Also, a modification of the previously proposed algorithm is analyzed here.
Physics of Fluids, 2024
The continuing development of evaporative lithography is important for many areas such as the cre... more The continuing development of evaporative lithography is important for many areas such as the creation of photonic crystals for optronics and microelectronics, the development of biosensors for medical applications and biotechnology, and for the formation of functional coatings for nanotechnology, including the application of thin, protective polymer coatings. The article proposes a mathematical model that allows us to explain the basic mechanisms of the formation of thin polymer films (less than 50 μm thick) during their deposition onto a composite substrate by methanol evaporation from a solution. If the thermal conductivity of the substrate is spatially non-uniform, this results in inhomogeneous evaporation along the free film surface. Therefore, as the film dries, a patterned polymer coating is left behind on the substrate. The mathematical model described here is based on the lubrication approximation and takes into account the dependence of the solution density on the concentration. The numerical computation results are in qualitative agreement with the experimental data of other authors. The article shows that solutal Marangoni flow plays a primary role in the process under consideration. This study allows us to better understand the mechanisms that can be used in evaporative lithography.
arXiv (Cornell University), Jan 17, 2023
Journal of Physics: Conference Series, 2021
In this work, we continue to study the formation of particle chains (clusters) inside the annular... more In this work, we continue to study the formation of particle chains (clusters) inside the annular sediment during the drying of a colloidal droplet on a substrate. The average value of the cluster size was determined after processing experimental data from other authors. We performed a series of calculations and found the value of the model parameter allowed to get numerical results agreed with the experiment. Also, a modification of the previously proposed algorithm is analyzed here.
Advances in Colloid and Interface Science, 2020
The review covers experimental results of evaporative lithography and analyzes existing mathemati... more The review covers experimental results of evaporative lithography and analyzes existing mathematical models of this method. Evaporating droplets and films are applied in different fields, such as cooling of heated surfaces of electronic devices, diagnostics in health care, creation of transparent conductive coatings on flexible substrates, surface patterning. A method called evaporative lithography emerged after establishing the connection between the coffee ring effect taking place in drying colloidal droplets, and naturally occuring inhomogeneous vapor flow densities from fluid-vapor interfaces. Essential control of the colloidal particle deposit patterns is achieved in this method by producing ambient conditions that induce a nonuniform evaporation profile from the colloidal liquid surface. Evaporative lithography is part of a wider field, which is known as "Evaporative-induced self-assembly" (EISA). EISA involves methods based on the contact line processes, methods employing particle interaction effects and evaporative lithography. As a rule, evaporative lithography is a flexible and single-stage process with such advantages as simplicity, low price and possibility of application to almost any substrate without pretreatment. Since no mechanical impact on a template is present in evaporative lithography, the template integrity is preserved in the process. The method is also useful for creating materials with localized functions, such as slipperiness and self-healing. For these reasons, evaporative lithography attracts increasing attention and has a number of noticeable achievements at present. We also analyze limitations of the approach and ways of its further development.
Computer Research and Modeling, 2012
Выведены основные уравнения нестационарной математической модели одномерных (осредненных по высот... more Выведены основные уравнения нестационарной математической модели одномерных (осредненных по высоте капли) течений в высыхающей капле, покоящейся на твердом основании. В результате численных расчетов показано, что процессы в капле определяются законом испарения и значением капиллярного числа. При малых значениях капиллярного числа результаты, полученные с использованием нестационарной модели, мало отличаются от полученных при квазистационарном описании явления. При больших значениях капиллярного числа необходимо пользоваться полной формой записи уравнения. Ключевые слова: испаряющаяся капля, одномерное уравнение движения, нестационарная модель Работа выполнена при финансовой поддержке Министерства образования и науки Российской Федерации, проект 1.588.2011 «Математическое моделирование процессов самоорганизации в системах микро-и наночастиц».
Journal of Physics: Conference Series, 2019
The work is devoted to particles dynamics simulation in a colloidal drop, when it dries on a subs... more The work is devoted to particles dynamics simulation in a colloidal drop, when it dries on a substrate and the triple-phase boundary is fixed. Experimental observations [Deegan R. D. et. al., 2000] show a ring deposition on a solid substrate after full droplet desiccation. This phenomenon of macrolevel is known as coffee ring effect. There are other experiments that show a co-effect at the microlevel. We are talking about the formation of a quasicrystalline structure on the outer part of the ring and occurrence of an amorphous inner zone of ring [MarínÁ. G. et. al., 2011]. The goal of this work is to check the hypothesis of other authors that this phenomenon is explained by the competition between the characteristic times of diffusional displacement of particles and their transfer by a compensation flow [MarínÁ. G. et. al., 2011]. Numerical calculations using a two-dimensional model built on the basis of such assumptions and effects did not show formation of the amorphous zone. Probably, it is necessary to take into account the possibility of forming a multilayer structure of particles (3D-model).
Microgravity Science and Technology, 2017
The paper theoretically studies the method of evaporative lithography in combination with externa... more The paper theoretically studies the method of evaporative lithography in combination with external infrared heating. This method makes it possible to form solid microstructures of the required relief shape as a result of evaporation of the liquid film of the colloidal solution under the mask. The heated particles are sintered easier, so there are no cracks in the obtained structure, unlike the structure obtained employing the standard method of evaporative lithography. The paper puts forward a modification of the mathematical model which allows to describe not only heat and mass transfer at the initial stage of the process, but also the phase transition of colloidal solution into glass. Aqueous latex is taken as an example. The resulting final form of solid film is in good agreement with the experimental data of other authors.
Выведены основные уравнения нестационарной математической модели одномерных (осредненных по высот... more Выведены основные уравнения нестационарной математической модели одномерных (осредненных по высоте капли) течений в высыхающей капле, покоящейся на твердом основании. В результате численных расчетов показано, что процессы в капле определяются законом испарения и значением капиллярного числа. При малых значениях капиллярного числа результаты, полученные с использованием нестационарной модели, мало отличаются от полученных при квазистационарном описании явления. При больших значениях капиллярного числа необходимо пользоваться полной формой записи уравнения. The work aims to study the admissibility of the quasi-steady approach application in fluid flow modeling inside of evaporating drops placed on a solid horizontal substrate. Non-steady model has been developed to compare results with a quasi-steady model. For the first time one-dimensional motion equation of fluid in a drop is proposed from a momentum conservation law. We have shown that inward flow is possible on the edge of drop in one-dimensional models. It may be explained by existence of stagnation points.
Physics of Fluids, 2022
Colloidal droplets are used in a variety of practical applications. Some of these applications re... more Colloidal droplets are used in a variety of practical applications. Some of these applications require particles of different sizes. These include medical diagnostic methods, the creation of photonic crystals, the formation of supraparticles, and the production of membranes for biotechnology. A series of earlier experiments had shown the possibility of particle separation near the contact line, depending upon their size. A mathematical model has been developed to describe this process. Bi-dispersed colloidal droplets evaporating on a hydrophilic substrate are taken into consideration. A particle monolayer is formed near the periphery of such droplets due to the small value of the contact angle. The shape of the resulting deposit is associated with the coffee ring effect. The model takes into account both particle diffusion and transfers caused by capillary flow due to liquid evaporation. Monte Carlo simulations of such particle dynamics have been performed at several values of the particle concentration in the colloidal solution. The numerical results agree with the experimental observations, in which small particles accumulate nearer to the contact line than do the large particles. However, the particles do not actually reach the contact line but accumulate at a small distance from it. The reason for this is the surface tension acting on the particles in areas, where the thickness of the liquid layer is comparable to the particle size. Indeed, the same mechanism affects the observed separation of the small and large particles.
Journal of Physics: Conference Series, 2019
The work is devoted to particles dynamics simulation in a colloidal drop, when it dries on a subs... more The work is devoted to particles dynamics simulation in a colloidal drop, when it dries on a substrate and the triple-phase boundary is fixed. Experimental observations [Deegan R. D. et. al., 2000] show a ring deposition on a solid substrate after full droplet desiccation. This phenomenon of macrolevel is known as coffee ring effect. There are other experiments that show a co-effect at the microlevel. We are talking about the formation of a quasicrystalline structure on the outer part of the ring and occurrence of an amorphous inner zone of ring [Marín Á. G. et. al., 2011]. The goal of this work is to check the hypothesis of other authors that this phenomenon is explained by the competition between the characteristic times of diffusional displacement of particles and their transfer by a compensation flow [Marín Á. G. et. al., 2011]. Numerical calculations using a two-dimensional model built on the basis of such assumptions and effects did not show formation of the amorphous zone. Probably, it is necessary to take into account the possibility of forming a multilayer structure of particles (3D-model).
Physics of Fluids, 2022
Colloidal droplets are used in a variety of practical applications. Some of these applications re... more Colloidal droplets are used in a variety of practical applications. Some of these applications require particles of different sizes. These include medical diagnostic methods, the creation of photonic crystals, the formation of supraparticles, and the production of membranes for biotechnology. A series of earlier experiments had shown the possibility of particle separation near the contact line, depending upon their size. A mathematical model has been developed to describe this process. Bi-dispersed colloidal droplets evaporating on a hydrophilic substrate are taken into consideration. A particle monolayer is formed near the periphery of such droplets due to the small value of the contact angle. The shape of the resulting deposit is associated with the coffee ring effect. The model takes into account both particle diffusion and transfers caused by capillary flow due to liquid evaporation. Monte Carlo simulations of such particle dynamics have been performed at several values of the particle concentration in the colloidal solution. The numerical results agree with the experimental observations, in which small particles accumulate nearer to the contact line than do the large particles. However, the particles do not actually reach the contact line but accumulate at a small distance from it. The reason for this is the surface tension acting on the particles in areas, where the thickness of the liquid layer is comparable to the particle size. Indeed, the same mechanism affects the observed separation of the small and large particles.
Вестник Самарского государственного технического университета. Серия «Физико-математические науки»
Массоперенос в высыхающих каплях и пленках интересен с практической точки зрения, так как применя... more Массоперенос в высыхающих каплях и пленках интересен с практической точки зрения, так как применяется в задачах испарительной литографии. При создании условий неравномерного испарения с поверхности жидкого слоя возникают компенсационные потоки, перемещающие коллоидные частицы в области интенсивного испарения. Это позволяет получать на твердой поверхности микро- и наноструктуры требуемой формы. В работе описана нестационарная модель массопереноса в капельно-пленочных системах. Особенность модели заключается в совместном учете вязких, гравитационных и капиллярных сил. Для решения неустойчивой дискретной задачи о высыхающей капле (пленке) предложена регуляризованная разностная схема, на базе которой разработан комплекс программ. По результатам проведенных вычислительных экспериментов предложен способ получения кольцевых структур из микро- и наночастиц методом испарительной литографии.
Physics of Fluids, 2021
This work is devoted to a method to generate particle cluster assemblies and connected to evapora... more This work is devoted to a method to generate particle cluster assemblies and connected to evaporative lithography. Experiments are carried out using nonuniform evaporation of an isopropanol film containing polystyrene microspheres in a cylindrical cell. The local inhomogeneity of the vapor flux density is achieved by exploiting the temperature gradient. A copper rod is mounted in the central part of the bottom of the cell for further heating. The thermocapillary flow resulting from the surface tension gradient, due in turn to the temperature drop, transfers the particles that were originally at rest at the bottom of the cell. The effect of the initial thickness of the liquid layer on the height and base area of the cluster formed in the central region of the cell is studied. The velocity is measured using particle image velocimetry. A model describing the initial stage of the process is developed. The equations of heat transfer and thermal conductivity are used to define the temperature distribution in the liquid and in the cell. The fluid flow is simulated using the lubrication approximation. The particle distribution is modeled using the convection–diffusion equation. The evaporation flux density is calculated using the Hertz–Knudsen equation. The dependence of the liquid viscosity on the particle concentration is described by Mooney's formula. Numerical results show that the liquid film gradually becomes thinner in the central region, as the surface tension decreases with the increasing temperature. The liquid flow is directed to the heater near the substrate, and it transfers the particles to the center of the cell. The volume fraction of the particles increases over time in this region. The heat flow from the heater affects the geometry of the cluster for two reasons: First, the Marangoni flow velocity depends on the temperature gradient, and second, the decrease in film thickness near the heater depends on the temperature. The results of the simulation are in general agreement with the experimental data.
Journal of Physics: Conference Series, 2021
In this work, we continue to study the formation of particle chains (clusters) inside the annular... more In this work, we continue to study the formation of particle chains (clusters) inside the annular sediment during the drying of a colloidal droplet on a substrate. The average value of the cluster size was determined after processing experimental data from other authors. We performed a series of calculations and found the value of the model parameter allowed to get numerical results agreed with the experiment. Also, a modification of the previously proposed algorithm is analyzed here.