The process of restoration of museum exhibits is associated with the forming of various structural media, for example, drying of paints layers, varnishes and hardening of gypsum and concrete solutions during the restoration of statues, elements of room decor. The mechanics of such media is characterized by spectra of viscous, plastic and elastic properties in their various combinations. The forming of these substances is influenced by the microclimatic conditions of the premises, in which these processes take place. In technological operations, as a rule, large shear deformations take place, which greatly exceed the elastic limit. Thus, the most significant for technological calculations are viscoplastic properties, which reflect the relationship between the existing shear stresses and the rate of irreversible shear deformation. For a qualitative description of this relationship, it is customary to use consistency curves that relate shear stresses to the rate of irreversible shear deformation or the dependence of the effective viscosity on the rate of irreversible shear deformation. Structure formation is one of the main processes in the technology of processing solidifying paste-like and liquid-like media when their characteristics approach those inherent in the corresponding capillary-porous bodies. The properties of such media depend on the type and nature of the structure. The study and control of the process of structure formation to obtain a medium with desired properties is an important technological task, which can be solved, in particular, by microclimate systems. The change in the structural state of the solidifying medium can be estimated from the corresponding changes in plastic and conventional mechanical strength, degree of hydration, heat release, elastic modulus, etc. In this work, structure formation is understood as a process, as a result of which the characteristics of the material approach the characteristics of the corresponding capillary-porous body (CPB). The main parameter that determines this approximation is the degree of completeness of structure formation. Analysis of the hardening process of the considered pasty and liquid-like media on the basis of the moisture state diagram makes it possible to fix the structural state of the capillary-porous structure of these media and to evaluate the interaction of chemical reactions and the process of structure formation. And the resulting changes in the rate of structure formation allows to identify and evaluate the destructive processes that occur during solidification of the substance.

Fundamental analysis of the thermal conductivity and viscosity of quasi-solid capillary-porous bodies (CPBs), which are museum exhibits’ materials, is presented. The air environment parameters change leads to a temperature gradient in the CPBs. Non-uniform heating of the solid medium, in particular, quasi-solid CPB, is not accompanied by convection, and heat transfer is carried out only due to the mechanism of thermal conductivity. In order to create a mathematical model of this process in CPB, a system of partial differential equations in time and space coordinates is obtained. The resulting system adequately describes the thermal conductivity process in quasi-solid CPBs. The anisotropy of CPB’s thermal parameters, especially, its coefficients of thermal expansion and thermal conductivity, is also taken into account. Theoretically, the deformation process during motion in quasi-solid CPB is taken as reversible. In real conditions, the process is thermodynamically reversible only when it occurs at an infinitesimal speed. Then at each point in time, the CPB is able to establish a thermodynamic equilibrium state. Real motion occurs at a finite velocity, the CPB is not in an equilibrium state at any given moment, so there are endogenous processes that try to get it into a balanced condition. The occurrence of these processes causes the irreversibility of motion, which acts, in particular, through the dissipation of mechanical energy, which eventually turns into heat. The energy dissipation is caused by irreversible processes of thermal conductivity and processes of internal friction or viscosity. The dissipative function for isotropic and anisotropic cases was determined in order to analyze the viscosity of quasi-solid CPBs. The viscosity in the equations of motion can be considered by replacing the stress tensor with a tensor, which additionally takes into account the "dissipative" stress tensor.

Анотація. Наведений фрактальний аналіз довгострокових рядів параметрів колоїдних капілярно-пористих тіл, які знаходяться в умовах тепломасообміну з навколишнім середовищем і викликаної цим процесом деформації. Здійснене фрактальне оцінювання відповідної статистичної інформації щодо вологовмісту, температури та деформації вказаних тіл. Алгоритм розрахунку показника Херста заснований на R/S-аналізі. На основі методики передпрогнозного фрактального аналізу часових рядів (яка базується на послідовному R/S-аналізі) визначений рівень персистентності й розраховані параметри (середні величини) неперіодичних циклів часових рядів. Запропоновано критерій визначення середньої довжини періодичного і неперіодичного циклів, який заснований на згладжуванні V-статистики за допомогою звичайних плинних середніх та адаптивної плинної Кауфмана. Запропоновано також процедуру якісного аналізу часових рядів, для яких не підтверджується гіпотеза про наявність тренда, із застосуванням методів нелінійної динаміки й теорії хаосу. Розглянуті реальні часові ряди, що характеризують параметри тепломасообміну (температура, вологовміст), напруження та деформації у колоїдних капілярно-пористих тілах (модель художніх картин), які беруть участь у конвективному тепломасообміні з середовищем, яке їх оточує (приміщення, де розміщені музейні експонати); до складу останнього входять також системи штучного клімату музейних приміщень і потік відвідувачів музею, які знаходяться в цьому приміщенні на даний момент часу. Обґрунтуванням для подібних досліджень є теорема Такенса. Хаотичність досліджуваної динамічної системи, що задана часовими реалізаціями, встановлена за допомогою показника Ляпунова. Оцінка стійкості стану оцінювалася фрактальною розмірністю Хаусдорфа та індексом фрактальності. Візуальна оцінка часового ряду проводилася за допомогою процедури відновлення фазових траєкторій. У результаті аналізу фазових точок фазового простору виявлений розщеплений атрактор, що дає можливість говорити про його біфуркацію.

The drying and humidifying processes of capillary-porous (colloid) bodies occur during the production of various materials for the consumer goods industry, building materials, storage of museum pieces, etc. It is known that the main linkage forms of the moisture and colloid capillaryporous bodies (CCPBs), namely adsorption, capillary condensation and capillary linkage of the free moisture in the cavities of the above bodies, depend on the temperature and relative humidity of drying/humidifying agent. It means that the CCPBs behave in a peculiar way depending on the temperature and humidity fields. The problems of CCPBs drying (or humidifying) process include the issue of the heat and humidity transfer both in the middle of the body and in the boundary layer on the interface of phases "body (object of drying/humidifying process) -environment". The drying/humidifying intensity is at its maximum when the possibilities of the heat and mass transfer in the boundary layer correspond to the possibilities of moisture and heat moving inside the object of drying/humidifying process. The properties of the CCPB as material possessing specific elastic-viscous properties are described within the framework of O.Y. Ishlinskiy -O.R. Rzhanitsin generalized elasticviscous body theory. A comparative analysis of the above mentioned CCPB's properties from the point of view of Zener thermodiffusion theory is conducted. The mechanism of moisture transferring from the CCPBs' central layers (as object of drying/humidifying process) up to their surfaces is developed. The theoretical researches examined the drying/humidifying phenomena for both the entire volume of the CCPB and three structural directions. It is noted that drying/humidifying of CCPBs is a complicated heat and mass transfer process accompanied by mechanisms of molecular nature determining the kinetics of their running. It is shown that the appropriate equations' solution of molecular-molar heat and moisture transfer under the appropriate boundary (limit) conditions allows to describe the fields, i.e. the distribution of transfer potentials (the temperature and moisture content in the CCPB as object of drying/humidifying) at any time of the appropriate process. The drying/humidifying curves ("drying/humidifying rate versus CCPB humidity") and the temperature curves ("CCPB temperatures versus CCPB humidity") reflect the nature of the drying/humidifying processes. In the framework of the proposed generalized rheological model of CCPB, the residual deformations of bodies for various load types (the time-varying stress applied to the CCPB) is estimated.