*3.2.2 Model of dynamic processes in microdispersed water media*

Let the volume of a colloidal system be a cube with edge length *L*. Let this cube house *N1* hydrophilic particles – seeds around which liquid crystal water spheres

#### **Figure 28.**

*Scheme of cyclic physicochemical transformations in colloidal system. Background coloring intensity corresponds to the concentration of ions and particles in dispersive phase 1 – Initial state, quasi-homogenous distribution of particles with small EZs; 2 – EZs growth around some particles is more intense than around others; 3 – giant EZ-balls aggregate and begin destruction due to high osmotic pressure; chains of particles coagulated on the surface of water balls remain in solution; 4 – destruction process continues, osmotic pressure decreases progressively; 5 – EZs are ready to grow again.*

reversible assembly [63, 64]. The authors of [62] showed that in the system with negligible van der Waals forces a simple competition between repulsive screened Coulomb and attractive critical Casimir forces can account quantitatively for the reversible aggregation. Above the temperature Ta, the critical Casimir force drives aggregation of the particles into fractal clusters, while below Ta, the electrostatic repulsion between the particles breaks up the clusters, and the particles resuspend by thermal diffusion [62]. If the gap between the interacting surfaces is filled with a specially designed substance, the attraction between the surfaces can change their repulsion. If such interaction of surfaces with a dielectric constant Ɛ1 or Ɛ2, respectively, occurs in a medium with a dielectric constant Ɛ3, they will be attractive at (Ɛ1 - Ɛ3) (Ɛ2 - Ɛ3) ˂ 0, and repulsive at (Ɛ1 - Ɛ3) (Ɛ2 - Ɛ3) ˃ 0. These interactions are extremely sensitive to temperature, chemical composition of the medium and its physical characteristics [65, 66]. According to our data, the observed process is characterized by cyclic changes both in liquid solute concentration due to displacement of the ions and particles from Exclusion Zones (EZs) to the bulk, and in particle surface properties due to EZ shell growth around them. As these zones routinely generate protons in the water regions beyond, unequal proton concentrations in the respective areas may be responsible for creating both the pH and potential gradients, which may be ultimately responsible for the osmotic drive [30]. On the other hand, the surface water has different water activity and chemical potential to the bulk, leading to differences in osmotic pressure and other colligative properties [25]. When this increase in osmotic pressure next to the surface reaches a threshold, the mechanical instability of the system sharply growths, velocity of microstreams enhances, and aggregates of EZ spheres start to collapse. They break into small pieces and melt. Solute concentration and osmotic pressure decline. Free colloidal particles are distributed uniformly. Chains of particles coagulated on the surface of the water balls remain in solution. Growth of EZ balls begins again and the process recurs (**Figure 28**). As similar events (EZ growth) are registered for other polar liquids, we believe that the autonomous fluctuations based on rhythmic formation and destruction of liquid crystal spheres are the universal law of the nature. The considered processes have been used for creation of a phenomenological model showing a possibility of the existence of self-oscillatory modes in similar

*Colloids - Types, Preparation and Applications*

systems.

**Figure 28.**

**112**

*progressively; 5 – EZs are ready to grow again.*

*3.2.2 Model of dynamic processes in microdispersed water media*

Let the volume of a colloidal system be a cube with edge length *L*. Let this cube house *N1* hydrophilic particles – seeds around which liquid crystal water spheres

*Scheme of cyclic physicochemical transformations in colloidal system. Background coloring intensity corresponds to the concentration of ions and particles in dispersive phase 1 – Initial state, quasi-homogenous distribution of particles with small EZs; 2 – EZs growth around some particles is more intense than around others; 3 – giant EZ-balls aggregate and begin destruction due to high osmotic pressure; chains of particles coagulated on the surface of water balls remain in solution; 4 – destruction process continues, osmotic pressure decreases*

(EZ) are formed. Let n be the number of ions and colloidal particles determining osmotic pressure *P* at the interface between water spheres of radius *r* and dispersive medium. *V* is the amplitude of mean speed of microflows with a characteristic lateral dimension smaller than *πr*. This corresponds to the excited mode of mechanical instability for the sphere surface: 2*πr=m*, where *m* = 2, 3, 4, 5 … The estimated equations for integral processes in such a system can be written down in the following form: EZ growth near a seed particle can be described as (2).

$$d\sigma/dt = l\_0/\tau\_{gr}(\mathbf{1} - \mathbf{V}/V\_{crit})\tag{2}$$

where *V* is the average velocity of microstreams in bulk near the water balls; *Vcrit* is the critical velocity of microstreams in bulk with sufficient energy for destruction of external borders of the water balls; *l*<sup>0</sup> is the increment of EZ shell thickness around a hydrophilic particle during time *τgr*. From the works [68, 69] and our own experiments we know that *l*<sup>0</sup> /*τgr*≈ 1 – 10 μm/sec. Formation of microstreams near the interface between the EZ shell and free water on achieving critical osmotic pressure *Pcrit* can be described as (3)

$$d\mathbf{V}/dt = -\mathbf{V}/\tau\_{visc} + 4\pi r^2 \cdot \boldsymbol{\gamma}\_m \cdot \mathbf{P} \cdot \mathbf{F}\_{[\mathbf{x}]} \cdot [\mathbf{P} - \mathbf{P}\_{crit}] \tag{3}$$

where *τvisc* is the characteristic time of reduction of microstreams velocity due to solution viscosity; *τvisc*≈const; *γ<sup>m</sup>* is the coefficient characterizing average change of destruction force depending on the created mode of spatial nonuniformity on the destroyed external border of EZ; *F[x]* is the step-type function equal to zero if

*x=P-Pcrit 0,* and equal to 1 if *x=P-Pcrit > 0.*

We assume that the speed of diffusion of ions and colloidal particles is much more than the growth rate of EZ shell and speeds of delay of microstreams. Then we can use Vant Hoff's law for stationary conditions (4)

$$P = n \cdot R \cdot T / V \tag{4}$$

where *R* is universal gas constant, T is absolute temperature.

The volume of colloidal liquid except for the volume of water spheres is found from equation (5)

$$V = L^3 \cdot \left[1 - 4/3\pi r^3 \cdot N\_1/L^3\right] \tag{5}$$

Thus, the status of water spheres in the bulk of the remaining colloidal liquid can be described by Eqs. (2)–(5). We introduce the following notation:

$$
\beta = 4\pi \text{N}\_1 / \text{3L}^3 \tag{6}
$$

$$a = 4\pi\gamma\_m \cdot nRT/L^3 \cdot V\_{crit} \tag{7}$$

$$\chi = \mathbf{V}/\mathbf{V}\_{\rm crit} \tag{8}$$

and rewrite the above equations correspondingly:

$$\int dr/dt = l\_0/\tau\_{\rm gr}(1-\chi)\tag{9}$$

$$\begin{cases} \int d\chi/dt = -\chi/\tau\_{\rm{visc}} + ar^2/\mathbf{1} - \beta r^3 \cdot F\_{\left[\mathbf{x}\right]} \cdot \left[P - P\_{\rm{crit}}\right] \end{cases} \tag{10}$$

$$\int P = \boldsymbol{n} \cdot \boldsymbol{R} \cdot \boldsymbol{T}/L^3 \cdot (\mathbf{1} - \beta \boldsymbol{r}^3) = (V\_{crit}/4\pi\chi\_m) \cdot \boldsymbol{a}/(\mathbf{1} - \beta \boldsymbol{r}^3) \tag{11}$$

On the basis of this system of equations and understanding of the physics of the dynamical process we can distinguish 3 stages of the process:


Let us consider the dynamics of the process based on Eqs. (9)–(11) in simplified form.

Stage 1. EZ shell growth around hydrophilic colloidal particles (12)–(14):

$$\int dr/dt = \mathbb{I}\_0/\tau\_{\mathbb{S}^r}(1-\chi), \qquad \qquad \chi > 1 \tag{12}$$

$$\begin{cases} \mathbf{\hat{u}} \cdot \mathbf{\hat{n}} = \mathbf{\hat{x}} \cdot \mathbf{\hat{s}} \mathbf{\hat{z}} \text{ ( $\mathbf{z} \times \mathbf{\hat{u}}$ )} \mathbf{\hat{n}}, & \mathbf{\hat{x}} \cdot \mathbf{\hat{n}} = \mathbf{\hat{x}} \mathbf{\hat{z}} \\\\ \mathbf{d}\boldsymbol{\chi}/\mathbf{d}\mathbf{t} = -\boldsymbol{\chi}/\mathbf{\hat{r}}\_{\text{visc}}, & \boldsymbol{\chi} \approx \mathbf{0} \end{cases} \tag{13}$$

$$\begin{cases} P = (V\_{crit}/4\pi\chi\_m) \cdot a/(1-\beta r^3) \\ \end{cases} < P\_{crit} \tag{14}$$

Stage 2. Development of instability and destruction of water spheres (15)–(17):

$$\begin{cases} P = P\_{\text{crit}} \end{cases} \tag{15}$$

$$\begin{cases} r^3 = r\_{crit}^3 = \mathbf{1}/\beta \left[ \mathbf{1} \left( a \cdot \mathbf{V}\_{crit}/\mathbf{4} \,\pi \boldsymbol{\chi}\_m \cdot \mathbf{P}\_{crit} \right) \right] \tag{16}$$

$$d\,\chi/dt = (\chi\_{\text{max}} - \chi) / \tau\_{\text{visc}},\tag{17}$$

where χmax = α• τ*visc* •r 2 *crit*/ (1 - *β*�r 3 *crit*). If χ ≤ 1, then r continues to grow. According to our observations, r*crit* ≈ 250 μm.

Stage 3. Microflows slowdown.

Since turbulent flows are formed at this stage, τ*gr* may depend on χ and P. However, for our simplified representation, we shall assume that τ*visc* = const, as in the case of laminar flow (18)–(21):

$$\int \mathbf{P} \mathbf{$$

measured parameter were noticed. Additional studies showed that, simultaneously with the above mentioned parameter, there occurred coordinated fluctuations of the surface tension and the character of structuring in drying drops. It had been found earlier that parameters of fluctuations depended on the extent of dilution and did not depend on additional hashing of solution and shielding from external electromagnetic fields [53, 54]. So, it was decided to elucidate the mechanism of such fluctuations in liquid phase. The basis for such a study was, on the one hand, information available on reversible formation of voids inside colloidal dispersions [34–36] and, on the other hand, description of slow fluctuations and inhomogeneity of fluids of different types obtained in the light scattering studies [33, 49, 50]. Moreover, it had been earlier described similar fluctuations of optical density in blood and plasma diluted with physiological saline solution in different proportions [27]. For the liquid phase study, the method of flattened drop and smears of freshly prepared coffee solution were used. The existence of spherical structures in the liquid phase of coffee, their periodical occurrence, growth, destruction and reemergence, which agreed with fluctuations of physicochemical parameters of the system, was described for the first time. It had been showed morphologically that these spheres are liquid crystal water which forms EZs around hydrophilic colloidal particles. Agglomerates of such crystal water spheres look like voids inside colloidal dispersions under confocal scanning laser microscope. These findings are based on modern and last-century studies of wall layer of water mentioned in the book of Gerald Pollack [45]. We proposed a water-induced mechanism of self-oscillatory

*Qualitative description of cyclic changes of variables in the course of growth of water spheres, their destruction and formation of conditions for their new growth: (a) - view of phase trajectories: process begins at the zero point (*χ *= 0;* r *= 0) and reaches limit cycle; (b) - temporary change of radius of water spheres; (c) - temporary change*

**Figure 29.**

**115**

*of velocity of microstreams.*

*Structure and Dynamics of Aqueous Dispersions DOI: http://dx.doi.org/10.5772/intechopen.94083*

$$\left\{ \begin{array}{c} \text{....} \\ \text{d} \mathbf{r}/\text{d} \mathbf{t} = \text{l}\_{0}/\text{\tau}\_{\text{gr}} \,(\mathbf{1}-\chi), \chi>\mathbf{1} \end{array} \right. \tag{19}$$

$$\mathbf{d}\chi/\mathbf{dt} = -\chi/\mathfrak{r}\_{\text{vic}}\tag{20}$$

$$\mathbf{u}\mathbf{\overline{x}}/\mathbf{u} = -\mathbf{\overline{x}}/\mathbf{r}^{\text{visc}} \tag{20}$$

$$\mathbf{P} = (\mathbf{V}\_{crit}/4\,\pi\mathbf{\underline{y}}\_m)\bullet\mathbf{a}/(\mathbf{1}-\beta\mathbf{r}^3) < \mathbf{P}\_{crit} \tag{21}$$

This dynamics can also be represented on phase plane in χ and r coordinates (**Figure 29**).

#### **4. Conclusions**

In this part of work an instant coffee as a sample of complex colloidal system was used. Making long repeated measurements of the dynamics of complex mechanical properties of drying drops by DDT [55, 56] slow periodic fluctuations of the

*Structure and Dynamics of Aqueous Dispersions DOI: http://dx.doi.org/10.5772/intechopen.94083*

#### **Figure 29.**

On the basis of this system of equations and understanding of the physics of the

a. EZ shell growth around hydrophilic colloidal particles to the size of huge liquid crystal water spheres; osmotic pressure growth in a bulk;

b. Osmotic pressure growth in bulk over critical value, forming conditions for the development of mechanical instability at the interface between water

microstream strengthening, causing erosion until complete destruction of

c. Microstreams slowdown due to viscosity and transition of the system to stage 1.

Let us consider the dynamics of the process based on Eqs. (9)–(11) in simplified

*dr=dt* ¼ *l*0*=τgr*ð Þ 1 � *χ* , *χ* > 1 ð12Þ *dχ=dt* ¼ �*χ=τvisc*, *χ* ≈ 0 at t ðÞ ð ¼ 0 13Þ *<sup>P</sup>* <sup>¼</sup> ð Þ� *Vcrit=*4*πγ<sup>m</sup> <sup>α</sup><sup>=</sup>* <sup>1</sup> � *<sup>β</sup>r*<sup>3</sup> ð Þ <sup>&</sup>lt; *Pcrit* <sup>ð</sup>14<sup>Þ</sup>

*P* ¼ *P*crit ð15Þ

*d χ=dt* ¼ ð Þ *χmax*–*χ =τvisc*, ð17Þ

*crit* ¼ 1*=β* 1–ð Þ *α* � *Vcrit=*4 *πγ<sup>m</sup>* � *Pcrit* ½ �ð16Þ

P< P*crit:* ð18Þ dr*=*dt ¼ l0*=*τ*gr* ð Þ 1–χ , χ>1 ð19Þ dχ*=*dt ¼ �χ*=*τ*visc* ð20Þ

<sup>3</sup> � �<P*crit* <sup>ð</sup>21<sup>Þ</sup>

*crit*). If χ ≤ 1, then r continues to grow.

Stage 1. EZ shell growth around hydrophilic colloidal particles (12)–(14):

Stage 2. Development of instability and destruction of water spheres (15)–(17):

spheres and bulk (similar to the Rayleigh-Taylor instability [67]);

dynamical process we can distinguish 3 stages of the process:

*Colloids - Types, Preparation and Applications*

water spheres.

8 >><

>>:

*<sup>r</sup><sup>3</sup>* <sup>¼</sup> *<sup>r</sup><sup>3</sup>*

2

According to our observations, r*crit* ≈ 250 μm.

8 >>>>><

>>>>>:

*crit*/ (1 - *β*�r

3

Since turbulent flows are formed at this stage, τ*gr* may depend on χ and P. However, for our simplified representation, we shall assume that τ*visc* = const, as in

P ¼ ð Þ V*crit=*4 πγ*<sup>m</sup>* • α*=* 1 � βr

This dynamics can also be represented on phase plane in χ and r coordinates

In this part of work an instant coffee as a sample of complex colloidal system was used. Making long repeated measurements of the dynamics of complex mechanical properties of drying drops by DDT [55, 56] slow periodic fluctuations of the

8 >><

>>:

Stage 3. Microflows slowdown.

the case of laminar flow (18)–(21):

where χmax = α• τ*visc* •r

(**Figure 29**).

**114**

**4. Conclusions**

form.

*Qualitative description of cyclic changes of variables in the course of growth of water spheres, their destruction and formation of conditions for their new growth: (a) - view of phase trajectories: process begins at the zero point (*χ *= 0;* r *= 0) and reaches limit cycle; (b) - temporary change of radius of water spheres; (c) - temporary change of velocity of microstreams.*

measured parameter were noticed. Additional studies showed that, simultaneously with the above mentioned parameter, there occurred coordinated fluctuations of the surface tension and the character of structuring in drying drops. It had been found earlier that parameters of fluctuations depended on the extent of dilution and did not depend on additional hashing of solution and shielding from external electromagnetic fields [53, 54]. So, it was decided to elucidate the mechanism of such fluctuations in liquid phase. The basis for such a study was, on the one hand, information available on reversible formation of voids inside colloidal dispersions [34–36] and, on the other hand, description of slow fluctuations and inhomogeneity of fluids of different types obtained in the light scattering studies [33, 49, 50]. Moreover, it had been earlier described similar fluctuations of optical density in blood and plasma diluted with physiological saline solution in different proportions [27]. For the liquid phase study, the method of flattened drop and smears of freshly prepared coffee solution were used. The existence of spherical structures in the liquid phase of coffee, their periodical occurrence, growth, destruction and reemergence, which agreed with fluctuations of physicochemical parameters of the system, was described for the first time. It had been showed morphologically that these spheres are liquid crystal water which forms EZs around hydrophilic colloidal particles. Agglomerates of such crystal water spheres look like voids inside colloidal dispersions under confocal scanning laser microscope. These findings are based on modern and last-century studies of wall layer of water mentioned in the book of Gerald Pollack [45]. We proposed a water-induced mechanism of self-oscillatory

processes in colloidal systems and confirmed the principle possibility of its existence by a simple mathematical model. These data allow a fresh look at the process of aggregation - disaggregation of colloidal particles in the solution. The experiments showed that the growth of water spheres pushes colloidal particles to the borders of the spheres, promotes their crowding and coagulation. On the border of water spheres, the particles form chains (reticular structures) which exist some time in liquid phase after destruction of liquid crystal water shells. Thus, all complex dynamics is controlled by the phase transitions of water – from the free to the bound (liquid crystal) state and back. Osmotic pressure acts as the intermediary messenger and the synchronizer of these transformations in a whole volume of liquid. Actually, these processes are not very sensitive to temperature (unlike the models based on calculation of Casimir forces [61–66]), and do not notably depend on liquid disturbance by hashing. Hashing by a turning of a test tube initiates emergence of streams of liquid with a characteristic size of an order of the size of a test tube (1.5 9.0 cm [53]), when the most part of the brought energy is spent for movement of spheres in bulk. Destruction of water spheres happens at initiation of microstreams of 10-100 μm in size, which correspond to the sizes of the destroyed objects. Osmotic pressure P in accordance with Eq. (3) is proportional to the absolute temperature (≈295 K). Possible changing the temperature at a few degrees is negligible to affect the considered processes. For obvious reasons parameters of fluctuations depend on concentration of the components. The described mechanism can explain some phenomena that were not clear before and deserves special research. The authors believe that we deal with a universal phenomenon of undoubted importance for fundamental and applied science. We are sure that our hypothesis will stimulate researchers with other ideas and other tool kits to join this direction of study.

The authors regard this work as a stage on the path of knowledge, which must be

This project was funded by the Ministry of Education and Science of Russia

refined and corrected on the endless path of the development of science.

The authors declare no conflict of interest.

*Structure and Dynamics of Aqueous Dispersions DOI: http://dx.doi.org/10.5772/intechopen.94083*

**Conflict of interest**

(project no 14.Y26.31.0022).

**Funding**

**Author details**

Tatiana Yakhno<sup>1</sup>

**117**

\* and Vladimir Yakhno1,2

2 Lobachevsky University of Nizhny Novgorod, Russia

\*Address all correspondence to: yakhta13@gmail.com

provided the original work is properly cited.

1 Institute of Applied Physics of Russian Academy of Sciences, Russia

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