Liquid Structurisation in the process of GDV.

For understanding the process of obtaining information on the structure of liquids using GDV the hypothesis was put forward that under the influence of impulse electrical field with reversed polarity micro-particles, present in the liquid start precession movements due to the polarization. These movements create spatial distribution of heterogeneity in liquid that may be registered by GDV.

Let us calculate this process for cylinder of radii R suspended in liquid at rest (fig.1). Amplitude of oscillations a<<R . It was demonstrated [1] that liquid tearing off from the surface happens only if the way passed by cylinder from the beginning of movement So >= 0.351R (for ball S0 >= 0.392R). So, if

then instant speed of oncoming torrent follows the eqiatation

and speed at the surface of cylinder changes as [1]

where x counted along cylinder surface (fig.1)
Eq.4. may be written as follows

where is angular coordinate describing position at the surface of cylinder.
Pressure gradient at the surface of cylinder will be

Fig.2 . Angular dependence of calculated parameter

Fig.3. results of calculation of torrent field

where U(x,t) will be

From average of both parts (6) and (7) we find

take integral of both parts (8) by x

Averaged pressure in the critical point x = 0, denoted in (9) as , depends on the average of speed pressure (t), where U (t) is determined by (3):

Task of pressure distribution along the surface of oscillating cylinder is equivalent to the problem of flowing liquid along vibration direction with a speed
(12)

But the difference is that for oscillating cylinder particles of liquid at different sides of cylinder move to the different directions, and in case of flow all particles move in the same direction.

So the task may be formulated as calculation of the speed field from the given stationary distribution of pressure nearby round contour. At the surface of contour pressure is determined by (11), that is illustrated by fig.2. Distribution of pressure nearby the cylinder is given by [1]

where r >= R - radii of the circle where pressure is determined, Ø = x/R -- same angle as in (5). At r = R (13) transforms to (11).

Naïve-Stocks equation in cylindrical coordinates (r, ) for stationary slow current (we neglect non-linear members in left part) [1] for the infinite round cylinder will be as follows:

As gradients of pressure in left parts of (14), (15) are fixed (pressure is given by (13)), integration of (14), (15) should fulfil boundary requirements at cylinder surface:

and fulfill indissolubility condition (16).
Eqiuation for left parts of (14), (15), from (13):

Transform (14), (15), (16) to the dimensionless representation by choosing characteristic speed Vm = an, and cylinder radii R as characteristic size. Dividing left and right parts of (14),(15) by , and left part of (16) by , we have dimensionless (14), (15), (16) taking into account (19) and (20):

Parameter Sk is analogous to the Reynolds number, but together with (R) it includes viscosity (n) , frequency (n) and amplitude (a).

With (24) (21)-(23) will be as follows:

place (28) into (25) we get equation for the unknown

or

Boundary terms for (29):

There are two members in (29): r > 1 first member have the magnitude compared with a second. So (29) may be transformed to :

that fulfill (30).
Place (32) into (31) and making zero members with equal power of r, we get a system of differential equations relative

As common solution of (34) should be zero, as at Sk = 0 there are no current nearby the cylinder.
From (35) with consideration (38)

Integration constants in (39) solution should equal zero for the same reason. So at , as follows from (36).
So

Using (40), with (28) we may calculate rectangular components of at r>=1:

Eq. (40) and (42) denote stationary flow picture near oscillating cylinder in liquid. From (40), (42) may be constructed approximation as follows:

Computer modeling based on these equations demonstrated that liquid structurisation found far away from the oscillating cylinder (fig.3). Presence of several particles form interferential field of currents, depending on the characteristics of liquid and particles. Structure formed determines quasi-momentary distribution of electrical field in the volume and at the surface of liquid influencing parameters of the GDV-grams.

Conclusion.
Calculations presented above testify to the forming of stationary currents nearby the oscillating particles. Speed of currents may be presented as follows

Round cylinder of radii R:

where uµ - central angle from the direction of vibration; r - dimensionless distance from cylinder centre, divided to R.

where ø -- central angle from the angle of vibration; r - dimensionless distance from sphere centre, divided to R.

and (78)
where R - radii., a - amplitude of vibration, n - vibration frequency in sec -¹, v -- cinematic viscosity of liquid.
These results create conceptual basis for the understanding of results of GDV testing of different liquids. Natural biological liquids: blood, urine have some natural microparticles that polarize in electric field, start oscillating and form inhomogeneous structural distribution, influencing GDV process. Of course, this is only one possible mechanism.
1 - Shlihting G. Theory of boundary layer. // Nauka. - ?., 1974. - 711 p

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