Viscosity viscous friction

It is well known, that under industrial conditions a method of introducing filler into the polymer mixture is used. In this case, the filler is introduced in the form of paste containing up to 60 per cent water in order to reduce viscosity, As heating is affected by viscous friction, the temperature conditions are not stable on mixing and, therefore, conductivity of the conducting polymer composite becomes unreproducible. Up to now this factor has not been taken into consideration. 

A flowing fluid is required to do work to overcome viscous frictional forces so that in practice the quantity W0 is always positive. It is zero only for the theoretical case of an inviscid fluid or ideal fluid having zero viscosity. The work W, may be done on the fluid by a pump situated between points 1 and 2. 

In practical applications, the increase of viscous friction with speed is often lower than expected from Eq. (11.9). The explanation is that friction leads to an increased temperature of the lubricant which reduces the viscosity. For most lubricants the temperature dependence of the viscosity is given by... 

A cylindrical axis of 1 cm diameter and 10 cm length is rotating in a precision bearing with an inner diameter, which is only 6 /xm larger. We use octadecane as the lubricant. Due to friction it heats up to 50°C, where its viscosity is 2.49 mPa s. The axis rotates with 80 rotations per second. What is the torque we have to apply to overcome the viscous friction ... 

If two systems, such as a model and its prototype or two pipelines with different fluids, are to be dynamically equivalent so far as inertia and viscous friction are concerned, they must both have the same value of Nr. For the same fluid in both cases, the equation shows that a high velocity must be used with a model of small linear dimensions. It is also possible to compare the action of fluids of very different viscosities, provided only that L and V are so chosen as to give the same value of Nr. 

If the medium is considered incompressible and neglecting gravity, the main forces present are the inertial force due to the acceleration or deceleration of small fluid masses near the body and the viscous friction forces which arise due to the viscosity of the medium. For similarity these forces must be in the same ratio at any instant. Then... 

Inertial regime. For low-viscosity liquids like molten metals, the use of the viscous friction model is questionable because inertial forces can become very important. For a sessile drop of mass ma, the inertial force is given by ... 

To understand the mechanism of the turbulent mixing process occurring in pipe reactors, we have to consider first some of the properties of fluid flow in pipes. Resistance to fluid flow in a pipe has two components, the viscous friction of the fluid itself within the pipe, which increases as the fluid viscosity increases, and the pressure differential caused by a liquid level difference or a pressure difference between the two vessels. 

Veo at a large distance from the wall (see Figure 5.67). The magnitude of this electroosmotic velocity was calculated by von Smoluchowski under the assumptions that (1) the ion distribution in the diffuse layer obeys the Poisson-Boltzmann equation, (2) at each point the electrical force is balanced by the viscous friction, and (3) the liquid viscosity in the diffuse layer is equal to that of the bulk liquid, ii. The final result reads ... 

Such quadratic dependence between dissipated power and the shear rate is characteristic of the viscous friction. A cylinder with a loose piston filled with some viscous medium (Fig. IX-5) may serve as a model of viscous behavior. In this model it is assumed that the ratio of applied force to the speed of piston motion, Ft (dl/dt), is numerically equal to viscosity of described fluid,... 

As a result of the motion of the interface, the viscous friction is lower and the drop velocity higher. Hence the transfer rate is increased by a factor approximately equal to 1.9(Ap,) compared with the rigid drop. One may expect circulation to increase with drop size and the viscosity ratio nJn of the two fluids. 

Based on the Stokes law (viscous friction hypothesis), for a sphere with r, radius moving with a relative velocity, through a medium with ij viscosity, the friction force is of... 

Newton s law in hydrodynamics, or in flnid mechanics, models the viscous friction between fluid elements. It links what is classically called a gradient of velocity (in fact a lineic density) to the local pressure P through a coefficient 77 called dynamic viscosity. This coefficient is a scalar in isotropic media and a tensor otherwise (Phan-Tien 2002). 

As for Ohm s law, which works equally well at the global level and in spatial reduction, for which one can link the conductance to the conductivity, it is possible to link the coefficient of friction (or of viscous friction) fc defined at the global level to the dynamic viscosity. The relation between these two system properties derives from the principle of circularity ... 

Entropy production by viscous friction is illustrated by Example 4 in a perfect fluid (with zero viscosity), no pressure would be lost and no entropy produced. Imagine an ideal gas in (6.2.31). The factor Tq is due to the hypothetical possibility of expanding the gas isothermally at given temperature T (giving TQ instead of Tq (2s ) recover the supplied heat g by a... 

These equations are strikingly simple. Both the liquid s velocity and its flow rate are proportional to the driving force. This property is known as Poiseuille law. One can define a hydrodynamic conductivity, which is the ratio Q// and is inversely proportional to the viscosity p. The viscosity is an intrinsic property of the liquid (for a given force, the greater the viscosity, the lower the flow rate). However, this conductivity depends mainly on the thickness of the liquid film, actually varying as the cube of that thickness. A film twice as thick will support eight times the hydrodynamic flow. This is an important characteristic that comes up in most interface hydrodynamics problems, which are generally dominated by viscous friction. 

The carrier liquid of the ferrofluid used in the experiment (APG S lOn, Ferrotec) was a synthetic ester oil which was immiscible in silicone oil. The viscosity rj, density /O, and surface tension a of the ferrofluid at 25 °C were 0.406 kg/ms, 1330 kg/s, and 32xlO N/m, respectively. The saturation magnetization and the initial susceptibility X of this ferrofluid were 44 mT and 1.6, respectively. Two silicone oils with different viscosities were used to investigate the effect of viscous friction [—Si(CH3)20—] , with a kinematic viscosity of V = 50 cSt, and [—C7H80Si—], with a kinematic viscosity of 100 cSt. Both oils had approximately the same surface tension of 2.03 x 10 N/m and a density of 960kg/m. In the experiments, the ferrofluid droplet was surrounded... 

This quadratic dependence is characteristic of viscous friction. The viscous behavior of a body can be modeled by a dashpot (Figure 3.5). In this model, it is assumed that the ratio of the acting force F to the velocity of a piston, F/(d//dt), is equal to the viscosity of fluid. 

---