Viscosity of a Fluid

1 Viscosity of a Fluid Solutions of a high-molecular-weight polymer, even at low concentrations, can flow only slowly. Addition of a small amount of the polymer to the fluid can make it viscous, thereby preventing unwanted turbulence in the flow. 

To move the top plate at a constant velocity, a constant force must be applied in the X direction. The same applies to any small volume of the fluid. We consider a small disk parallel to the plates at distance y from the bottom plate (see Fig. 3.29). The disk has a height of dy. The fluid on the lower base flows at v, and the fluid on the upper base flows at + (dv / dy)dy. To make this velocity difference possible, a constant force needs to be exerted on the disk in the jc direction. The force per area is called shear stress and has a dimension of the pressure. The shear stress a-y denotes the force per area in the x direction exerted across the plane normal to y. To be precise, o- is a tensor of the second rank. It is synunetric, that is, o-j, = o-, and so forth. The regular pressure is expressed as a-yy, and In the isotropic fluid, cr = cTyy = (T, and it is called hydrostatic pressure. 

We next examine the relationship between a-y and dvjdy. When dvjdy = 0, (Ty = 0. If there is no velocity gradient, then no force exists. When flow direction changes, both a-y and dvjdy change their signs. Therefore, o-, is proportional to dvj dy when dvj dy is sufficiently small (Newtonian fluid)  

The proportionality coeflFicient 17 is called the viscosity. Because dy has a dimension of s and a-yj, has a dimension of N/m the unit of 17 is N s/m = kg/(m s) in the SI unit. In the cgs system, the unit is g/(cm s), which defines poise. Because most low-molecular-weight liquids have a viscosity of around 0.01 poise at room temperature, centipoise [cP equal to 0.01 poise] is commonly used for the unit of viscosity. Note that 1 cP = 10 kg/(m- s). 

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In all of these derivations concerning rigid bodies, no other walls are considered except the particle surfaces. Before we turn to the question of the intrinsic viscosity of flexible polymers, let us consider the relationship between the viscosity of a fluid and the geometry and dimensions of the container in which it is measured. 

Plow chaiacterlstic.s. Angle of repose and flowability are measurable charac teristics for which standard tests are available (e.g., ASTM Test B213-48, Flow Rate of Metal Powders, etc.). A steeper angle of repose would indicate less flowability. The term Hubricity has sometimes been used for solid particles to correspond roughly to viscosity of a fluid. 

Note that the kinematic viscosity of a fluid is defined as the ratio of its viscosity to the fluid density. The c.g.s. unit of kinematic viscosity is usually called the stoke, and is equal to 1 cmVsec. 

The viscosity of a fluid arises from the internal friction of the fluid, and it manifests itself externally as the resistance of the fluid to flow. With respect to viscosity there are two broad classes of fluids Newtonian and non-Newtonian. Newtonian fluids have a constant viscosity regardless of strain rate. Low-molecular-weight pure liquids are examples of Newtonian fluids. Non-Newtonian fluids do not have a constant viscosity and will either thicken or thin when strain is applied. Polymers, colloidal suspensions, and emulsions are examples of non-Newtonian fluids [1]. To date, researchers have treated ionic liquids as Newtonian fluids, and no data indicating that there are non-Newtonian ionic liquids have so far been published. However, no research effort has yet been specifically directed towards investigation of potential non-Newtonian behavior in these systems. 

Taylor, G. I., The viscosity of a fluid containing a small drops of another fluid. Proc. R. Soc. A138, 41-48 (1932). 

Kinematic viscosity is the ratio of dynamic viscosity and density, and can be obtained by dividing the dynamic viscosity of a fluid with its mass density, as shown by Equation 18.2 ... 

The viscosity of a fluid is an important property in the analysis of liquid behavior and fluid motion near solid boundaries. Viscosity is the fluid resistance to shear or flow and is a measure of the adhesive/cohesive or frictional fluid property. The resistance is caused by intermolecular friction exerted when layers of fluids attempt to slide by one another. 

The viscosity of a fluid is highly temperature dependent and, for either dynamic or kinematic viscosity to be meaningful, the reference temperature must be quoted. In ISO 8217 the reference temperature for a residual fluid is 100°C. For a distillate fluid the reference temperature is 40°C. 

Schmidt number 3 phys chem A dimensionless number used In electrochemistry, equal to the product of the dielectric susceptibility and the dynamic viscosity of a fluid divided by the product of the fluid density, electrical conductivity, and the square of a characteristic length. Symbolized SC3. shmit. nam bar thre ) Schoeikopf s acid orgchem A dye of the following types l-naphthol-4,8-dlsulfonlc acid, l-naphthylamine-4,8-disulfonicadd,and l-naphthylamine-8-sulfonicadd may be toxic. shol.kopfs, as-3d ... 

A viscometer is an apparatus that measures the viscosity of a fluid. A common style consists of an outer fixed cylinder with an inner rotating cylinder. One that is being used has an outer cyhnder radius of 15 cm, an inner radius of 14.25 cm, and a height of 22 cm. It takes a torque (force time radius) of 0.07 N-m to maintain an angular speed of 50 rpm at 4°C. What is the viscosity of the fluid that fills the annular region of the cylinders What fluids could this be ... 

Brookfield Viscosity A measurement of the apparent viscosity of a fluid using a Brookfield viscometer. This viscometer is a variable-sheer, variable-rpm viscometer. 

Kinematic Viscosity A coefficient defined as the ratio of the dynamic viscosity of a fluid to its density. The centistoke is the reported value of kinematic viscosity measurement. 

Equations (1) and (3) are equivalent as definitions of the viscosity of a fluid. To convince ourselves that 17 as defined by these expressions does indeed measure resistance to flow, consider two liquids of widely different viscosity, say, water and molasses ... 

In 1906 Albert Einstein (Nobel Prize, 1921) published his first derivation of an expression for the viscosity of a dilute dispersion of solid spheres. The initial theory contained errors that were corrected in a subsequent paper that appeared in 1911. It would be no mistake to infer from the historical existence of this error that the theory is complex. Therefore we restrict our discussion to an abbreviated description of the assumptions of the theory and some highlights of the derivation. Before examining the Einstein theory, let us qualitatively consider what effect the presence of dispersed particles is expected to have on the viscosity of a fluid. 

What is meant by rheology What role does viscosity of a fluid play in rheology ... 

An experiment to measure the viscosity of a fluid is shown schematically in Fig. 12.1. In this experiment the fluid is confined between two parallel plates. The bottom plate is held stationary, and the top plate, at a distance a away in the z direction, moves at constant velocity U in the x direction. The thin layer of fluid adjacent to each wall assumes the velocity of that wall that is, the gas at height z = 0 has zero velocity, and the layer of gas at z — a moves with x velocity u = U. At steady state, a linear velocity profile is set up across the gas, with the upper and lower limits just mentioned. Therefore the velocity gradient du/dz has the value Ula across the channel. It is found that that the force required to maintain the constant velocity of the upper plate is proportional to the area of the plates and the velocity U, and is inversely proportional to the separation a. Thus the retarding force of the fluid per unit area (of the plates) is proportional to the velocity gradient du/dz ... 

When we cool a liquid off, its viscosity markedly increases. I cannot generalize—it depends on the fluid. But I can say that increasing the viscosity of a fluid from 2 to 40 cP could reduce the observed heat-transfer efficiency (U) from 100 to 25.1 know this from my experience in preheating cold, viscous, Venezuelan crude oil, off-loaded from tankers. 

The viscosity of a fluid corrected for its density is also known as the absolute or kinematic viscosity. 

There are a substantial number of ways in which the viscosity of a fluid can be measured. Not all of these can be adapted easily to on-line process measurement. It is convenient to classify viscometers according to the type of physical measurement made. 

Apparent viscosity the viscosity of a fluid, or several fluids flowing simultaneously, measured in a porous medium (rock), and subject to both viscosity and permeability effects also called effective viscosity. 

The viscosity of a fluid, rj, is defined in terms of a test in which it is sheared. The viscosity is the ratio of the shear stress to the shearing strain rate y,r] = x/y. The strain rate, y, is the rate of shearing between two planes divided by the distance between them. Determine the SI units for viscosity. 

The Couette apparatus was developed by Maurice Couette in 1890 as a means for measuring the viscosity of a fluid at small imposed angular velocities of the cylinders. 

The Prandtl number via has been found to be the parameter which relates the relative thicknesses of the hydrodynamic and thermal boundary layers. The kinematic viscosity of a fluid conveys information about the rate at which momentum may diffuse through the fluid because of molecular motion. The thermal diffusivity tells us the same thing in regard to the diffusion of heat in the fluid. Thus the ratio of these two quantities should express the relative magnitudes of diffusion of momentum and heat in the fluid. But these diffusion rates are precisely the quantities that determine how thick the boundary layers will be for a given external flow field large diffusivities mean that the viscous or temperature influence is felt farther out in the flow field. The Prandtl number is thus the connecting link between the velocity field and the temperature field. 

T P is the dynamic viscosity of a fluid in which there is a tangential force of 1 dyn/cm2 resisting the flow of two parallel fluid layers past each other when their differential velocity is 1 cm/s per centimeter of separation. When there is a possibility of confusion with the symbol for radian, rd may be used as the symbol for rad. 

The viscosity of supercrital fluids increases with pressure, but approaches that of a liquid less rapidly than the density. Even if very high pressures are used, the viscosity of a fluid in a supercritical state is inferior to that of a liquid. This is followed by improved penetration in porous materials coupled with a rapid kinetic. 

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