Basic knowledge of viscosity

Thread Content

The flowing liquid can be considered as multiple layers of liquid moving parallel to each other; each layer has a different velocity, resulting in a velocity gradient (dv/dx), which is a fundamental characteristic of flow (see figure). Due to this velocity gradient, the layers with slower velocities hinder the flow of those with faster velocities, and thus resistance to motion arises in the liquid. To maintain a certain velocity gradient in these layers, it is necessary to apply a force in the opposite direction to that of the resistance. The force applied per unit area of the liquid layer is called shear stress τ (N/m2). The rate of change of velocity (D) is given by D = dv/dx (S-1). Shear stress and the rate of change of velocity are two basic parameters that characterize the rheological properties of a system. Newton defined the viscosity of fluids using the model shown in Figure 4-1. Two fluids in different planes but parallel to each other, having the same area “A”, separated by a distance “dx”, and flowing in the same direction at different speeds “V1” and “V2”. Newton assumed that the force responsible for this difference in speeds is proportional to the relative velocity or velocity gradient of the fluids; that is: τ = ηdv/dx = ηD (Newton’s formula). Here, η is related to the properties of the material, and it is referred to as “viscosity”. 　　Definition of viscosity: When two plates with an area of 1 m2 are immersed in a liquid, with a distance of 1 meter between them, if a shear stress of 1 N is applied to achieve a relative velocity of 1 m/s between the plates, then the viscosity of this liquid is 1 Pa·s. 　　Newtonian fluid: A fluid that obeys Newton’s law. Viscosity depends only on temperature and not on the shear rate; τ is proportional to D. 　　Non-Newtonian fluids: They do not obey Newton’s law τ/D=f(D). The viscosity at a constant value of (τ/D) is denoted by ηa, and it is known as the apparent viscosity. 　　There are three methods for viscosity measurement: dynamic viscosity, kinematic viscosity, and conditional viscosity. 　　(1) Dynamic viscosity: ηt is the resistance generated when two liquid layers separated by 1 centimeter, each with an area of 1 square centimeter, move relative to each other at a speed of 1 centimeter per second; its unit is grams per centimeter-second. 1 gram/cm·second = 1 poise. Generally, poise is used as the unit for dynamic viscosity in industry. 　　(2) Kinematic viscosity: At a temperature of t℃, kinematic viscosity is denoted by the symbol γ. In the International System of Units, its unit is the stokes, which is equivalent to m2/s. In practical measurements, centistokes (cst) are commonly used; 1 cst corresponds to 1 mm2/s. Kinematic viscosity is widely used to determine the viscosity of liquid petroleum products such as jet fuel, diesel, and lubricating oils, as well as of dark-colored petroleum products, used lubricating oils, and crude oil. The determination of kinematic viscosity is carried out using the counter-current method. (3) Conditional viscosity: This refers to the viscosity measured using different specific viscometers and expressed in conditional units. The three most commonly used conditional viscosities around the world are as follows: ① Engler viscosity, also known as Stokes viscosity. It is the ratio of the time required for a certain amount of sample to flow 200 milliliters from an Engler viscometer at a specified temperature (such as 50°C, 80°C, 100°C) to the time required for distilled water to flow the same volume at 20°C, expressed in seconds. At temperature tº, Engler viscosity is denoted by the symbol Et, and its unit is conditional degrees. 　　②Sagbolt viscosity, also known as Sagbolt viscosity. It is the number of seconds required for a certain amount of sample to flow 200 milliliters through a Saybolt viscometer at a specified temperature (such as 100ºF, 210ºF, or 122ºF, etc.), measured in seconds. Saybolt viscosity is further divided into Saybolt universal viscosity and Saybolt heavy oil viscosity (or Saybolt Furol viscosity). 　　③Ree’s viscosity is also known as Redwood viscosity. It is the number of seconds required for a certain amount of sample to flow 50 milliliters from a Reay thermometer at a specified temperature, measured in ‘seconds’. Ree’s viscosity is further divided into Ree’s No. 1 (denoted as Rt) and Ree’s No. 2 (denoted as RAt). 　　The above three viscosity measurement methods are commonly used in European and American countries. In China, aside from the use of the Engler viscometer for measuring dark lubricants and residue oils, the other two types of viscometers are rarely utilized. The three methods for expressing conditional viscosity have different units, but their relationships can be converted using charts. At the same time, Engler viscosity and kinematic viscosity can also be converted to each other, which makes things much more convenient and flexible. 　　There are many methods for measuring viscosity, such as the rotating barrel method, falling ball method, damped vibration method, cup viscometer method, capillary method, and so on. For fluids with low viscosity, such as water, ethanol, carbon tetrachloride, etc., capillary viscometers are commonly used for measurement ； For fluids with higher viscosity, such as castor oil, transformer oil, engine oil, glycerin, and other transparent (or semi-transparent) liquids, the falling ball method is commonly used for measurement ； For liquids with viscosities in the range of 0.1 to 100 Pa•s, the rotating cylinder method can also be used for measurement. 　　The principle behind measuring viscosity in the laboratory generally involves deriving expressions for the coefficient of viscosity from Stokes’ law and Poiseuille’s law, in order to determine this coefficient. 　　The viscosity depends on the properties of the liquid and its temperature; as the temperature rises, the viscosity decreases rapidly. Therefore, it is meaningful to measure viscosity only by accurately controlling temperature changes. The determination of viscosity parameters is of great significance for predicting process control during product production, the flow properties of the products, and their ease of use; it holds importance in various industries such as printing, pharmaceuticals, petroleum, and automotive manufacturing. 　　In 1845, the British mathematician and physicist G. G. Stokes (1819–1903) and the Frenchman C.L.M.H. Navier, among others, derived the most fundamental set of equations in viscous fluid mechanics, namely the Navier-Stokes equations, which laid the foundation for classical fluid mechanics. 　　In 1851, Stokes derived a formula for calculating the resistance experienced by a solid sphere moving slowly through a viscous medium; he found that, under the action of a given force (gravity), the resistance is proportional to the flow velocity and the viscosity coefficient – this is Stokes’ law of resistance. 　　The Navier-Stokes equations belong to one of the most difficult nonlinear equations in mathematics, and finding their exact solutions is a very challenging task. To this day, there are only about 70 exact solutions, and just over a hundred particular solutions have been found; it is one of the most complex and yet-to-be-completely-solved world-class mathematical problems.