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Piezoelectric balance presented by Pierre Curie to Lord Kelvin, Hunterian Museum, Glasgow. Piezoelectricity [note 1] is the electric charge that accumulates in certain solid materials—such as crystals, certain ceramics, and biological matter such as bone, DNA, and various proteins—in response to applied mechanical stress.
The first constitutive equation (constitutive law) was developed by Robert Hooke and is known as Hooke's law.It deals with the case of linear elastic materials.Following this discovery, this type of equation, often called a "stress-strain relation" in this example, but also called a "constitutive assumption" or an "equation of state" was commonly used.
The piezoelectric coefficient or piezoelectric modulus, usually written d 33, quantifies the volume change when a piezoelectric material is subject to an electric field, or the polarization on the application of stress.
The converse piezoelectric effect (CPE) describes how an applied electric field will create a resultant strain which in turn leads to a physical deformation of the material. This effect can be described through the constitutive equations. [4] The CPE can be written as =
The difference with water pollution, however, is that the problems that cause local water quality issues differ from those that create regional air pollution problems. Discharges into water are difficult to measure and effects are dependent on a variety of other factors and vary with weather and location.
The Sauerbrey equation was developed by the German Günter Sauerbrey in 1959, while working on his doctoral thesis at Technische Universität Berlin, Germany. It is a method for correlating changes in the oscillation frequency of a piezoelectric crystal with the mass deposited on it. He simultaneously developed a method for measuring the ...
The above equation is a vector form of the most general equation for fluid flow in porous media, and it gives the reader a good overview of the terms and quantities involved. Before you go ahead and transform the differential equation into difference equations, to be used by the computers, you must write the flow equation in component form.
Strictly speaking the above equation holds also for systems with chemical reactions if the terms in the balance equation are taken to refer to total mass, i.e. the sum of all the chemical species of the system. In the absence of a chemical reaction the amount of any chemical species flowing in and out will be the same; this gives rise to an ...