Maxwell stress tensor

At the same time, the coulomb attraction acts between the charges on the particle surface and the counterions within the electrical double layer, which is obtained by integrating the Maxell stress tensor over an arbitrary surface surrounding the particle. The Maxwell stress tensor is given by... 

The interaction force P can be calculated by integrating the excess osmotic pressure An and the Maxwell stress tensor T over an arbitrary closed surface 21 enclosing either one of the two interacting particles (Fig. 8.3), which is written as [8]... 

The effective electrical tension, transmembrane potential, Pja, is defined by the Maxwell stress tensor [59, 89, 92]... 

UtiUzing that V x E = 0 (i.e., dEJdxj = dEjIdXi) and noting that/j- = dxyldxj (where x,y is the Maxwell stress tensor), one can write, for... 

In the above equations, 7 is the identity tensor and T is the Maxwell stress tensor Ty is the representation of this tensor with Einstein notation. 

The coupling between the hydrodynamics and the electric field therefore arises through the Maxwell stress tensor. The total electric force density comprises the sum of the Coulombic force arising from the presence of free charges... 

As well documented in literatures, the electromagnetic force F that the tip feels is given by the integral of the Maxwell stress tensor T j over the entire tip surface,... 

In the absence of a magnetic held the Maxwell stress tensor is given in a vacuum by... 

Calculation of the Maxwell Stress Tensor and the Poisson-Boltzmann Force on a Solvated Molecular Surface Using Hypersingular Boundary Integrals. 

Now we come to the additional equations that are specific to the processes driving the instability. In EHC the bulk force in the Navier-Stokes Equation 14 is derived from the Maxwell stress tensor, which here reduces to... 

In the previous equations, integration is extended over the full solid angle, and r indicates the radius of a spherical volume surrounding the center of the particle and to be considered as large as possible (ideally infinite). Finally, an important role is played by , which is the time-averaged Maxwell stress tensor in the form of Minkowski ... 

Under these approximations (i.e., the flow is along the x direction), the force creating the flow Fx is obtainable from the Maxwell stress tensor ... 

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