Electrophoretic effect force

Removal of Cake by Mass Forces. This method of limiting cake growth employs mass or electrophoretic forces on particles, acting tangentially to or away from the filter medium. Only mass forces are considered here because the electrophoretic effects have been discussed previously. 

The Dehye-Hbckel theory of electrolytes based on the electric field surrounding each ion forms the basis for modern concepts of electrolyte behavior (16,17). The two components of the theory are the relaxation and the electrophoretic effect. Each ion has an ion atmosphere of equal opposite charge surrounding it. During movement the ion may not be exacdy in the center of its ion atmosphere, thereby producing a retarding electrical force on the ion. 

Debye and Falkenhagen predicted that the ionic atmosphere would not be able to adopt an asymmetric configuration corresponding to a moving central ion if the ion were oscillating in response to an applied electrical field and if the frequency of the applied field were comparable to the reciprocal of the relaxation time of the ionic atmosphere. This was found to be the case at frequencies over 5 MHz where the molar conductivity approaches a value somewhat higher than A0. This increase of conductivity is caused by the disappearance of the time-of-relaxation effect, while the electrophoretic effect remains in full force. 

As soon as the concentration of the solute becomes finite, the coulombic forces between the ions begin to play a role and we obtain both the well-known relaxation effect and an electrophoretic effect in the expression for the conductivity. In Section V, we first briefly recall the semi-phenomenological theory of Debye-Onsager-Falkenhagen, and we then show how a combination of the ideas developed in the previous sections, namely the treatment of long-range forces as given in Section III and the Brownian model of Section IV, allows us to study various microscopic... 

Because of the nature of electroporation, virtually any molecule can be introduced into cells. For transfer of DNA, the electroporation forces are important. An electrophoretic effect of the field causes the polyanion DNA to travel toward the positive electrode. Fluorescence studies have shown that DNA enters the cell through the pole facing the negative electrode, where the membrane is more destabilized and where the field will drive the DNA towards the center of the cell (245). Membrane resealing occurs after pore formation. Whereas pore formation happens in the microsecond time frame, membrane resealing happens over a range of minutes with variations depending on electrical parameters and temperature (246). 

The numerical results show that the polarization effect of the double layer impedes particle s migration because an opposite electric field is induced in the distorted ion cloud, which acts against the motion of the particle. For a given ica, the electrophoretic mobility increases first, reaches a maximum value and then decreases as the absolute zeta potential is increased. This maximum mobility arises because the electrophoretic retarding forces increase at a faster rate with zeta potential than does the driving force. 

The influence of the interionic forces is due to two phenomena, namely, the electrophoretic effect and the time-of-relaxation effect. The net ionic atmosphere around a given ion carries the opposite charge and therefore moves in a direction opposite to the central ion. The final result is an increase in the local viscosity, and retardation of the central ion. This is called the electrophoretic effect. The time-of-relaxation effect is also related to the fact that the ionic atmosphere around a given ion is moving and therefore disrupted from its equilibrium configuration. It follows that the ionic atmosphere must constantly be re-formed from new counter ions as the ion under observation moves through the solution. The net effect is that the electrical force on each ion is reduced so that the net forward velocity is smaller. 

As already mentioned it has been customary to deal with the ionic atmosphere as if it were a reality, and the derivation just given assumes that an electric force acting on the ion atmosphere will produce a motion of the solvent. However, the effect of a potential gradient cannot be directly on the solvent, but must have its influence indirectly through the ions. The fundamental explanation of the electrophoretic effect must therefore be sought in a modification of inter-reactions between ions and solvent produced by the ion atmosphere, and the latter is, as we have seen, due in turn to a time average of the distribution of the ions. 

Cross term due to (i) An applied external field has an indirect effect on the solvent through the ions. The force exerted on the moving central ion by the solvent in between the ions of the ionic atmosphere is dependent on the ionic distribution in the ionic atmosphere. Hence the interaction between the ions and the solvent will be determined by the interactions between the ions themselves. If the symmetrical distribution is perturbed by the externally applied field this will have an effect on the interactions between an ion and the solvent, and this will result in an additional solvent flow about the ion. For a calculation of the electrophoretic effect this asymmetry should be considered, but in this derivation it is not and it is assumed that the symmetrical distribution given by Equation (12.3) can be used. This added effect is considered in more advanced treatments (see Section 12.10). 

Since the electrophoretic effect manifests itself as a modified viscous drag on the ion by the solvent, the force on the ion due to electrophoresis can be given by Stokes Law. The change in velocity Ay, can then be given in terms of the two Stokes Law terms one for the viscous drag due to the solvent in the absence of electrophoresis, and the other due to the modified viscous drag resulting from electrophoresis. 

The force on the moving central 7-ion due to the external field under ideal conditions is ZjeX. The effective force on the moving central ion once the electrophoretic and relaxation effects are taken into consideration will be ... 

Before opening the illumination shutter, we applied a long electric prepulse on the same electrodes that are used for the electric stimulation of luminescence. Thus, we were able to study the effect of an electric prepulse on the EPL signal. To avoid electrode polarization, the electrophoretic driving force consisted of a train of 1-ms-long electrical pulses at a relatively high frequency (usually 200 pulses/ s). To detect possible polarization of the electrodes, we continuously monitored the current shape and amplitude produced during the prepulse. 

If the solution of electrolyte is not infinitely dilute, the ion is retarded in its motion because of the electrical attraction between ions of opposite sign (asymmetry effect), and because the positive and negative ions are moving in opposite directions each carrying some solvent (electrophoretic effect). Both of these effects are intensified as the concentration of the electrolyte increases so that the retarding forces increase and the conductivity decreases. 

When the ions in solvent are forced to move by an external field two effects start to influence conductance. The ions of opposite charge move in opposite directions and their movement is slowed down by the collision of the ionic atmosphere with the solvent molecules. The symmetry of ion distributions is disturbed. These phenomena are called the electrophoretic effect and relaxation effect, respectively. The decrease in conductance resulting from both effects is the basis of the Debye-Hiickel-Onsager theory of conductance [31]... 

In addition to the electrophoretic drag force, there is an additional effect because a moving ion deforms its own ion atmosphere. As shown in Fig. 3.4b an ion tends to pile up charge in front of it as it moves and tends to leave a diminishing wake behind as the atmosphere tries to readjust and reform the spherical distribution about the ion. The effect is to separate charge which produces an electric field called the relaxation field E, in the direction of, but opposing the applied field. Considering both electrophoresis and relaxation the local field at the ion is E — E — E. Since the mean... 

Estimates of E and E in dilute solution can be obtained using Debye-Huckel theory in its simplest form. Assume the electrolyte to be point charges interacting via coulomb forces only. Ignore the molecular structure of both solvent and ions. Since the electrophoretic effect is due to the migration of the ion cloud through the fluid, the reduction in ion mobility can be calculated using Stokes law (3.21)... 

Electrophoretic Effect While the central ion moves in one direction, the ionic atmosphere which consists of ions of opposite charge move in the opposite direction. Thus, the central ions are forced to move against a stream of solvent. Their velocities are consequentiy reduced. 

Movement of ions through a solution is induced by the imposition of an electric field - a consequence of the applied potential between the electrodes. The electric field force experienced by an ion causes it to accelerate. This acceleration, however, is opposed by the retarding forces of the asymmetry and electrophoretic effects as well as by the solvent viscosity, so that an ion ultimately moves with a uniform velocity determined by a balance of these opposing forceg. For a concentration c of a 1 1 strong electrolyte the concentration of cations, c+, is equal to that of anions, c. If the speeds of cations and anions are, respectively, u+ and u, the amount of charge crossing unit area of solution in unit time is... 

In solution, not only the central cation but also the surrounding ionic cloud moves, however, with its opposite excess charge in the opposite direction (Figure 1.7b). Therefore, the central cation feels a larger velocity relative to its local environment and thus is exposed to higher friction forces. In consequence, this ion is slowed down relative to the laboratory system in comparison with a situation with a missing ionic cloud. This is the electrophoretic effect expressed by Equation 1.29, where qy is the viscosity of the electrolyte. 

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