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E-International Scientific Research JournalISSN: 2094-1749 Volume: 2 Issue: 4, 2010and amplitudesRemark that these amplitudes are pure numbers. There,is the step-function. Wehave used the notation , where is the particle diameter. Then, thelength D may be viewed as a renormalized particle size.Now, let us discuss the derived expression for the induced force.Firstly, we emphasize that we have ignored higher order cumulants describing threebodyinteractions and more. In this sense, formula (18) is exact only when one is concernedwith two-body interactions. Also, in the bulk Hamiltonian, we have ignored nonquadratictermsas and , which must contribute when one performs loopexpansion[41,42],in field theory language. These terms are discarded here, since the meanfieldtheory we consider is just the zeroth order approximation of the loop expansion.Secondly, we note that, in thelimit, that is when one is exactly at the consolutepoint, we recover the previous results of Ref. [27]. Indeed, in this limit, wehave .Thirdly, the contribution of the surface chemical potentials difference dominates. Thismeans that the direct interactions between the mixture and particles play only a minor role.Fourthly, the dependence of the force on the particle size is trivial and appears throughthe renormalized diameter D.Fifthly, the decreasing character of the Bessel function indicates that, as it should be,the force below the consolute point is more important than above, when one is at the samedistance from . Notice thatSixthly, for all temperatures around the consolute oneand at fixed inter particledistancer, the force is less important than at. This is due to the fact that the two scalingfunctions and are bounded from above by 1, that is and ,325