Mathematical Determination of the Critical Absolute Hamaker Constant of the Serum (As an Intervening Medium) Which Favours Repulsion in the Human Immunodeficiency Virus (HIV)- Blood Interactions Mechanism C.H. Achebe, Member, IAENG, S.N. Omenyi Abstract - HIV-blood interactions were studied using the Hamaker coefficient approach as a thermodynamic tool in determining the interaction processes. Application was made of the Lifshitz derivation for van der Waals forces as an alternative to the contact angle approach. The methodology involved taking blood samples from twenty HIV-infected persons and from twenty uninfected persons for absorbance measurement using Ultraviolet Visible Spectrophotometer. From the absorbance data the variables (e.g. dielectric constant, etc) required for computations were derived. The Hamaker constants A 11, A 22, A 33 and the combined Hamaker coefficients A 132 were obtained. The value of A 132abs = 0.2587x10 -21 Joule was obtained for HIV-infected blood. A significance of this result is the positive sense of the absolute combined Hamaker coefficient which implies net positive van der Waals forces indicating an attraction between the virus and the lymphocyte. This in effect suggests that infection has occurred thus confirming the role of this principle in HIV- blood interactions. A near zero value for the combined Hamaker coefficient for the uninfected blood samples A 131abs = 0.1026x10 -21 Joule is an indicator that a negative Hamaker coefficient is attainable. To propose a solution to HIV infection, it became necessary to find a way to render the absolute combined Hamaker coefficient A 132abs negative. As a first step to this, a mathematical derivation for A 33 ≥ 0.9763x10 -21 Joule which satisfies this condition for a negative A 132abs was obtained. To achieve the condition of the stated A 33 above with possible additive(s) in form of drugs to the serum as the intervening medium will be the next step. Index Terms - Absorbance, Dielectric Constant, Hamaker Coeficient, Human Immunodeficiency Virus, Lifshitz formula, Lymphocyte, van der Waal I. THEORETICAL CONSIDERATIONS A. Concept of Interfacial Free Energy THE work done by a force F to move a flat plate along Manuscript received January 29, 2013; revised February 16, 2013. C.H. Achebe is with the Department of Mechanical Engineering, Nnamdi Azikiwe University, PMB 5025, Awka (Phone: +2348036662053; e-mail: chinobert2k@yahoo.com ). S.N. Omenyi is with the Department of Mechanical Engineering, Nnamdi Azikiwe University, Awka. another surface by a distance dx is given, for a reversible process, by; δw = Fdx (1) Fig. 1. Schematic Diagramme Showing Application of a Force on a Surface However, the force F is given by; F = Lγ Where L is the width of the plate and γ is the surface free energy (interfacial free energy) Hence; δw = Lγdx But; dA =Ldx Therefore; δw = γdA (2) This is the work required to form a new surface of area dA. For pure materials, γ is a function of T only, and the surface is considered a thermodynamic system for which the coordinates are γ, A and T. The unit of γ is Joules. In many processes that involve surface area changes, the concept of interfacial free energy is applicable. B. The Thermodynamic Approach to Particle-Particle Interaction The thermodynamic free energy of adhesion of a particle P on a solid S in a liquid L at a separation d 0 [1], is given by; F pls adh (d o ) = γ ps – γ pl - γ sl (3) Where F adh is the free energy of adhesion, integrated from infinity to the equilibrium separation distance d o ; γ ps is the interfacial free energy between P and S; γ pl is that between P and L and γ sl that between S and L. For the interaction between the individual components, similar equations can be written also; F ps adh (d 1 ) = γ ps – γ pv - γ sv (4) F sl adh (d 1 ) = γ sl – γ sv - γ lv (5) F pl adh (d 1 ) = γ pl – γ pv - γ lv (6) For a liquid, the force of cohesion, which is the interaction with itself is described by; F dx Proceedings of the World Congress on Engineering 2013 Vol II, WCE 2013, July 3 - 5, 2013, London, U.K. ISBN: 978-988-19252-8-2 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online) WCE 2013