Vectorial flows

As an attempt to connect the first discussion, which was concerned with diffusion-reaction coupling, with Dr. Williams presentation of enzymes as dynamic systems, I wanted to direct attention to a number of specific systems. These are the energy-transducing proteins that couple scalar chemical reactions to vectorial flow processes. For example, I am thinking of active transport (Na-K ATPase), muscular contraction (actomyosin ATPase), and the light-driven proton pump of the well-known purple... 

Another well-known example is the coupling between mass flow and heat flow. As a result, an induced effect known as thermal diffusion (Soret effect) may occur because of the temperature gradient. This indicates that a mass flow of component A may occur without the concentration gradient of component A. Dufour effect is an induced heat flow caused by the concentration gradient. These effects represent examples of couplings between two vectorial flows. The cross-phenomenological coefficients relate the Dufour and Soret effects. In order to describe the coupling effects, the thermal diffusion ratio is introduced besides the transport coefficients of thermal conductivity and dififusivity. 

The flows may have vectorial or scalar characters. Vectorial flows are directed in space, such as mass, heat, and electric current. Scalar flows have no direction in space, such as those of chemical reactions. The other more complex flow is the viscous flow characterized by tensor properties. At equilibrium state, the thermodynamic forces become zero and hence the flows vanish... 

Simultaneous heat and mass transfer plays an important role in various physical, chemical, and biological processes hence, a vast amount of published research is available in the literature. Heat and mass transfer occurs in absorption, distillation extraction, drying, melting and crystallization, evaporation, and condensation. Mass flow due to the temperature gradient is known as the thermal diffusion or Soret effect. Heat flow due to the isothermal chemical potential gradient is known as the diffusion thermoeffect or the Dufour effect. The Dufour effect is characterized by the heat of transport, which represents the heat flow due to the diffusion of component / under isothermal conditions. Soret effect and Dufour effect represent the coupled phenomena between the vectorial flows of heat and mass. Since many chemical reactions within a biological cell produce or consume heat, local temperature gradients may contribute in the transport of materials across biomembranes. 

Equations (9.130) and (9.134) suggest that the cross coefficients Zrq andZrS are related to the gradients concentration and temperature. This reflects the vectorial character of the coupling coefficients Lrq and Trs, as they relate the vectorial flows of heat and mass with the scalar reaction velocity. 

According to the Curie-Prigogine principle, a scalar flow, such as the rate of reaction, cannot be coupled with a vectorial flow of a transport process in an isotropic medium where an equilibrium-dividing surface is symmetric with respect to rotations around any local normal vector. However, the symmetry properties alone are not sufficient for identifying physical coupling the actual physics considered in deriving the entropy production equation and the specific structure, such as anisotropy, are necessary. 

Consider an ensemble of enzyme molecules or membrane proteins in the coupled processes of reactions and vectorial flows. Such systems consist of a set of cycles and subcycles of reactions and transport processes. For a flow in cycle k as Jk (k = a,b,..., h), the first two steady-state flows are given by the following relations... 

In the phenomenological treatment of the directed drift that the field brings, we take the attitude that there is a stream of cations going toward the negative electrode and anions going toward the positive one. We now neglect the random diffusive movements they do not contribute to the vectorial flow that produces an electrical current. 

By definition, an isotropic system cannot support a vector quantity associated with it. Therefore, the vectorial flows can only be related to the vector forces. The scalar reaction rates can be functions of the scalar forces and the trace of the dyadic, but not the vector forces. According to the Curie-Prigogine principle, vector and scalar quantities interact only in an anisotropic medium. This principle has important consequences in chemical reactions and transport processes taking place in living cells. 

Therefore, to design a better molecular photodiode the distance and AG dependence should be kept in mind. In Fig. 18(b), the energy diagram of the A/S/D molecular photodiode is depicted as a function of distance across the LB film. If the forward processes indicated by arrows with solid lines are accelerated, and the backward processes with dashed lines are retarded by setting the distances and the energy levels appropriately, the photoinduced vectorial flow of electrons can be achieved, that is, the acceleration by setting AG° equal to X is assumed for the forward electron transfer processes (ii) and (iii), while the retardation, as a consequence of the inverted region, is assumed for the back-electron transfer processes (iv) and (v). Once an electron-hole pair is separated successfully, the recombination of... 

The summation is carried out over all conductive and convective surfaces. A net conductive (vectorial) flow to the system is now given by ... 

Besides these vectorial flows, scalar flows also contribute to the entropy production. For scalar flows Aed should be interpreted as a volume. The most relevant scalar flow is the production of a chemical species. The flowrate is the reaction rate, driven by the chemical affinity. 

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