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The equation for the frictional force caused by non-retarded van der Waals interactions has been found in the régime linear with respect to velocity. This force is generated because of the effect of field intrainment by a moving medium.

The behavior of the interface in a two-phase immiscible fluid flow in a randomly heterogeneous porous medium is investigated. The medium is described by the permeability distribution which represents a random field with given statistical characteristics. When the approach proposed is used, it turns out to be possible to relate the statistical characteristics of the interface with the statistical characteristics of the permeability field and the properties of the phases. On the basis of this relation an important characteristic of the two-phase flow, namely, the average saturation distribution in the neighborhood of the interface, can be calculated.Keywords: displacement front, random permeability field, stochastic approach, variance of the front shape fluctuations. FLUID DYNAMICS Vol. 41 No. 5 2006 FLUID DYNAMICS Vol. 41 No. 5Accordingly, K(S) and K −1 (S) are also discontinuous functions and can be written in the form:As a result, taking into account the properties of the distributions ∂ i sign[ϕ(r)] = 2∂ i ϕ(r)δ [ϕ(r)], sign(x)δ (x) = 0

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