There will be influence by sigma only if the object has a fluid surface somewhere.

Example 1: a small gas bubble ascending in water with small amount of surfactant due to buoyancy. If the surface is clean, it will move faster than a solid particle (Stokes) but slower than a bubble in clean water (Hadamard-Rybczynski) due to the Marangoni effect, i.e. due to grad(sigma).

Example 2: a large gas bubble ascending in water with a lot of surfactant due to buoyancy. This time the surface will be tangentially immobile as if it is solid, but the shape will change according to the balance between sigma (that wants a sphere) and the viscous forces (that elongate the bubble), affecting the velocity.

Example 3: a hydrophobic solid particle with a rough surface moving fast in water (turbulent flow). Such a particle will entrap a lot of air at the surface (Cassie-Baxter state), and each entrapped bubble will have a liquid surface exposed to the shear. This will dramatically change the turbulent friction. How much air will be entrapped depends not only on the surface tension of water, but also on the contact angle (and the solid|water and solid|air surface tensions, respectively).

Finally, in turbulent flows, the solid surface roughness plays an important role even without the bubbles, and this roughness is in principle related to the surface tension of the solid|liquid or solid|air interface (a surface of lower energy can be expected to be rougher). This might be quite important if the solid is soft enough so that shear leads to plastic deformation and decrease of the roughness.

Very explicit answer. Thanks. Certainly I need to study some terms that you mentioned.

Can I conclude that in solid / liquid interface, if the solid is for instance steel, won't be any effect?

Thanks!

For laminar flow, yes. For turbulent, there could be, but only in special cases.

The “Surface tension (ST)” in fluid mechanics is two-fold product of atomic-molecular interaction.

In conventional Euler or Navier-Stokes fluid mechanics ST is introduced as specific pressure applied to infinitely thin free  surface and is used only in boundary condition on contact surfaces fluid - (vacuum, gas, fluid_I, solid). No variations of the surface – no manifestation.

In thermodynamics ST if part of energy, for example Gibbs’ potential (free enthalpy), describing specific available surface potential energy which is result of molecular interactions anisotropy in the fluid body with a free surface. This part of energy is associated with the surface area and must be taken into account in total energy balance and theory of fluid flows (which is not performed properly).

In modern physics ST is investigated in the layer of molecular cluster thickness

(order 10^(-6) cm) in contrast with the thickness of surface which is order of molecular size 10^(-8) cm). Due to smallness of thickness of the surface layer the density of energy is high. The time of potential surface energy release is defined by the velocity of atomic-molecular motion and can be high enough to produce macroscopic effects (for example to shock the surface of submerging drop in the fluid by small secondary droplets: Ilynykh A.Yu., Chashechkin Yu. D. Hydrodynamics of a falling drop of contact with the free surface of the liquid // Fluid Dynamics, 2016, Vol. 51, No. 2, pp. 127–135.

Or short version:

Chashechkin Yu.D., Ilyinykh A. Yu. Capillary waves on the surface of the liquid droplets in submerging in a fluid drop // Doklady Physics. 2015. V. 465 (4), pp. 434-440.

So the ST effects need in variation of the surface area or value of ST coefficient (in your case the value of ST coefficient must be different for fluid-wall and fluid-sphere contact surfaces).

Generally speaking the total energy (macroscopic and internal) effects in fluid flows are not investigated properly and need in further theoretical and experimental studies (Chashechkin Yu. D. Differential fluid mechanics – harmonization of analytical, numerical and laboratory models of flows. P. 61-91. // Mathematical Modeling and Optimization of Complex Structures. Springer Series “Computational Methods in Applied Sciences” 2016. V. 40. 328 p. available on RG).

I guess what is important in your case is the surface tension in the interface “body-fluid”. If it is non-uniform over the interface (e.g., due to gradients of temperature or chemical composition), the surface tension affects the motion of the body.