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So, I know that a hydrophilic material is defined as those with a special affinity for water, opposite to hydrophobic, those that naturally repel water.

I am investigating the impact of spheres with water surfaces, and the splashes caused by them. However, one research paper focuses on the difference between the fluid dynamics of hydrophilic spheres and hydrophobic spheres, and the difference in the cavities they make when they sink underwater.

I understand what a hydrophobic sphere is, but what is a hydrophilic sphere? Like a rolled up ball of tissue paper? Or the water absorbing waterbeads/orbeez that get bigger(the ones children play with)?

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The answer to your question depends on the size level (microscopic or not). But it sounds like you are referring to spheres at a size that you can hold, or larger.

A hydrophilic sphere could simply be a sphere of some solid material (like plastic), coated with a layer of hydrophilic material/substance.

This page on hydrophilic coatings has some information on what this material may be.

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Here is a educational reference: '19.2 COORDINATION CHEMISTRY OF TRANSITION METALS, to quote:

The coordination sphere consists of the central metal ion or atom plus its attached ligands. Brackets in a formula enclose the coordination sphere; species outside the brackets are not part of the coordination sphere. The coordination number of the central metal ion or atom is the number of donor atoms bonded to it. The coordination number for the silver ion in [Ag(NH3)2]+ is two (Figure 3). For the copper(II) ion in [CuCl4]2−, the coordination number is four, whereas for the cobalt(II) ion in [Co(H2O)6]2+ the coordination number is six. Each of these ligands is monodentate, from the Greek for “one toothed,” meaning that they connect with the central metal through only one atom. In this case, the number of ligands and the coordination number are equal.

So, in the presence of a water ligand, the adjective 'hydrophilic' is appropriate. The sphere, itself, is the central metal ion and associated ligand enclosed in brackets, where per my readings, the brackets are sometimes missing.

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    $\begingroup$ I suppose the OP has in his mind the size range micrometers to centimeters, and perhaps rather the latter than the former. $\endgroup$ – Poutnik Mar 24 at 7:46

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